Axiomatized Relationships Between Ontologies. Carmen Chui

Transcription

1 Axiomatized Relationships Between Ontologies by Carmen Chui A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto c Copyright 2013 by Carmen Chui

2 Abstract Axiomatized Relationships Between Ontologies Carmen Chui Master of Applied Science Graduate Department of Mechanical & Industrial Engineering University of Toronto 2013 This work focuses on the axiomatized relationships between different ontologies of varying levels of expressivity. Motivated by experiences in the decomposition of firstorder logic ontologies, we partially decompose the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) into modules. By leveraging automated reasoning tools to semi-automatically verify the modules, we provide an account of the meta-theoretic relationships found between DOLCE and other existing ontologies. As well, we examine the composition process required to determine relationships between DOLCE modules and the Process Specification Language (PSL) ontology. Then, we propose an ontology based on the semantically-weak Computer Integrated Manufacturing Open System Architecture (CIMOSA) framework by augmenting its constructs with terminology found in PSL. Finally, we attempt to map two semantically-weak product ontologies together to analyze the applications of ontology mappings in e-commerce. ii

3 Acknowledgements I would like to thank Professor Michael Grüninger for his support and guidance over the course of my undergraduate and graduate studies. It is through our various discussions and brainstorming sessions that the theme for this thesis arose. His passion and enthusiasm to explain concepts found within the fields of ontologies and logic have guided me throughout the course of writing this thesis. As well, his suggestions and criticisms have been invaluable in this work. Thank you to the members on my thesis committee, Professor Mark Fox, Professor Li Shu and, my supervisor, Professor Michael Grüninger. I would also like to thank Mark van Berkel of Hunch Manifest, Inc. for providing an opportunity to explore and analyze the applications of ontologies and their mappings in e-commerce. During my time as a member of the Semantic Technologies Lab, I have been privileged to work with a wonderful group of people. Thank you to my colleagues, Bahar Aameri, Megan Katsumi, and Torsten Hahmann, for sharing the graduate student experience with me. Finally, I would like to thank my family and friends for their confidence in me, and the values that they have instilled in me. I am extremely grateful for the tolerance that they have demonstrated with me, and I feel so fortunate for their continued support of my academic endeavours. iii

4 Contents 1 Introduction Ontologies & the Semantic Web Motivations Contributions The Big Picture Background Usage of First Order and Common Logic Representation Common Logic (CL) The COmmon Logic Ontology REpository (COLORE) Relationships Between Hierarchies Verification of Ontologies The Process Specification Language (PSL) Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) Assumptions and Simplifications Made to DOLCE Overview of Concepts Found in DOLCE Ontology Decomposition: Verification of DOLCE Modularizing DOLCE Modules from Consistency of DOLCE Our Approach to Modularization iv

5 3.1.3 Usage of Bipartite Incidence Structures The DOLCE Hierarchy (H dolce ) & Its Modules DOLCE s Taxonomy (T dolce taxonomy ) DOLCE s Time Mereology (T dolce time mereology ) Axiomatization of T dolce time mereology Reduction of T dolce time mereology DOLCE s Mereology (T dolce mereology ) A Taxonomy of Lines (T taxonomy ) Theory of Being Present (T dolce present ) Axiomatization of T dolce present Reduction of T dolce present Theory of Temporary Parthood (T dolce temporary parthood ) Axiomatization of T dolce temporary parthood Reduction of T dolce temporary parthood Theory of Constitution (T dolce constitution ) Axiomatization of T dolce constitution Reduction of T dolce constitution Summary of DOLCE Modules Ontology Composition: Interpretations Between DOLCE & COLORE Relationship with PSL and COLORE Theories Temporal Theories in COLORE The Timepoints Hierarchy (H timepoints ) The Periods Hierarchy (H periods ) The Combined Time Hierarchy (H combined time ) Composing T interval with endpoints Extending T psl core Theory of PSL-Core Root (T psl core root ) v

6 4.3.2 Theory of Mandatory Participation (T mandatory ) The Interval PSL Hierarchy (H interval psl ) Theory of PSL-Core with Intervals (T interval psl core ) Theory of Mandatory Intervals (T interval mandatory ) Interpretations Between DOLCE and Theories in COLORE Interpretations Between T interval psl core and T dolce present Interpretations Between T interval mandatory and T dolce participation Insights Semantic Augmentation: The CIMOSA Process Ontology Background & Motivation The Computer Integrated Manufacturing Open System Architecture Methodology Identification of Competency Questions Utilizing CIMOSA s Grammar Identifying Keywords to Piece Together Behavioural Rules Axiomatizing the Behavioural Rule Set Through Identification of Similar PSL Constructs The Proposed CIMOSA Process Ontology Lexicon Behavioural Rules for Well-Structured Processes Behavioural Rules for Semi-Structured Processes Discussion Limitations of the Ontology Inability to Test and Verify Axioms for its Intended Semantics The Need for Ontology Design Best Practices Challenges & Difficulties Encountered Insights vi

7 6 Ontology Mapping: ServicedAtHome Background & Motivation Hunch Manifest, Inc Semantic Integration of Product and Service Data Infrastructure of Mapping Services & Ontologies Methodology Acquiring Sample Vendor Product Details Developing the Vendor API Ontologies Identifying the Concepts to be Mapped Preliminary Mappings Between Vendors Preliminary Mappings Between HSO and GoodRelations Transforming XML Product Data into RDF Mapping the Vendor Product Data Product Mappings in RDF and OWL Mappings Between HSO and Amazon Mappings Between HSO and Sears Mappings Between Amazon and Sears Mappings Between HSO and GoodRelations Testing the Mappings via SPARQL Queries Cheapest Products Cheapest Products Based on Keyword Average Price of Products Based on Keyword Average Price of Products for Both Vendors Combination of Product Data with DBPedia Data Average Price of Products for Both Vendors Based on Keyword All Known Product Attributes for a Combined Product Model Discussion vii

8 6.6.1 Limitations of the Vendor Ontologies Usage of RDF/XML to Test the Mappings The Need for Adoption of Semantic Technologies in e-commerce No One General Methodology for Ontology Mapping Existing Product Ontologies are Insufficient Insights Conclusion Open Issues Future Work Bibliography 168 Glossary 176 A Additional Background Information 185 A.1 The PSL Ontology A.1.1 Axioms of T psl core A.1.2 Core Theories of the PSL Ontology A.2 PSL Lexicon B Additional DOLCE Information 189 B.1 DOLCE Axioms from WonderWeb B.2 Additional DOLCE Axioms B.2.1 Axiomatization of T dolce present C Additional CIMOSA Information 193 C.1 Axiomatizations of PSL Constructs Used in the CIMOSA Ontology C.2 Common Logic Version of the CIMOSA Ontology viii

9 D Additional HomeServices Information 201 D.1 Sample Item XML Result from Amazon D.2 Sample Item XML Result from Sears D.3 API Queries for Product Information Retrieval D.4 Transforming Raw Vendor Product Data D.4.1 Using GRDDL to Transform XHTML/XML into RDF D.4.2 Using xsltproc D.5 Using AllegroGraph to Test Product Mappings D.5.1 Importing the Data into AllegroGraph D.5.2 Using AllegroGraph s Materializer and Reasoner D.6 Results from SPARQL Queries for HSO Mappings D.7 Sample GoodRelations Tags in Sears Product Pages ix

10 List of Tables 2.1 Basic Categories in DOLCE Summary of concepts found in DOLCE CIMOSA behavioural rules Definition of Terms Found in CIMOSA Lexicon for CIMOSA in first-order logic Comparison between CIMOSA and PSL s lexicons Excerpt of metadata tags found in Amazon product data Excerpt of metadata tags found in Sears product data Mappings between Amazon and Sears OWL ontologies Mappings between GoodRelations and HomeServices/GIST OWL ontologies A.1 Lexicon used in the core theories of the PSL ontology D.1 Results of finding the cheapest price of products D.2 Results of finding the cheapest price of products based on keyword D.3 Results of finding the average price of products based on keyword D.4 Results of finding the average price of products and lists them according to manufacturer number D.5 Results of finding the average price of products based on keyword for both vendors and lists them according to manufacturer number x

11 D.6 Results of finding the combined product model, sorted by manufacturer part number. (Results are truncated due to limited page space.) D.7 Results of the federated query. Note that the results are incorrect and that the branddbpediauri field is empty xi

12 List of Figures 2.1 Classification of DOLCE categories from [51] Structure of DOLCE s subtheories Relationships between DOLCE modules Mappings between DOLCE and COLORE theories Example of mereological foliation (T m foliation ) Ontologies in H subposet Ontologies in H mereology Ontologies in H ordering Relationships between DOLCE modules with mathematical structures in COLORE Axioms outlining the subsumption constraints of T dolce taxonomy Axioms outlining the disjointness constraints of T dolce taxonomy Axioms outlining the disjointness constraints of T dolce taxonomy Axioms of T dolce time mereology Axioms of T dolce mereology Axioms of T dolce mereology Corresponding taxonomies of DOLCE categories and lines Axiomatization of T taxonomy, used in our DOLCE modularization Axioms of T dolce present Axioms of T dolce temporary parthood xii

13 3.19 Axioms of T dolce temporary constitution Relationships between DOLCE modules and theories in COLORE Relationships between theories found in the Combined Time hierarchy, H combined time Axioms found in T mandatory Relationships between theories found in the PSL hierarchy Axioms of T interval psl core Graphical depiction of the overlay(x, y, z) relation Relationships between the Interval PSL, PSL, and Combined Time hierarchies Interpretations between DOLCE modules and theories in COLORE Graphical depiction of the P (x, y) translation definition Graphical depiction of the SUM(z, x, y) translation definition The CIMOSA modelling approach CIMOSA modelling constructs Relationship between the different API technologies and ontologies Relationship between the mappings across the different ontologies The Semantic Web Stack A.1 The core theories of the PSL Ontology B.1 Axioms of T dolce present D.1 Copying queries into Amazon s Product Advertising API Scratchpad D.2 Selecting rules for AllegroGraph s materializer D.3 Enabling reasoning in the SPARQL query xiii

14 Chapter 1 Introduction The use of ontologies in knowledge representation has become increasingly popular of over the years. Ontologies are shared conceptualizations that formally define the concepts, relationships, and semantics of a given domain of discourse. As well, ontologies can be described in languages of varying degrees of formality and expressivity. The development of automatic reasoning systems have enabled the community to determine the validity of logical inferences of ontologies by checking the truth of entailments in a given theory or instance of a model. For this reason, we are interested in ontologies defined in the language of first-order logic (FOL) since its expressiveness allows us to define complex concepts and relationships and to verify them with well-defined inference methods and tools. There exist various relationships between ontologies that have been studied extensively, and some not as much. In this work, we consider and examine four of these ontology relationships: ontology composition, ontology decomposition, semantic augmentation, and ontology mapping. An underlying aspect of the relationships we have chosen to examine is that these relationships have been axiomatically defined in a logic. By examining the similarities and differences between various first-order ontologies, we aim to gain a better understanding of the underlying relationships between ontologies as 1

15 Chapter 1. Introduction 2 a whole. We briefly introduce the topic of ontologies and, more specifically, describe the four ontology relationships we have chosen to examine. We then discuss the motivations of approach this research problem, outline the major contributions of this work, and provide an overview of the work done in this thesis. 1.1 Ontologies & the Semantic Web An ontology is simply defined to be an explicit specification of a conceptualization [20]. Since domains of discourse can be represented and modelled in different ways, ontologies are known to be a shared conceptualization that allows shareability and reusability within various groups in industry [31]. Despite the various degrees of formality between what one refers to as ontologies 1, they are composed of a vocabulary of terms, and a specification of meaning of the terms. Languages for formal ontologies are closely related to mathematical logic: knowledge is specified as theories in ontologies, in which semantics are based on the notion of mathematical interpretations (models of the ontology). By writing axioms in first-order logic, it allows the verification of theories through the use of (semi)automatic theorem provers that read in a computer-interpretable version of the ontology. Without explicit semantics, the inference process needs to be conducted by an engineer, a consultant, or a domain expert. If (semi)automated analysis is not needed, two domain experts will need agree on the verification or validation of a model of the ontology; however, it is often the case such experts are not available, so explicit semantics need to be defined. The primary goal of the Semantic Web is to have a web of data that can be easily processed by machines to allow greater reuse of data across different software applications. This reuse of data leads to greater semantic interoperability, which is the seamless exchange of information between software applications. With the growth of the World 1 These include taxonomies, thesauri, data models, and other various representations.

16 Chapter 1. Introduction 3 Wide Web and consequently the Semantic Web, however, there has been an increase in the number of ontologies being created and utilized within the community. This growth is due to the many different ontologies that represent and mean the same thing, which has attributed to the semantic heterogeneity problem within the Semantic Web. Consequently, a primary area of research is to examine the various relationships between ontologies of the same, or different, domain. We have chosen to examine four ontology relationships that have been axiomatized in first-order logic: Ontology Decomposition (Modularization): The extraction of a subset of a given ontology that captures all of the ontology s knowledge about a specified set of terms is not a simple task. The ontology modularity community is primarily interested in promoting the greater reuse of ontologies; consequently, modularity is central to reducing the complexity of designing and understanding ontologies, as well as facilitating ontology verification, reasoning, development, maintenance and integration. In this work, we partially decompose the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) ontology into modules and verify these modules with mathematical theories found in the COmmon Logic Ontology Repository (COLORE). Ontology Composition: The task of (re)composing existing ontologies, or ontology modules, together to form a new ontology arises from the interest of greater reuse of ontologies. Within larger domains of discourse, there is an implicit agreement about the terms and concepts defined in individual and independent ontologies. Such terms need to be consistent in interoperable environments and integration scenarios [44, 57]. In this work, we combine mathematical theories with the Process Specification Language (PSL) ontology, both of which are found in COL- ORE, to understand the similarities between the notions of activity participation found in the PSL and DOLCE ontologies.

17 Chapter 1. Introduction 4 Semantic Augmentation: In the context of developing ontologies and providing additional semantics to ontologies without any concrete definitions or axioms, semantic augmentation links the constructs to be defined with concepts from predefined theories and axioms found in other ontologies. By semantically augmenting ontologies together, users are able to fully benefit from the reasoning capabilities of semantic technologies that utilize computer-interpretable ontology formats. In this work, we propose a process ontology for the Computer Integrated Manufacturing Open System Architecture (CIMOSA) framework that utilizes terminology found in the PSL ontology to define CIMOSA constructs and behavioural rules. Ontology Mapping: With respect to ontology mapping, the research community is interested in determining whether two contextually equivalent ontologies contain the same, or similar, axioms and descriptions of concepts. We make the following distinction between ontology mapping from ontology composition to avoid confusion: the intent of ontology mapping is to make semantic matches between the ontologies and to utilize these matches to aid us in reasoning tasks, whereas ontology composition is intended to aggregate ontologies together with minimal mismatch and to define concepts and relations with vocabularies between both ontologies [44, 42]. In this work, we consider the application of ontology design and ontology mappings in e-commerce. 1.2 Motivations The primary motivation of this work is to give better insight of axiomatized relationships between ontologies, and to uncover any implicit relationships of which users the ontologies should be aware. Originally, the intent of the thesis was to explore ontology mappings and the various techniques of developing mappings, but upon examining the literature, it was found that there exist many terms used to describe the notion of mapping. For

18 Chapter 1. Introduction 5 example, the authors of [42] and [10] survey the state of the art with ontology mapping and make note of the following terms used to describe mapping formalisms and techniques in the existing mapping literature: bridge axioms, ontology alignment, ontology articulation, ontology integration, ontology mapping, ontology merging, ontology reconciliation, ontology transformation, and ontology translation. Definitions of the terminology used in [50], [10], [65], and [42] can be found in the Glossary on page 175. Since there does not appear to be a clear and community-accepted distinction between the terms used, nor is there one ultimate definition of ontology mapping, we opted to refrain from providing definitive definitions of these terms. However, we made note that there is still something that bridges two ontologies together. Be it translation definitions, mapping axioms, subsumption relationships, or what the authors of [67] call bridge axioms, we were particularly interested in exploring the different relationships that arise between ontologies that may or may not be in the same domain of discourse. Furthermore, our examination of these ontology relationships arose from interests in analyzing how weak and strong ontologies can form relationships with one another. A weak ontology is characterized by the lack of the expressible or characterizable semantics and the ability to express very simple meaning [55, 31]; in contrast, a strong ontology is characterized by its ability to characterize complex semantics in a set of axioms to allow valid inferences and enforce sound semantic constraints through the use of theorem provers [55]. In particular, we examine the relationships between two strong ontologies (DOLCE and PSL), strong and weak ontologies (PSL and CIMOSA, respectively), and two weak ontologies based on raw product data provided by e-commerce vendors. Since there exist more analysis techniques for strong ontologies, such as those described in [29], [43], and [48], we take these techniques into consideration in our work, whereas our analysis of the weaker ontologies will be more ad-hoc in nature due to the lack of methodologies for analyzing weak ontologies. Exploring all of the possible relationships between ontologies was beyond the scope of

19 Chapter 1. Introduction 6 this thesis. Instead, we opted to examine four relationships between ontologies that have been axiomatized in a formal logic. Consequently, we present these four relationships as individual case studies, each of which will be discussed in more detail in their respective chapters: 1. Ontology Decomposition: translation definitions are used in the modularization of the strong DOLCE ontology. 2. Ontology Composition: the combination of strong theories pertaining to geometry, mereology, and time found in COLORE outlines the relationships between the strong DOLCE and PSL ontologies. 3. Ontology Mapping: equivalent concepts between two weak vendor product ontologies are defined through the usage of mappings. 4. Semantic Augmentation: translation definitions are used to define relations in the weak CIMOSA ontology using terminology found in the strong PSL ontology. 1.3 Contributions This thesis makes several contributions to the ontology and modularity communities. Firstly, we have partially modularized an upper ontology that is used by the community and verified its modules in order to understand the meta-theoretic interactions between the axioms found in these theories. Secondly, the application of mathematical theories in the modularization of DOLCE provides the research community with a better understanding how the DOLCE ontology can be utilized with mathematical theories. Similarly, the composition of theories from DOLCE and PSL enabled us to formally identify common intuitions between the two ontologies. Furthermore, we develop a process ontology to describe the behavioural rules found in the CIMOSA modelling framework. The development of this process ontology has identified the need for a general methodology for designing ontologies where semantics are not formally specified in logic. The lack of a methodology has identified additional areas of research for the community to examine, particularly in situations where ontologies need to be developed and evaluated for seman-

20 Chapter 1. Introduction 7 tically weak standards. Finally, we examine an application of ontology mappings in the world of e-commerce and outline the beneficial uses of ontologies in practical applications. 1.4 The Big Picture This thesis is structured as follows: in Chapter 2, we discuss the motivations for this research opportunity, describe the background theories used, and outline the methodologies taken; in Chapter 3, we outline the techniques used to decompose DOLCE into modules and discuss our findings; in Chapter 4, we outline our approach to mapping DOLCE with theories found in COLORE and discuss our findings; in Chapter 5, we describe the process ontology developed for CIMOSA and its potential applications within the community; in Chapter 6, we discuss the techniques used to map web services together with the use of ontologies and their applications in e-commerce; and finally, in Chapter 7, we discuss the insights gained from this thesis, any open issues, and areas of future work.

21 Chapter 2 Background In this chapter, we introduce the usage of first-order representations of ontologies in this thesis. As well, we introduce the repository environment that contains the theories and ontologies that are mapped to the DOLCE ontology. We explain the choice of focusing on these first-order logic theories and ontologies, which are axiomatized in the Common Logic Interchange Format (CLIF) notation, in relation to their relationships with concepts found in DOLCE. We define the notions of interpretability for comparing theories that use different non-logical lexicons and the translation definitions required to translate axioms from one theory into the language of the other. Then, we describe and outline the modifications made to the DOLCE ontology required for our modularization. 2.1 Usage of First Order and Common Logic Representation In order to capture the semantics of concepts utilized in this work, first-order logic is utilized due its expressive power and usages in the ontologies we have examined. Other ontology languages, such as the Resource Description Framework (RDF) and Web Ontology Language (OWL), have expressive limitations that would have prevented us from 8

22 Chapter 2. Background 9 developing a computer-interpretable version of DOLCE that remains true to its semantics as defined in [51]. While there exists an OWL version of the DOLCE ontology, known as DOLCE-LITE 1, it is grossly simplified with the removal of temporal-indexed relations and inconsistent renaming of relations [52]; the temporal-index relations are vital to the ontology as a whole, so it was more beneficial to utilize a logic with maximal expressivity in this work. Furthermore, our usage of first-order logic in this work aids us in developing a computer-interpretable version of the DOLCE ontology in the Common Logic (CL) and Prover9 syntaxes (with some modifications which are outlined in Section 2.2). The authors of [51] only provide the DOLCE ontology in first-order logic sentences with modal operators, and do not provide the ontology in a computer-interpretable format that allows users to analyze and verify their axioms. The authors of [48] provided a set of computer-interpretable axioms for their modular consistency proof of DOLCE in the Common Algebraic Specification Language (CASL) syntax; these axioms form the basis of the work in Chapter 3, but we have modified and extended them in the Common Logic and Prover9 syntaxes to carry out our modularization of DOLCE and other mapping tasks. As we will see in later chapters, higher-order logic was not required in our modularization of the DOLCE ontology Common Logic (CL) We utilized a repository environment to store these computer-interpretable ontologies and theories in the Common Logic syntax. Common Logic is a standardized logical language for the specification of first-order ontologies and knowledge bases, and its details can be found in the ISO 24707:2007 document [41]. The author of [34] discusses the flexibility of the CLIF and its ability to support the high-level of expressibility in first-order logic. Consequently, all of the ontologies and theories found in the repository environment are 1 DOLCE-LITE can be accessed via owl.

23 Chapter 2. Background 10 written in Common Logic. With this in mind, we are able to examine meta-theoretic relationships between ontologies found in COLORE and, where applicable, prove them based on the first-order notions of interpretability and representation. The soundness and completeness of first-order logic aids us in the verification of theories: anything proven using the axioms of a theory holds for all possible models of that theory. For readability purposes, axioms are written in the traditional first-order logic syntax in this work, and the CLIF versions can be found online in the repository The COmmon Logic Ontology REpository (COLORE) The COmmon Logic Ontology REpository 2 is an open repository of first-order ontologies that serves as a test environment for the design, evaluation, and application of these ontologies. The existence of the repository gives the community a common foundation for developing complex ontologies and allows the exploration and examination of stored ontologies in an efficient and directed manner. Ontologies that share a similar domain are explicitly linked in the CLIF files, allowing users to explore a hierarchy composed of the related ontology modules, along with any extensions derived from mapping modules together. All theories within the repository are organized into hierarchies; a detailed discussion of the organization of theories within hierarchies can be found in [29]. Since each module of an ontology represents a different set of ontological commitments, having the repository connect all ontologies that share logical similarities allows greater reuse of these modules; for example, when two ontologies are connected through the repository, they are able to use translation definitions within the repository to share their modules. Thus, as the repository grows, the number of semantic integration possibilities increases as well to enable users to gain a better understanding of what information can be shared between modules along with the various relationships between these modules. 2 COLORE can be accessed via

24 Chapter 2. Background 11 Hierarchy Structure of Ontologies in COLORE Prior to discussing what it means for a set of theories or ontologies to be in a hierarchy, we adopt the following definitions from [14]. Definition A first-order theory is a set of first-order sentences that are closed under logical entailment. Definition The signature, or the non-logical lexicon, of a first-order theory T is denoted by Σ(T ). It is the set of all constant symbols, function symbols, and relation symbols that are used in T. The language of T, denoted by L(T ), is the set of first-order formulae that only use the non-logical symbols in the signature Σ(T ). Definition Let T 1 and T 2 be two first-order theories such that Σ(T 1 ) Σ(T 2 ). T 2 is an extension of T 1 iff for any sentence σ L(T 1 ), if T 1 = σ, then T 2 = σ. T 2 is a conservative extension of T 1 iff for any sentence σ L(T 1 ), T 2 = σ iff T 1 = σ. T 2 is a non-conservative extension of T 1 iff T 2 is an extension of T 1 and there exists a sentence σ Σ(T 1 ) where T 1 = σ and T 2 = σ. A first-order ontology is a set of first-order sentences (axioms) that characterize a firstorder theory, which is the closure of the ontology s axioms under logical entailment. Two ontologies O 1 and O 2 that use the same non-logical lexicon Σ have logically equivalent theories if all sentences σ expressed in Σ can be represented as follows: O 1 = σ O 2 = σ

25 Chapter 2. Background 12 With these definitions, we are able to order sets of theories that are expressed in the same signature. We adopt the definition used in [29] to describe the notion of a hierarchy. Definition A hierarchy H = H, is a partially ordered, finite set of theories H = T 1,..., T n, such that: 1. For all i and j, Σ(T i ) = Σ(T j ), 2. T i T j iff T j is an extension of T i, 3. T i < T j iff T j is a non-conservative extension of T i. All theories in a particular hierarchy share the same set of non-logical symbols, and are ordered by non-conservative extensions, such that the extensions restrict the set of models of which the theory extends. This ordering relation allows us to say that a theory T i is stronger than a theory T j if T i is a non-conservative extension of T j. We also adopt the following definition of a root theory from [29]: Definition A theory T in a hierarchy is a root theory iff it does not non-conservatively extend any other theory in the same hierarchy Relationships Between Hierarchies An ontology repository like COLORE allows us to examine the network of meta-theoretic relations defined between the theories found in the repository. These relationships allow us to compare the theories easily rather than simply examining the models generated from the axioms. This comparison enables us to determine one theory is stronger, weaker, equivalent to, or inconsistent with another. New theories can also be defined to capture shared, or overlapping, models between two theories.

26 Chapter 2. Background 13 Hierarchies and Conservative Extensions We adopt the following theorem from [29] to show that a hierarchy H 1 is not necessarily a non-conservative extension of another hierarchy H 2, since new theories can always be added to H 2 that are conservatively extended by theories in H 1. Theorem Suppose T 1 and T 2 are theories that are in different hierarchies such that Σ(T 1 ) Σ(T 2 ). If T 2 is a non-conservative extension of T 1, then there exists a theory T 3 such that: T 2 is a conservative extension of T 3, and T 3 is compatible with the hierarchy of T 1 : Σ(T 3 ) = Σ(T 1 ). Interpretability In order to compare ontologies that are axiomatized in different and disjoint non-logical lexicons, there is a need to translate a theory from one lexicon to the other while preserving the original semantics of the relations. The following definitions are adopted and adapted from [14] and [29]. Definition An interpretation π of a theory T 1 with the signature Σ(T 1 ) into a theory T 2 with the signature Σ(T 2 ) is a function on the set of non-logical symbols of Σ(T 1 ) and formulae in L(T 1 ), such that 1. π assigns to a formula π of L(T 2 ), in which at most the variable v 1 occurs free, such that T 2 = ( v 1 )π 2. π assigns to each n-place relation symbol P a formula π P of L(T 2 ), in which at most the variable v 1,..., v n occur free. 3. For any sentence σ L(T 1 ), T 1 = σ T 2 = π(σ) The mapping π is an interpretation of T 1 if it preserves the theorems of T 1 ; we say that T 1 is interpretable in T 2.

27 Chapter 2. Background 14 Definition An interpretation π of a theory T 1 into a theory T 2 is a faithful interpretation, if and only if, for any sentence σ L(T 1 ), T 1 = σ T 2 = π(σ) Thus, the mapping π is a faithful interpretation of T 1 if it preserves satisfiability with respect to T 1. We will also refer to this by saying that T 1 is faithfully interpretable in T 2. With this in mind, the definition of definable equivalence is also adopted from [29] to generalize the notion of logical equivalence between theories that do not have the same signature. Definition Two theories, T 1 and T 2, are definably equivalent iff T 1 is faithfully interpretable in T 2, and T 2 is faithfully interpretable in T 1. An example of definably equivalent theories can be found in temporal ontologies, such as between the mathematical theories of timepoints and linear orderings axiomatized in [35]. In contrast, the theory of partial orderings is interpretable in the theory of timepoints, but these two theories are not definably equivalent because the theory of timepoints is not interpretable in the theory of partial orderings. Thus, we can say that faithful interpretations are a generalization of the notion of conservative extensions, so we can generalize the following [29]: Theorem T 1 is faithfully interpretable in T 2 iff there is theory T 3 such that T 1 is definably equivalent to T 3 and T 2 is a conservative extension of T 3. The proof for this theorem can be found in [29]. Reducibility of Theories Another approach to modularity is based on the relationship of reducibility, in which one ontology is definably equivalent to the union of existing modules found in different hierarchies [28, 29]. We adopt the following definition of reducibility from [29].

28 Chapter 2. Background 15 Definition A theory, T, is reducible to a set of theories T 1,..., T n iff: T faithfully interprets each theory T i, and T 1... T n faithfully interprets T. In the remainder of this work, we refer to the set of theories T 1,..., T n as the reduction of T in COLORE. From this definition, we can see that two definably equivalent theories are reducible to each other. A trivial example can be found in the Combined Time hierarchy of COLORE, where the theory of timepoints is reducible to the theory of linear orderings, and vice versa. A non-trivial example of reducibility can be seen with the PSL-Core theory, T psl core, found in the PSL Ontology (described in Section 2.1.5). In [28], the authors show that T psl core is reducible to T linear, T partition, and T graph incidence. This example illustrates how reducibility leads to the decomposition of a theory that is treated as a module within a larger ontology [28], thus we adopt the following from [29]: Theorem Let T 1,..., T n be a set of theories such that Σ(T i ) Σ(T j ) = for all i j, j n, i j. A theory T is reducible to T 1,..., T n iff T is definably equivalent to T 1... T n. The proof for this theorem can be found in [29]. From this theorem, the following corollary is also defined: Corollary If T 1 is definably equivalent to T 2, then T 1 is reducible to T 2. Translation Definitions In order to map concepts between ontologies, we specify the semantic mappings in the form of translation definitions; this definition is adopted from [29] and [14]. Definition Let T 0 be a theory with the signature Σ(T 0 ) and T 1 be a theory with the signature Σ(T 1 ), such that Σ(T 0 ) Σ(T 1 ) =. If there is an interpretation of

29 Chapter 2. Background 16 T 0 in T 1, then there exists a set of sentences that axiomatizes the mapping, called a translation definition, in the language of L 0 L 1 of the form: ( x)p i ( x) Φ x where p i ( x) is a relation symbol in L 0 and (Φ x) is a formula in L 1 whose only free variables are x. From [60], translation definitions can be considered to be an axiomatization of the interpretation of T 0 into T 1, where they conservatively extend T 0 and definitionally extend T 1. Proving Relationships Between Theories We utilized a semi-automated procedure to verify theories with the aid of the Prover9 and Mace4 software applications 3. Prover9 is an automated theorem prover for firstorder logic that uses resolution to prove goal sentences which are entailed by the inputted theory; Mace4 is a finite model generator that complements Prover9 since it searches for countermodels of the inputted goal. To prove relationships between two theories found in different hierarchies, we adopt the methodology used in [29] to determine the definable equivalence of theories. Suppose 12 and 21 are the translations for T 1 into T 2 and T 2 into T 1, respectively. To verify that two theories, T 1 and T 2, are definably equivalent, we carry out the following reasoning problems: 1. T 1 T 2 12 is consistent, 2. T 1 12 = T 2, 3. T 1 T 2 21 is consistent, and 4. T 2 21 = T 1. 3 Prover9 and Mace4 are available via mccune/mace4/.

30 Chapter 2. Background 17 If all four reasoning problems produce successful results, then it means that theories T 1 and T 2 are definably equivalent. This means that T 1 and T 2 are alternative axiomatizations of the same set of models. If steps 1 or 3 fail, then the translation definitions between the theories are inconsistent and the two theories have two disjoint sets of models; this means that they are not translatable into one another. If step 2 fails, then it indicates that T 1 may be weaker than T 2 ; likewise, if step 4 fails, then T 2 may be weaker than T 1. For these weaker theory scenarios, one theory is strictly weaker than the other if it is possible to find a definably equivalent theory of the stronger theory in the core hierarchy of the weaker theory, and show that it non-conservatively extends the weaker theory Verification of Ontologies To verify an ontology, we apply model-theoretic notions in our analysis of the DOLCE ontology. We characterize the semantics of an ontology as a set of intended structures 4. We specify these structures with well-understood mathematical theories to determine whether the axiomatization of an ontology matches its intended models; these theories include partial orderings, lattices, incidence structures, geometries, and algebra [23, 28]. If an ontology s axiomatization contains unintended models, then it is possible to find sentences that are entailed by the intended models, but these sentences are not provable from the axioms of the ontology. Such models provide barriers to semantic interoperability between software systems and may prevent the entailment of sentences [23, 28]. By verifying an ontology, we would like to characterize its models up to isomorphism to determine whether or not these models are equivalent to the intended structures of the ontology [23]. To do this, we utilize the mathematical notion of representation theorems, where we prove that every intended structure is a model of the ontology and that every model of the ontology is elementary equivalent to some intended structure. In this work, 4 Adopted from [23] for the ontology, an intended structure is a set of structures that characterizes the semantics of an ontology s terminology.

31 Chapter 2. Background 18 we leverage work done by mathematicians for theories such as orderings, lattices, algebra, and incidence structures to verify the ontologies of domains such as time, process and mereology The Process Specification Language (PSL) The Process Specification Language (PSL) is designed to facilitate the correct and complete exchange of process information among manufacturing systems [31]. With the increasing use of information technology in manufacturing systems, it has been increasingly important to integrate different software applications together to ensure interoperability among them. However, these applications may use the same or different terminology to associate different semantics with the terms in the domain. This is still evident if two applications utilize the same terminology - they may associate different semantics with the terms. This clash of meaning between terms prevents seamless exchange of information among software applications [31]. Consequently, PSL was designed to create a process representation that is common to all manufacturing applications, generic enough to be decoupled from any given application and robust enough to represent the necessary process information for any given application [13]. PSL is meant to be a neutral, interchange language that integrates multiple processrelated applications throughout the manufacturing life cycle [12]; typically, point-to-point translation programs are created to facilitate communication between applications, but with the increasing number of such programs, it has become very difficult for software developers to provide translators between different pairs of applications [31]. The PSL Ontology is organized into PSL-Core and a partially ordered set of extensions. All axioms are first-order sentences written in Common Logic and can be found in COLORE 5. Within PSL, two types of extensions exist: core theories and definitional extensions. Core theories introduce and axiomatize new relations and functions that 5 psl_core.clif The first-order logic version of the ontology is also included in Appendix A.1.1.

32 Chapter 2. Background 19 are primitive, whereas definitional extensions consist of conservative definitions that use the terminology of the core theories, meaning that they add no new expressive power to PSL-Core. The PSL ontology also includes a set of extensions that introduce new terminology. Any extension of PSL can axiomatize concepts that are not explicitly specified in PSL-Core. All core theories within the PSL ontology are consistent extensions of PSL-Core (T psl core ). Appendices A.1.2 and A.2 contain a depiction of the relationships between these core theories, as well as list the key terms in the lexicon of the core theories of the PSL ontology. Within T psl core, the following basic ontological distinctions are made (adapted from [22]): Activities: a repeatable pattern of behaviour that may have multiple occurrences, or may never occur. Activity Occurrences: corresponds to a concrete instantiation of a unique activity. Activity occurrences are not instances of activities, since activities are not classes within the PSL ontology. Time: each activity occurrence is associated with unique timepoints that mark the beginning and end of the occurrence. The set of timepoints is linearly ordered, forwards into the future and backwards into the past; this linear ordering is captured in the PSL Ontology with the before relation. Objects: those elements that are not activities, occurrences, or timepoints. State and Change: process ontologies are used to represent dynamic behaviour in the world to allow software systems to make predictions about the future and explanations with the past. PSL-Core captures basic intuitions about state and its relationship to activities with fluents which are properties in the domain that can change. A fluent is changed by the occurrence of activities, and a fluent can only be changed by the occurrence of activities. Since the PSL ontology contains axioms that have been well-defined and standardized in ISO :2004, it was appropriate to utilize this ontology to examine whether it could be mapped with concepts found in the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE), which is described in the next section.

33 Chapter 2. Background Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) The Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) is a foundational ontology of particulars 6 that captures ontological categories found in natural language and human common sense [51]. It is the first module found in the WonderWeb Foundational Ontologies Library 7 (WFOL). There is a cognitive bias in how DOLCE captures these categories since they are considered to be cognitive artifacts that are derived from human perception, cultural imprints, and social conventions; these categories are graphically shown in Figure 2.1, and listed in Table 2.1. DOLCE is based on the distinction between endurants and perdurants. Endurants are continuants that are perceived at any given point in time, whereas perdurants are occurrents that are partially present at any given point in time. Thus, endurants and perdurants in DOLCE are characterized by whether or not they can exhibit change in time. Endurants are considered to genuinely change in time - in the sense that the endurant, as a whole, can have incompatible properties at different times. In contrast, perdurants cannot change in this sense, since none of their parts keeps its identity in time. We do not give an extensive discussion on the metaphysical properties of these concepts, and direct the reader to [51] for a better understanding of the authors design choices in developing DOLCE Assumptions and Simplifications Made to DOLCE In our work with DOLCE, we have had to make assumptions and simplifications in order to compare our modularization techniques with the work done in [48]. We outline these 6 The authors of [51] use this to identify that the ontology s domain of discourse is restricted to these particulars, meaning it is an ontology of instances, rather than an ontology of universals or metaproperties. 7 The WonderWeb Foundational Ontologies Library can be accessed via semanticweb.org/deliverables/d17.shtml.

34 Chapter 2. Background 21 Figure 2.1: Classification of DOLCE categories from [51].

35 Chapter 2. Background 22 Table 2.1: Basic Categories in DOLCE. Abbreviation AB ACC ACH APO AQ AR AS ASO ED EV F M MOB NAPO NASO NPED NPOB PD PED POB PQ PR PRO PT Q R S SAG SC SL SOB ST STV T TL TQ TR Category Abstract Accomplishment Achievement Agentive Physical Object Abstract Quality Abstract Region Arbitrary Sum Agentive Social Object Endurant Event Feature Amount of Matter Mental Object Non-agentive Physical Object Non-agentive Social Object Non-physical Endurant Non-physical Object Perdurant, Occurrence Physical Endurant Physical Object Physical Quality Physical Region Process Particular Quality Region Space Region Social Agent Society Spatial Location Social Object State Stative Time Interval Temporal Location Temporal Quality Temporal Region

36 Chapter 2. Background 23 assumptions and simplifications in the subsequent sections that follow. Removal of Modal Logic Operators Similar to [48], we have ignored all modal logic operators found in the DOLCE axioms due to difficulties in representing modality in Common Logic and in verifying axioms in the Prover9 syntax. For axioms that include the modal logic, we simply stripped off the modal operators; we demonstrate this with the original definition of specific constant dependence (Dd69 in [51]): SD(x, y) ( t(p RE(x, t)) t(p RE(x, t) P RE(y, t))) becomes SD(x, y) ( t(p RE(x, t)) t(p RE(x, t) P RE(y, t))) Thus, in this work, all modal logic operators ( for necessarily and for possibly) have been removed in any references of the schematic axioms that are utilized in our modularization. These include the following axioms found in [51]: Dd1, Dd2, Dd3, Dd4, Dd7, Dd10, Dd13, Dd56, Dd57, Dd58, Dd59, Dd60, Dd61, Dd62, Dd69, Dd70, Dd71, Dd78, Dd79, Dd80, Dd81, Dd82, Dd83, Dd84, Dd85, Dd86, Dd96, Dd97, and Dd98. Weakening Mereological Sum and Fusion Axioms Ad9 and Ad15 in [51] are weakened assuming only the existence of binary sum and binary difference, respectively, as specified by the authors of [48] and in their CASL specification of DOLCE in many-sorted logic document 8. Consequently, the definition for mereological sum (Dd19 in [51]) is weakened into two relations Sum(z, x, y) and Dif(z, x, y) as follows: x σxφ(x) ιz y (O(y, z) w (φ(w) O(y, w))) 8 This DOLCE-CASL specification document can be accessed via: tripod.com/dolce-s-specification-in-many-sorted-first-order-logic.html.

37 Chapter 2. Background 24 becomes Sum(z, x, y) ( x y w z (O(w, z) (O(w, x) O(w, y)))) Dif(z, x, y) ( x y w z P (w, z) (P (w, x) O(w, y))) Similarly, the definition for mereological sum of temporal properties (Dd27 in [51]) is weakened as shown below. x σ te xφ(x) ιz y t (O(y, z, t) w (φ(w) O(y, w, t))) becomes tsum(z, x, y) ( x y w z (O(w, z, t) (O(w, x, t) O(w, y, t)))) tdif(z, x, y) ( x y w z P (w, z, t) (P (w, x, t) O(w, y, t))) These two rewritten axioms only apply to the relations that are all of the same type of property (e.g., for all endurants); in the DOLCE-CASL specification used in [48], the binary sum and binary difference axioms apply to sorts of the same type. As well, the authors of [48] include additional axioms to the DOLCE specification for extensionality and existence of binary difference, existence of the sum, parts of the sum, and proper parts of the sum: x y P (x, y) z (Dif(z, x, y)) x y P (x, y) z (Sum(z, x, y) x y z Sum(z, x, y) P (x, z) P (y, z) x y z P (x, y) Sum(z, x, y) P P (y, z)

38 Chapter 2. Background 25 Similarly, for temporal binary sums and differences, the existence of the sum and extensionality (and existence of the difference) are given as follows: x y t t 1 t 2 z tsum(z, x, y) x y ( t P (x, y, t)) z (tdif(z, x, y)) x y z t P RE(x, t) tsum(z, x, y) P (x, z, t) All of the above additions have also been included in the Common Logic axioms used in this work. Treating Being Present as Primitive The relation P RE(x, t) is assumed to be a primitive relation due to the fusion operators found in the definitional axioms for quality and quales (refer to Axioms Dd28 to Dd39 in [51]). Similar to what the authors of [48] have done, we have not expanded out the definitions of being present to include the fusion operator. The spatial inclusion relation is not defined, nor used, in [48], so we have also decided not to include this in our work. Thus, axioms Ad19, Ad28, and Ad68 are not included in our Common Logic version of DOLCE. Exclusion of Quality, Quales, and Dependence in DOLCE We note here that this work partially modularizes the DOLCE ontology. Due to time constraints and problems with how the dependence axioms in DOLCE interact with each other, we opted to partially decompose the DOLCE ontology. For example, the interplay between the DOLCE categories in the mutual specific constant dependence axiom MSD(T Q, P D) (Ad67 in [51]) causes issues when we attempt to verify this module of DOLCE; from the definitional axioms, this axiom becomes the conjunction of two specific constant dependence axioms: MSD(T Q, P D) SD(T Q, P D) SD(P D, T Q).

39 Chapter 2. Background 26 The definition of specific constant dependence itself is a more complex axiom that requires further expansion: SD(φ, ψ) DJ(φ, ψ) ( x (φ(x) ( y (ψ(y) SD(x, y))))) Thus, we do not include axioms Ad67 to Ad74 from [51] in our work. In DOLCE, qualities are considered to be basic entities that can be perceived or measured. These include shapes, colors, sizes, sounds, smells, as well as weights, lengths, and electrical charges [51]. While the term quality is often synonymous with the term property, this is not the case in DOLCE: qualities are considered to be particulars, and properties are universals [51]. Every entity, including qualities themselves, comes with certain qualities, which exist as long as the entity exists. Furthermore, DOLCE makes the distinction between a quality (such as the colour of a specific rose) and a quale, its value (a particular shade of red) [51]. We do not go into more detail about the distinctions between qualities and quales, and direct the reader to [51], [19], and [9] for additional information about trope theory, from which these distinctions are based. Similar to dependence, the axioms that involve quality, and temporal and spatial quales 9 are complex and involve many manual substitutions to arrive at the expanded forms of the axioms. Due to the complexity of these definitions and the semantic inaccuracy of simply declaring these dependence relations as primitive, we decided to examine axioms that did not involve nested and complicated substitutions. Thus, we only present six modules of the DOLCE ontology and the remainder of the ontology will be decomposed in future work discussed in Section The quality, and temporal and spatial quales are axioms Ad38 to Ad51, and Ad52 to Ad66 in [51], respectively.

40 Chapter 2. Background Overview of Concepts Found in DOLCE Here we discuss the major concepts found in the ontology that are examined in our partial modularization, and summarize these general concepts in Table 2.2. We also note that the original DOLCE axioms for these concepts can be found in Appendix B.1. Table 2.2: Summary of concepts found in DOLCE. DOLCE Concept Being Present Constitution Parthood Participation Temporary Parthood Description x is present at t P RE(x, t) x constitutes y during t K(x, y, t) (ED(x) P D(x)) (ED(y) P D(y)) T (t) x is part of y P (x, y) (AB(x) P D(x)) (AB(y) P D(y)) x participates in y during t P C(x, y, t) (ED(x) P D(y) T (t)) x is part of y during t tp (x, y, t) (ED(x) ED(y) T (t)) Endurants and Perdurants As we have mentioned earlier, DOLCE is based on the distinction between enduring and perduring entities: endurants ED(x) and perdurants P D(x), respectively. In philosophy, these entities are also referred to as continuants and occurrents, where the fundamental difference between the two is related to their behaviour in time [51]. Endurants are wholly present at any time, whereas perdurants extend in time by accumulating different temporal parts, so they are only partially present [51]. Endurants are entities that can be observed and perceived as a complete concept, regardless of a given snapshot of time. Material objects are classified as endurants; for example, apples and books are still wholly present when time is frozen. In contrast, perdurants are entities for which only a part exists if we look at them at any given snapshot in time. When time is frozen, we can only observe and perceive a part of the perdurant. For example, if we take the process of running and freeze time, we only see

41 Chapter 2. Background 28 a part of the running action; without any prior knowledge of the process, one may not be able to determine whether the actual process at that given snapshot in time is a process of running. Parthood and Temporary Parthood The distinction between endurants and perdurants also introduces two kinds of parthood relations in DOLCE: atemporal and time-indexed parthood. Atemporal parthood is used for entities which do not properly change in time, such as occurrences and abstracts [51]. On the other hand, time-indexed parthood holds for endurants since it is necessary to know when a specific parthood relationship holds [51]. Additionally, with time-indexed parthood, two notions are defined in [51]: 1. An endurant is mereologically constant iff all its parts remains the same during its life. For example, material objects are mereologically variable because they can lose or gain parts. 2. An endurant is mereologically invariant iff they remain the same across all possible worlds. For example, amounts of matter are mereologically invariant since all of their parts are essential parts. Being Present In DOLCE, temporal existence is modelled by the P RE(x, t) relation, which is read as x is present at time t. The authors of [51] and [6] note that the notion of time can be punctual or extended, and can adopt different structures on them, such as discrete or continuous time, and linear or branching time. As well, there are different ways of being in time: existing in time versus occurring in time, or being wholly present versus being partially present (recall the distinction between endurants and perdurants). Constitution Constitution is a widely debated concept in philosophy. Some philosophers insist that constitution is identity since distinct material objects cannot occupy the same place at

42 Chapter 2. Background 29 the same time; others, however, argue that constitution is not identity since, for example, a statue and the clay used to make the statue differ in various contexts. In this work, we adopt the definition that constitution is not parthood to be consistent with the views presented in [51]. DOLCE adopts a multiplicative approach in describing the concept of constitution, where different entities can be co-located in the same space-time since entities are given incompatible essential properties [51]. An example described in [51] is that a vase is constituted by an amount of clay, but the vase itself is not an amount of clay. There are certain properties that a particular amount of clay has when it was shaped by the vase-master which are considered as essential for the emergence of a new entity. In language and cognition, this new entity is referred to as a genuinely different thing: for instance, we say that a vase has a handle, but not that a piece of clay has a handle. Participation While we do not modularize axioms pertaining to participation in DOLCE, we briefly introduce the notion of participation here since it will be discussed in Chapter 4. In the context of DOLCE, the authors of [51] indicate that there are endurants involved in an occurrence, so the notion of participation is not considered parthood. In DOLCE, participation is time-indexed in order to account for the varieties of participation in time, such as temporary participation and constant participation. In DOLCE, P C(x, y, t) stands for the object x participates in an event y at time t. We note that additional participation axioms have been proposed by the authors of [6], which form the basis of what they call DOLCE-CORE. It is an ontology that is limited to entities that exist in time, referred to as temporal particulars in [6]. The primary difference between DOLCE and DOLCE-CORE is that the latter adopts a contextual perspective by introducing regions and spaces (part of the abstract AB category in Figure 2.1) as temporal entities that are created, adopted, and abandoned [6]. Simi-

43 Chapter 2. Background 30 lar to DOLCE in [51], DOLCE-CORE partitions temporal-particulars P T into six basic categories: objects O(x), events E(x), individual qualities Q(x), regions R(x), concepts C(x), and arbitrary sums AS(x). The original DOLCE categories for endurants ED(x) and perdurants P D(x) are renamed objects O(x) and events E(x), respectively. Furthermore, individual qualities in DOLCE-CORE are partitioned into quality kinds Q i which are associated to a region in one or more spaces S ij. Due to these modifications of the original DOLCE axioms and slight change in DOLCE constructs, we do not incorporate any of the DOLCE-CORE axioms in our work.

44 Chapter 3 Ontology Decomposition: Verification of DOLCE In this chapter, we outline and discuss our approach to modularizing the DOLCE ontology, as well as describe the axioms found in each of the generated modules. 3.1 Modularizing DOLCE In order to verify the axioms found in DOLCE, we applied the modularization techniques presented in [29] in order to determine whether DOLCE is decomposable and consistent. As a basis for comparison, we examined whether our modules are the same as, or similar to, the modules presented in [48], and noted the differences in both approaches to decomposing DOLCE Modules from Consistency of DOLCE In [48], the authors present a novel approach at establishing the consistency of DOLCE. They proposed a methodology that utilizes the Heterogeneous Tool Set (HETS) 1 to 1 HETS is available via formal_methods/cofi/hets/index_e.htm. 31

45 Chapter 3. Verification of DOLCE 32 develop an architectural specification for DOLCE that is used to produce relative consistency proofs based on conservativity triangles. In HETS, an architectural specification is essentially a software specification that decomposes a large theory into smaller subtasks, which includes the construction of models for these small theories, proving the conservativity of theory extensions, and determining whether the constructed theories can be amalgamated together [48]. Relative consistency proofs are used by HETS to provide theory interpretations into another theory that is known or assumed to be consistent. HETS visualizes these relationships between smaller theories via development graphs by denoting the dependencies between the theories. The approach presented in [48] constructed a global model for DOLCE that is built from smaller models of subtheories together with amalgamability properties between such models. The authors hand-crafted an architectural specification of DOLCE which reflects the way models of the theory can be built, and utilized HETS to automatically verify the amalgamability conditions and produce series of relative consistency proofs. The authors of [48] note that the axioms in the dependence theory of DOLCE introduced complications in their first modularization attempt since subtle dependencies between parts of DOLCE s taxonomy were involved. Consequently, they restructured their architectural specification for DOLCE to utilize DOLCE s temporal mereology in a bottom-up manner. While we do not modularize this theory of dependence in this work, we do make note of how the dependence axioms interact with the taxonomy in future work. As a result of these changes, the structure of HETS subtheories as found in [48] is graphically presented in Figure 3.1. The end result consisted of thirty eight units within the architectural specification and eighteen amalgamations, allowing the generation of various finite models for DOLCE [48]. Their architectural specification can be accessed via the authors anonymous Association for the Advancement of Artificial Intelligence (AAAI) 2011 submission 2 ; alternatively, the authors axioms in the Thousands of Prob- 2

46 Chapter 3. Verification of DOLCE 33 lems for Theorem Provers (TPTP) syntax can be accessed in COLORE in the DOLCE hierarchy 3. In [48], there is a lack of discussion of what each DOLCE module contains, along with which ovals in Figure 3.1 are modules of DOLCE since there are also ovals that represent theories that are external to the ontology. For example, there are individual ovals depicting Mereology, Mereology and TemporalPart, and Temporary Parthood; we are unsure of the distinction between these modules, and whether or not the Temporary Parthood module contains similar axioms found in Mereology and Mereology and TemporalPart since the only common imported module between them is the Time Mereology module. This unclear distinction between modules can also be seen in the ovals containing Being Present and Binary Present; we are unsure as to why this refinement was made in their modularization. Our modularization, on the other hand, is much more succinct and clear, since we do not introduce any external theories in the decomposition process Our Approach to Modularization In contrast to the work done in [48], we do not utilize HETS to produce a semi-automatic modularization of DOLCE. Instead, we opted to decompose DOLCE manually using the techniques from [29], as well as verify these modules with Prover9 by mapping them with pre-existing mathematical theories found in COLORE. We were interested in determining if the sets of models of two differently axiomatized ontologies are equivalent. While it is possible to define the CLIF theories as CASL specifications in HETS, a repository environment like COLORE is better-suited for managing varied ontologies and storing any meta-theoretic relationships between these stored theories. HETS is a tool focused more on modularizing a single theory instead of a repository that can manage a large number of varied ontologies and allow users to examine various relationships between 3

47 Chapter 3. Verification of DOLCE 34 Figure 3.1: Structure of DOLCE s subtheories in [48].

48 Chapter 3. Verification of DOLCE 35 these theories. The current framework for our modularization is shown in Figure 3.2 below. At the very bottom of the diagram is the DOLCE taxonomy module, T dolce taxonomy, which consists of the categorization of the constructs found in DOLCE. The DOLCE mereology and time mereology modules, T dolce mereology and T dolce time mereology, import the axioms of T dolce taxonomy, as denoted by the solid arrows in the figure. As well, T dolce mereology imports T dolce time mereology. We then see that the DOLCE present module, T dolce present, imports all of the axioms in T dolce time mereology, so T dolce taxonomy is included as well. Likewise, the DOLCE dependence, participation, and temporary parthood modules 4 import T dolce present and all of the axioms contained within. Finally, the DOLCE constitution module, T dolce constitution, imports all of the axioms in T dolce temporary parthood. To verify the DOLCE theories, we map them with existing theories found in COLORE. Figure 3.3 illustrates the mappings between the DOLCE theories and COLORE theories. Each of these verification tasks are discussed in their respective sections Usage of Bipartite Incidence Structures In our partial modularization of DOLCE, we utilized bipartite incidence structures found in mathematical theories of COLORE. Bipartite incidence structures are a generalization of geometries: there are two disjoint sets of points and lines, and the incidence relation, in(x, y), specifies the set of points that are incident with a line. We noticed that the constraints on points and lines in geometry were similar to constraints found in the DOLCE constructs, thus we utilized these bipartite incidence structures to assist us with verifying DOLCE. We briefly describe each of these structures below and direct the reader to [24], [25], and [26] for more detailed reading about these structures. 4 Denoted as T dolce dependence, T dolce participation, and T dolce temporary parthood, respectively.

49 Chapter 3. Verification of DOLCE 36 dolce constitution dolce temporary parthood dolce participation dolce dependence dolce present dolce mereology dolce time mereology DOLCE Hierarchy dolce taxonomy Figure 3.2: Relationships between DOLCE modules. Solid arrows denote conservative extensions, dashed arrows denote non-conservative extensions, and dashed boxes indicate individual hierarchies. dolce constitution dolce temporary parthood dolce present dolce time mereology ideal cem lower reflect down foliation ideal cem downward m foliation ideal cem wmg dolce temporary parthood dolce present dolce time mereology ideal cem downward m foliation ideal cem wmg dolce present dolce time mereology ideal cem wmg dolce time mereology cem mereology Figure 3.3: Mappings between DOLCE and COLORE theories. Solid arrows denote conservative extensions and solid lines indicate equivalence.

50 Chapter 3. Verification of DOLCE 37 Mereological Geometries, Bundles & Foliations In our reduction, we utilized structures from the mereological geometry, mereological bundle, and mereological foliations hierarchies: A mereological geometry 5 is the amalgamation of a bipartite incidence structure and a mereology that is specified on sets of collinear points (the points that are all incident with the same line). Sets of collinear points need to satisfy axioms for a given mereology, and there may be a global mereology on a set of all points, regardless of collinearity. In a mereological bundle 6, we find a generalization of the part(x, y) relation from mereology by introducing a ternary relation tpart(x, y, t) that specifies a relativized parthood relation on sets of lines that are coincident with the same point. In mereological bundles, a quasiorder is specified on the set of lines that are incident with a point; a mereology is not specified on sets of intersecting lines due to the notion of temporary parthood. In the philosophical literature, the relation for temporary parthood is not considered to be antisymmetric, in contrast to the parthood relation in a mereology. Due to this, mereological bundles contain quasiorderings on sets of intersecting lines. Mereological foliations 7 are simply an amalgamation of mereological geometries and mereological bundles. A mereology is specified on each set of collinear points and mereological bundle is specified on each set of intersecting lines. Figure 3.4 depicts a structure M M m foliation. Figure 3.4(a) shows the mereology within the mereological geometry, and Figure 3.4(b) shows the incidence structure. Note that this is the same incidence structure as the one in the mereological bundle. Figure 3.4(c) shows the mereological bundle: in particular, the quasiorder that is specified on the set of lines in N(p i ) for each point p i. Incidence Bundles & Foliations Similarly, we also utilize incidence bundles and incidence foliations in our reduction: With incidence bundles 8, an incidence structure is specified on the set of planes and lines that are incident with a point 5 mereological_geometry/ 6 mereological_bundle/ 7 mereological_foliation/ 8 incidence_bundle

51 Chapter 3. Verification of DOLCE 38 t1 t4 l1 l2 l3 t2 t3 t5 t6 t1 t2 t3 t4 t5 t6 (a) (b) l2 l1 l3 l1 l1 l3 l3 l2 (c) l2 Figure 3.4: Example of mereological foliation (T m foliation ). An incidence foliation 9 is an amalgamation of a mereological geometry and an incidence bundle: a mereology is specified on each set of collinear points and an incidence bundle is specified on each set of coincident lines and planes. Subposet Bundles & Foliations In addition to the mereological and incidence structures outlined above, we also utilize structures found in the subposet hierarchy 10, H subposet, in COLORE. Each ontology in this hierarchy is an extension of an ontology from the Mereology Hierarchy, H mereology, and an ontology from the Ordering Hierarchy, H ordering. The ontologies shown in Figure 3.5 form the basis for H subposet. The root ontology T subposet root is the union of T m mereology and T partial ordering, and is a conservative extension of each of these ontologies. Thus, each model of T subposet root (and hence each model of any ontology in the hierarchy) is the 9 incidence_foliation 10

52 Chapter 3. Verification of DOLCE 39 amalgamation of a mereology substructure and a partial ordering substructure. The ontologies shown in Figure 3.5 contain additional axioms that constrain how the mereology is related to the partial ordering. In models of T subposet, the mereology is a subordering of the partial ordering. T ideal strengthens this condition by requiring that the mereology is a subordering of the partial ordering which forms an ideal. In models of T chain antichain, elements that are ordered by the mereology are not comparable in the partial ordering. All ontologies within H subposet combine one of the ontologies in Figure 3.5 together with one of the ontologies in Figure 3.6 and one of the ontologies in Figure 3.7. In the following sections, we will explore how different ontologies in H subposet serve as design patterns. We utilized the following structures from H subposet in our reduction of DOLCE: A subposet bundle 11 is analogous to a mereological bundle: we find a generalization of the part(x, y) relation from mereology by introducing a ternary relation tpart(x, y, z) that specifies a relativized parthood relation on sets of lines that are coincident with the same point. We also find a generalization of the leq(x, y) relation from the ordering theories introducing a ternary relation tleq(x, y, z) that specifies a relativized ordering relation on sets of lines that are coincident with the same point. Subposet foliations 12 are an amalgamation of mereological geometries and subposet bundles. Naming Convention for Bipartite Incidence Structure Theories Due to the various combinations of incidence structures, the names of the theories in COLORE may appear confusing. Here we briefly outline the naming convention used to describe these incidence structure theories. Consider the theory T ideal cem wmg in COL- ORE 13. The name ideal cem wmg is broken down as follows: 11 bundle 12 foliation 13 mereological_geometry/ideal_cem_wmg.clif

53 Chapter 3. Verification of DOLCE 40 filter ideal upper_set lower_set subposet lower_reverse lower_preserve chain_antichain upper_preserve upper_reverse subposet_root mereology partial_ordering Figure 3.5: Ontologies in H subposet : the hierarchy of theories of relationships between partially ordered sets. Solid arrows denote conservative extensions and dashed arrows denote non-conservative extensions.

54 Chapter 3. Verification of DOLCE 41 cem_c cem_g cem_notg cem_notc cem_mereology mem_mereology em_mereology ex_cm_mereology ppp_mm_mereology inclusion_space tree_mm_mereology ppp_m_mereology cm_mereology ex_mm_mereology dense_mm_mereology ex_m_mereology mm_mereology tree_mereology prod_mereology sum_mereology dense_mereology discrete_mereology m_mereology Figure 3.6: Ontologies in H mereology. Solid arrows denote conservative extensions and dashed arrows denote non-conservative extensions.

55 Chapter 3. Verification of DOLCE 42 discrete linear_order no_end final_discrete linear_order initial_discrete linear_order bounded discrete linear_order initial_dense linear_order bounded dense linear_order final_dense linear_order dense linear_order no_end discrete linear_order bounded linear_order dense linear_order discrete_forest discrete_chains tree linear_order discrete semilinear_order forest dense semilinear_order semiorder dense weak_separative semilinear_order interval_order lattice discrete partial_order chains weak_order partial semiorder semilattice total_preorder dense partial_order series_parallel partial_order discreteness max_exists min_exists quasi-order density transitivity Figure 3.7: Ontologies in H ordering. Solid arrows denote conservative extensions and dashed arrows denote non-conservative extensions.

56 Chapter 3. Verification of DOLCE 43 ideal: collinear points form an ideal 14 in the global cem mereology cem: cem refers to cem mereology, which is the global mereology on all points in this structure wmg: collinear points form a weak mereology, wmg, which is a partial ordering The DOLCE Hierarchy (H dolce ) & Its Modules From our partial modularization, we came up with the following modules for DOLCE that are each discussed in the sections that follow: T dolce taxonomy T dolce time mereology T dolce mereology T dolce present T dolce temporary parthood T dolce constitution The reduction for each theory breaks down according to DOLCE s taxonomy, which is described in the next section. Figure 3.8 depicts how each DOLCE category (P D(x), ED(x), Q(x)) used in our modularization is associated with different mathematical structures found in COLORE. ideal cem lower reflect down foliation ideal cem lower reflect down foliation ideal cem downward foliation ideal cem wmg dolce constitution ideal cem downward m foliation ideal cem downward m foliation ideal cem wmg ideal cem wmg dolce temporary parthood Non-Physical Endurant NP ED(x) Physical Endurant P ED(x) ideal cem wmg ideal cem wmg ideal cem wmg dolce present Endurants ED(x) Perdurants P D(x) Qualities Q(x) Figure 3.8: Relationships between DOLCE modules with mathematical structures in COLORE. 14 An ideal is a set closed under the P (x, y) and sum(x, y, z) relations. For any two points, its sum is also in the set.

57 Chapter 3. Verification of DOLCE DOLCE s Taxonomy (T dolce taxonomy ) The taxonomy of DOLCE is not axiomatically defined in first-order, but is depicted graphically in [51], so we have provided our own subsumption and disjointness axioms to describe the relationships between the various categories of particulars. In [51], the DOLCE taxonomy is specified in a finite set of explicitly introduced individuals, labelled as Π X, of categories listed in Table 2.1. We define the overall set Π to be equivalent to the following: Π X = {P T, AB, R, T R, T, P R, S, AR, Q, T Q, T L, P Q, SL, AQ, ED, P ED, M, F, P OB, AP O, NAP O, NP ED, NP OB, MOB, SOB, ASO, SAG, SC, NASO, AS, P D, EV, ACH, ACC, ST V, ST, P RO} Furthermore, each category in the taxonomy is broken down into the subcategories depicted in Figure 2.1, so axiom definition Dd10 in [51] can be simplified as Φ which contains the leaves of the taxonomy: because of the assumption that the set Π is equivalent to Π X, L 1 (x), L 2 (x),..., L n (x) are leaves in Π X : L X (φ) (φ x L 1 (x) L 2 (x)... L n (x)) Consequently, Ad63 and Ad64 in [51] are instantiated by temporal (TL) and spatial locations (SL), time intervals (T), and space regions (S), as also specified in [48] and their DOLCE-CASL specification document. In our modularization, the taxonomy is a separate module that guides the remainder of this work; we used the taxonomy to help us decompose the ontology, as we will see in later sections. These taxonomic axioms are specified in first-order logic in Figures 3.9,

58 Chapter 3. Verification of DOLCE , and 3.11, and can be found in COLORE DOLCE s Time Mereology (T dolce time mereology ) Within DOLCE, there is a mereology on time intervals that is implicitly defined in the axiomatizations of temporal relations in [51]. We noticed patterns in how temporal relations are axiomatized in DOLCE where time intervals represent the temporal objects used throughout the ontology. Similar to the modularization of [48], we have formalized a module of DOLCE contains axioms that describe a mereology over time intervals. Recall that, in Figure 3.2, all of the subsequent modules of DOLCE import T dolce time mereology in their axioms; this indicates that T dolce time mereology plays a role in how the other DOLCE concepts are defined with respect to time intervals and how the mereology affects our usage of bipartite structures in the verification of these modules Axiomatization of T dolce time mereology In our axiomatization of T dolce time mereology, we have adopted the original DOLCE mereology axioms, but have placed argument restrictions of using time intervals on the sorts. As well, we have added in the mereology axioms for overlap, difference, sum, implied parts of sum, and implied proper parts of sum axioms into this new time mereology. These axioms are outlined in the next section. Figure 3.12 lists all of the axioms found in T dolce time mereology ; as well, the axioms can be found in COLORE 16. In contrast to the axioms used by [48] in the HETS modularization, we were unable to utilize some of the axioms provided by [51] because of the fusion operator, σ, as it requires higher order logic. As well, the authors of [48] utilize variants of the sum(z, x, y) and dif(z, x, y) relations that are not found in COLORE. In 15 taxonomy.clif 16 time_mereology/dolce_time_mereology.clif

59 Chapter 3. Verification of DOLCE 46 x ED(x) P D(x) Q(x) AB(x)) P T (x) (3.2.1) x P ED(x) NP ED(x) AS(x)) ED(x) (3.2.2) x EV (x) ST V (x)) P D(x) (3.2.3) x T Q(x) P Q(x) AQ(x)) Q(x) (3.2.4) x R(x)) AB(x) (3.2.5) x M(x) F (x) P OB(x)) P ED(x) (3.2.6) x NP OB(x)) NP ED(x) (3.2.7) x ACH(x) ACC(x)) EV (x) (3.2.8) x ST (x) P RO(x)) ST V (x) (3.2.9) x T L(x)) T Q(x) (3.2.10) x SL(x)) P Q(x) (3.2.11) x T R(x) P R(x) AR(x)) R(x) (3.2.12) x (AP O(x) NAP O(x)) P OB(x) (3.2.13) x MOB(x) SOB(x)) NP OB(x) (3.2.14) x T (x)) T R(x) (3.2.15) x S(x)) P R(x) (3.2.16) x (ASO(x) N ASO(x)) SOB(x) (3.2.17) x (SAG(x) SC(x)) ASO(x) (3.2.18) Figure 3.9: Axioms outlining the subsumption constraints of T dolce taxonomy.

60 Chapter 3. Verification of DOLCE 47 x (P T (x)) (ED(x) P D(x) Q(x) AB(x)) (3.2.19) x (ED(x)) P D(x) Q(x) AB(x) (3.2.20) x (P D(x)) Q(x) AB(x) (3.2.21) x (Q(x)) AB(x) (3.2.22) x (ED(x)) (P ED(x) NP ED(x) AS(x)) (3.2.23) x (P ED(x)) NP ED(x) AS(x) (3.2.24) x (N P ED(x)) AS(x) (3.2.25) x (P D(x)) (EV (x) ST V (x)) (3.2.26) x (EV (x)) ST V (x) (3.2.27) x (Q(x)) (T Q(x) P Q(x) AQ(x)) (3.2.28) x (T Q(x)) P Q(x) AQ(x) (3.2.29) x (P Q(x)) AQ(x) (3.2.30) x (P ED(x)) (M(x) F (x) P OB(x)) (3.2.31) x (M(x)) F (x) P OB(x) (3.2.32) x (F (x)) P OB(x) (3.2.33) Figure 3.10: Axioms outlining the disjointness constraints of T dolce taxonomy.

61 Chapter 3. Verification of DOLCE 48 x (EV (x)) (ACH(x) ACC(x)) (3.2.34) x (ACH(x)) ACC(x) (3.2.35) x (ST V (x)) (ST (x) P RO(x)) (3.2.36) x (ST (x)) P RO(x) (3.2.37) x (R(x)) (T R(x) P R(x) AR(x)) (3.2.38) x (T R(x)) P R(x) AR(x) (3.2.39) x (P R(x)) AR(x) (3.2.40) x (P OB(x)) ((AP O(x) NAP O(x)) (3.2.41) x (AP O(x)) NAP O(x) (3.2.42) x (NP OB(x)) ((MOB(x) SOB(x)) (3.2.43) x (M OB(x)) SOB(x) (3.2.44) x (SOB(x)) ((ASO(x) NASO(x)) (3.2.45) x (ASO(x)) N ASO(x) (3.2.46) x (ASO(x)) ((SAG(x) SC(x)) (3.2.47) x (SAG(x)) SC(x) (3.2.48) Figure 3.11: Axioms outlining the disjointness constraints of T dolce taxonomy.

62 Chapter 3. Verification of DOLCE 49 order to remain consistent with the mereological relations used in COLORE, we utilize the mereological definitions found within the theory of classical mereology (T cm mereology ) in COLORE, but add temporal constraints on the parameters to restrict the relations to time objects found in DOLCE Reduction of T dolce time mereology In our reduction, we hypothesize that the parthood relation P (x, y), when constrained with time intervals T (x) and T (y), is equivalent to the parthood relation in the theory of complete extensional mereology (T cem mereology ) in COLORE. As well, all constructs within this theory are equivalent to time intervals. Theorem T dolce time mereology is definably equivalent to T cem mereology. Proof Let be the set of translation definitions ( x, y) part(x, y) P (x, y) T (x) T (y) ( x) (x = x) T (x) T dolce time mereology = T cem mereology Let Π be the set of translation definitions ( x) T (x) (x = x) ( x, y) P (x, y) part(x, y) T cem mereology Π = T dolce time mereology Using Prover9, we have shown that: T cem mereology Π = T dolce time mereology and T dolce time mereology = T cem mereology Proofs for this theorem can be found in COLORE time_mereology/interprets/output/

63 Chapter 3. Verification of DOLCE 50 ( x y (P (x, y) T (y) T (y))). (3.3.1) ( x y (P (x, y) (T (x) T (y)))). (3.3.2) ( x y (T (x) P (x, x))). (3.3.3) ( x y (T (x) T (y) P (x, y) P (y, x) x = y)). (3.3.4) ( x y z (T (x) T (y) P (x, y) P (y, z) P (x, z))). (3.3.5) ( x y (T (x) T (y) P (x, y) ( z(t (z) P (z, x) O(z, y))))). (3.3.6) ( x y (T (x) T (y) P (x, y) ( z(p (z, x) DJ(z, y) T (z))))). (3.3.7) ( x y (T (x) T (y) (P P (x, y) P (x, y) P (y, x)))). (3.3.8) ( x y (T (x) T (y) (O(x, y) ( z(p (z, x) P (z, y) T (z)))))). (3.3.9) ( x y (T (x) T (y) (DJ(x, y) O(x, y)))). (3.3.10) ( x y (T (x) T (y) (U(x, y) ( z(p (x, z) P (y, z) T (z)))))). (3.3.11) ( x AtP (x) T (x) ( y(t (y) P (y, x) y = x)))). (3.3.12) ( x y (T (x) T (y) U(x, y) ( z (T (z) ( w(t (w) (O(w, z) O(w, x) O(w, y)))))))). (3.3.13) ( x y (T (x) T (y) O(x, y) ( z (T (z) ( w(t (w) (P P (w, z) P P (w, x) P P (w, y)))))))). (3.3.14) ( x y z (T (x) T (y) T (z) (SUM(z, x, y) ( w(t (w) (O(w, z) O(w, x) O(w, y))))))). (3.3.15) Figure 3.12: Axioms of T dolce time mereology.

64 Chapter 3. Verification of DOLCE DOLCE s Mereology (T dolce mereology ) Recall from Chapter 2 that the distinction between endurants and perdurants introduced two kinds of parthood relations: atemporal and time-indexed parthood. Here we consider parthood for entities which do not change in time. Within the T dolce mereology module, we have axioms that assign class restrictions to the arguments found in the binary atemporal parthood relation, P (x, y) (Axioms to 3.4.7). As well, the authors of [51] have indicated that they have adopted the axioms of atomic General Extensional Mereology (GEM), along with the classical definitions of overlap, underlap, disjoint, proper part, and mereological sum (Axioms to Axioms ). Figures 3.13 and 3.14 list all of the axioms found in T dolce mereology ; as well, the axioms can be found in COLORE 18. We note here that verification of this module was not carried out since all of the modules that follow focused primarily on mereologies on time and reused axioms from the T dolce time mereology module. 3.5 A Taxonomy of Lines (T taxonomy ) In the DOLCE taxonomy, there are subclasses and disjoint sets of categories; we took a bottom-up approach in our modularization and paired the categories found in Figure 3.15a with the structures of lines seen in Figure 3.15b. In Figure 3.15a, the abstract category (AB) that contains temporal objects T (x) from Figure 2.1 is not included; this is due to the fact that temporal objects are handled by T dolce time mereology. This taxonomy of lines is used to make distinctions between the various subclasses of lines and its axiomatization in first-order logic is shown in Figure 3.16 and can be accessed in COLORE 19. From this taxonomy, we have three disjoint sets of lines that can 18 mereology/dolce_mereology.clif 19 taxonomy/taxonomy.clif

65 Chapter 3. Verification of DOLCE 52 ( x y (P (x, y) (AB(x) P D(x)) (AB(y) P D(y)))). (3.4.1) ( x y (P (x, y) (P D(x) P D(y)))). (3.4.2) ( x y (P (x, y) (AB(x) AB(y)))). (3.4.3) ( x y (P (x, y) (T R(x) R(x)) (T R(x) T R(y)))). (3.4.4) ( x y (P (x, y) (P R(x) R(x)) (P R(x) P R(y)))). (3.4.5) ( x y (P (x, y) (AR(x) R(x)) (AR(x) AR(y)))). (3.4.6) ( x y (AB(x) P D(x) P (x, x))). (3.4.7) Figure 3.13: Axioms of T dolce mereology. be equated with the classification structure of particulars in DOLCE, which is specified as follows and depicted graphically in Figure 3.15a: ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x)

66 Chapter 3. Verification of DOLCE 53 ( x y (P (x, y) P (y, x) x = y)). (3.4.8) ( x y z (P (x, y) P (y, z) P (x, z))). (3.4.9) ( x y ((AB(x) P D(x)) P (x, y) ( z(p (z, x) O(z, y))))). (3.4.10) ( x y ( P (x, y) ( z(p (z, x) DJ(z, y))))). (3.4.11) ( x y (P P (x, y) P (x, y) P (y, x))). (3.4.12) ( x y (O(x, y) ( z(p (z, x) P (z, y))))). (3.4.13) ( x y (DJ(x, y) O(x, y))). (3.4.14) ( x y (U(x, y) ( z (P (x, z) P (y, z))))). (3.4.15) ( x (AtP (x) ( y (P (y, x) y = x)))). (3.4.16) ( x y (U(x, y) ( z v (O(v, z) O(v, x) O(v, y))))). (3.4.17) ( x y (O(x, y) ( z v (P P (v, z) P P (v, x) P P (v, y))))). (3.4.18) ( x y z (SUM(z, x, y) ( w (T (w) (O(w, z) O(w, x) O(w, y)))))). (3.4.19) Figure 3.14: Axioms of T dolce mereology. DOLCE Categories PT \AB(x) L ED(x) P D(x) Q(x) L 1 L 2 L 3 P ED(x) NP ED(x) (a) A taxonomy of DOLCE categories. L 4 L 5 (b) A taxonomy of lines. Figure 3.15: Corresponding taxonomies of DOLCE categories and lines.

67 Chapter 3. Verification of DOLCE 54 ( x(l 1 (x) L 2 (x)) (3.5.1) ( x) (L 1 (x) L 3 (x)) (3.5.2) ( x) (L 2 (x) L 3 (x)) (3.5.3) ( x) (L 4 (x) L 1 (x)) (3.5.4) ( x) (L 5 (x) L 1 (x)) (3.5.5) ( x) (L 4 (x) L 5 (x)) (3.5.6) Figure 3.16: Axiomatization of T taxonomy, used in our DOLCE modularization. 3.6 Theory of Being Present (T dolce present ) Recall that the concept of being present is modelled by the P RE(x, t) relation, which is read as x is present at time t. As we will see in the axiomatization of this module, there are different ways of being in time: existing in time versus occurring in time, or being wholly present versus being partially present (recall the distinction between endurants and perdurants) Axiomatization of T dolce present In this theory, we have axioms that describe the existence of an endurant ED(x), perdurant P D(x), or a quality Q(x) during a time interval T (x). Axiom outlines how the parthood relation P (x, y) applies to time intervals as well; if an endurant, perdurant, or quality exists during a time interval t, and t 1 is part of t, then it must also exist at t 1. Axiom shows that if an endurant, perdurant, or quality exists at two different time intervals t 1 and t 2, and that the time interval t is the sum of these two intervals, then it must also exist during t. Figure 3.17 lists all of the axioms found in T dolce present ; as well,

68 Chapter 3. Verification of DOLCE 55 ( x) (ED(x) P D(x) Q(x)) ( t) P RE(x, t) (3.6.1) ( x, t, t 1 ) P RE(x, t) P (t 1, t) P RE(x, t 1 ) (3.6.2) ( x, t) P RE(x, t) T (t) (3.6.3) ( x, t, t 1, t 2 ) P RE(x, t 1 ) P RE(x, t 2 ) SUM(t, t 1, t 2 ) P RE(x, t) (3.6.4) Figure 3.17: Axioms of T dolce present. the axioms can be found in COLORE Reduction of T dolce present We hypothesized that the primitive P RE(x, y) relation in DOLCE is equivalent to the incidence relation in(x, y) found in mereology with sort restrictions on its parameters: a point x which is incident on a line y is equivalent to an endurant ED(x), perdurant P D(x), or quality Q(x) that is present during a time interval T (x). Lemma Let be the set of translation definitions ( x, y)in(x, y) ((P RE(x, y) T (y) (ED(x) P D(x) Q(x))) (P RE(y, x) T (x) (ED(y) P D(y) Q(y))) ((x = y) (ED(y) P D(y) Q(y) T (y)))) ( x) line(x) ED(x) P D(x) Q(x) ( x) point(x) T (x) ( x, y) part(x, y) P (x, y) T (x) T (y) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) 20 present/dolce_present.clif

69 Chapter 3. Verification of DOLCE 56 ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce present = T ideal cem wmg T taxonomy Lemma Let Π be the set of translation definitions ( x, y) P RE(x, y) (in(y, x) line(x) point(y)) ( x) T (x) point(x) ( x) ED(x) line(x) L 1 (x) ( x) P D(x) line(x) L 2 (x) ( x) Q(x) line(x) L 3 (x) ( x, y) P (x, y) part(x, y) T ideal cem wmg T taxonomy Π = T dolce present Theorem T dolce present is definably equivalent to T ideal cem wmg T taxonomy. Proof Using Prover9, we have shown that: By Lemma T dolce present interprets T ideal cem wmg T taxonomy. By Lemma 3.6.2, T ideal cem wmg T taxonomy interprets T dolce present. Proofs for this theorem can be found in COLORE Theory of Temporary Parthood (T dolce temporary parthood ) Recall that time-indexed parthood holds for endurants since it is necessary to know when a specific parthood relationship holds [51]. We revisit the two notions of time-indexed 21 present/interprets/output/

70 Chapter 3. Verification of DOLCE 57 parthood as defined in [51], where an endurant can be mereologically constant (endurants remain the same during its entire life: if it gains or loses parts, it ceases to exist), or mereologically invariant (endurants always keep their parts across all possible words, such as amounts of matter) Axiomatization of T dolce temporary parthood In the original DOLCE axioms, the relation for temporary parthood is of the form P (x, y, t), but having the same names for relations of different arities, such as P (x, y) to denote atemporal parthood, causes issues in Prover9 22. Consequently, all temporal relations were renamed by appending a t in front of the relation name to distinguish these temporal relations with their atemporal counterparts. The relation tp (x, y, t) stands for x is part of y during time t, and analogously for temporary overlap to(x, y, t) and temporary proper part tp P (x, y, t). Figure 3.18 lists all of the axioms found in T dolce temporary parthood ; as well, the axioms can be found in COLORE 23. An observation from the temporary parthood axioms is that the relation tp (x, y, t) only affects endurants (Axiom 3.7.1): more specifically, Axiom applies to physical endurants P ED(x), and Axiom applies to non-physical endurants N P ED(x). Perdurants P D(x) and Qualities Q(x) are not affected by these temporary parthood axioms, so the verification tasks for these two DOLCE categories are different from the endurants, as described below Reduction of T dolce temporary parthood Within the theory of temporary parthood in DOLCE, we noticed that the tp (x, y, t) relation only applied to endurants, so the verification tasks were broken down into three 22 Input files in Prover9 cannot have a symbol with multiple arities; for example, having P (x, y) and P (x, y, t) in an input file will return an error because the theorem prover is unable to discern whether these are the same relations or one is a relation and the other is a function temporary_parthood/dolce_temporary_parthood.clif

71 Chapter 3. Verification of DOLCE 58 ( x, y, t) tp (x, y, t) ED(x) ED(y) T (t) (3.7.1) ( x, y, t) tp (x, y, t) (P ED(x) P ED(y)) (3.7.2) ( x, y, t) tp (x, y, t) (NP ED(x) NP ED(y)) (3.7.3) ( x, y, z, t) tp (x, y, t) tp (y, z, t) tp (x, z, t) (3.7.4) ( x, y, z, t) ED(x) ED(y) P RE(x, t) P RE(y, t) tp (x, y, t) ( z) tp (z, x, t) to(z, y, t) (3.7.5) ( x, t) ED(x) P RE(x, t) tp (x, x, t) (3.7.6) ( x, y, t) tp (x, y, t) P RE(x, t) P RE(y, t) (3.7.7) ( x, y, t 1 ) tp (x, y, t 1 ) (( t 2 ) P (t 2, t 1 ) tp (x, y, t 2 )) (3.7.8) ( x, y, t) P RE(x, y, t) P RE(y, t) tp (x, y, t) ( z) tp (x, y, t) tdj(z, y, t) (3.7.9) ( x, y, t) tu(x, y, t) ( z)( v) (to(v, z, t) (to(v, x, t) to(v, y, t))) (3.7.10) ( x, y, t) to(x, y, t) ( z)( v) (tp P (v, z, t) (tp P (v, x, t) tp P (v, y, t))) (3.7.11) Figure 3.18: Axioms of T dolce temporary parthood.

72 Chapter 3. Verification of DOLCE 59 parts: a task to handle physical endurants P ED(x), a task to handle non-physical endurants NP ED(x), and a task to handle both perdurants P D(x) and qualities Q(x). Collectively, P ED(x) and NP ED(x) make up endurants ED(x), but since they are disjoint constructs 24, we were required to create two sets of translation definitions, 1 and 2, to handle these endurant subcategories. The translation definitions for P D(x) and Q(x) are grouped together in 3 because the tp (x, y, t) does not involve either of these constructs. Similar to the reduction of T dolce present, we hypothesized that the primitive P RE(x, y) relation in DOLCE is equivalent to the incidence relation in(x, y) found in mereology with sort restrictions on its parameters: a point x which is incident on a line y is equivalent to either a physical endurant P ED(x), non-physical perdurant N P ED(x), or perdurant P D(x) or quality Q(x) that is present during a time interval T (x). Lemma Let 1 be the set of translation definitions ( x, y) part 1 (x, y) P (x, y) T (x) T (y) ( x, y)(in 1 (x, y) ((P RE(x, y) T (y) P ED(x)) (P RE(y, x) T (x) P ED(y)) ((x = y) (P ED(y) T (y)))) ( x) point 1 (x) T (x) ( x) line 1 (x) P ED(x) ( x, y, z) tpart 1 (x, y, z) tp (x, y, z) P ED(x) P ED(y) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) 24 Recall Axioms to in T dolce taxonomy.

73 Chapter 3. Verification of DOLCE 60 T dolce temporary parthood 1 = T 1 ideal cem downward m foliation T taxonomy Lemma Let 2 be the set of translation definitions ( x, y) part 2 (x, y) P (x, y) T (x) T (y) ( x, y)(in 2 (x, y) ((P RE(x, y) T (y) NP ED(x)) (P RE(y, x) T (x) NP ED(y)) ((x = y) (NP ED(y) T (y)))) ( x) point 2 (x) T (x) ( x) line 2 (x) NP ED(x) ( x, y, z) tpart 2 (x, y, z) tp (x, y, z) NP ED(x) NP ED(y) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce temporary parthood 2 = T 2 ideal cem downward m foliation T taxonomy Lemma Let 3 be the set of translation definitions ( x, y)in 3 (x, y) ((P RE(x, y) T (y) (P D(x) Q(x))) (P RE(y, x) T (x) (P D(y) Q(x))) ((x = y) (P D(y) Q(y) T (y)))) ( x) line 3 (x) (P D(x) Q(x)) ( x) point 3 (x) T (x) ( x, y) part 3 (x, y) P (x, y) T (x) T (y)

74 Chapter 3. Verification of DOLCE 61 ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce temporary parthood 3 = T 3 ideal cem wmg T taxonomy Lemma Let Π be the set of translation definitions ( x, y, z) tp (x, y, z) tpart 1 (x, y, z) tpart 2 (x, y, z) ( x, y) P RE(x, y) ((in 1 (y, x) point 1 (y) line 1 (x)) (in 2 (y, x) point 2 (y) line 2 (x)) (in 3 (y, x) point 3 (y) line 3 (x))) ( x) T (x) point 1 (x) ( x) T (x) point 2 (x) ( x) T (x) point 3 (x) ( x) ED(x) line 1 (x) line 2 (x) ( x) P D(x) line 3 (x) L 2 (x) ( x) Q(x) line 3 (x) L 3 (x) ( x) P ED(x) line 1 (x) ( x) NP ED(x) line 2 (x) ( x, y) P (x, y) part 1 (x, y) ( x, y) P (x, y) part 2 (x, y) ( x, y) P (x, y) part 3 (x, y) ( x) ED(x) L 1 (x) ( x) P ED(x) L 4 (x) ( x) NP ED(x) L 5 (x) T 1 ideal cem downward m foliation T 2 ideal cem downward m foliation T 3 ideal cem wmg T taxonomy Π = T dolce temporary parthood

75 Chapter 3. Verification of DOLCE 62 Theorem T dolce temporary parthood is definably equivalent to T 1 ideal cem downward m foliation T 2 ideal cem downward m foliation T 3 ideal cem wmg T taxonomy Proofs for this theorem can be found in COLORE Theory of Constitution (T dolce constitution ) Recall that the authors of [51] make the distinction that constitution is not considered to be parthood. DOLCE describes the concept of constitution as the co-location of different entities in the same space-time since entities are given incompatible essential properties [51]. For example, a vase is constituted by an amount of clay, but the vase itself is not an amount of clay. The vase and clay are considered to be different things due to their properties: for instance, we say that a vase has a handle, but not that a piece of clay has a handle Axiomatization of T dolce constitution Similar to the axioms of T dolce temporary parthood, the axioms in the theory of constitution only applied to the physical endurants P ED(x), non-physical endurants N P ED(x), and perdurants P D(x); these correspond to Axioms to 3.8.4, respectively. Figure 3.19 lists all of the axioms found in T dolce constitution ; as well, the axioms can be found in COLORE 26. We observed that the constitution axioms require the first two arguments 25 temporary_parthood/interprets/output/ 26 constitution/dolce_constitution.clif

76 Chapter 3. Verification of DOLCE 63 ( x, y, t) K(x, y, t) (ED(x) P D(x)) (ED(y) P D(y)) T (t) (3.8.1) ( x, y, t) K(x, y, t) (P ED(x) P ED(y)) (3.8.2) ( x, y, t) K(x, y, t) (NP ED(x) NP ED(y)) (3.8.3) ( x, y, t) K(x, y, t) (P D(x) P D(y)) (3.8.4) ( x, y, t) K(x, y, t) K(y, x, t) (3.8.5) ( x, y, z, t) K(x, y, t) K(y, z, t) K(x, z, t) (3.8.6) ( x, y, t) K(x, y, t) P RE(x, t) P RE(y, t) (3.8.7) ( x, y, t) K(x, y, t) (( t 2 ) P (t 2, t) K(x, y, t 2 )) (3.8.8) ( x, y, t, y 1 ) K(x, y, t) tp (y 1, y, t) ( x 1 ) tp (x 1, x, t) K(x 1, y 1, t) (3.8.9) Figure 3.19: Axioms of T dolce temporary constitution. to be of the same category; for example, only two non-physical endurants NP ED(x) can constitute each other during a given time interval t. The remainder of the axioms show that constitution is irreflexive, transitive, enforces the existence of the two endurants or perdurants that are being constituted, constitution still holds for subintervals of a time interval, and that temporary parts of an endurant are also constituted (Axioms to 3.8.9, respectively) Reduction of T dolce constitution Within the theory of constitution in DOLCE, we noticed that the K(x, y, t) relation only applied to endurants and perdurants, so the verification tasks were broken down into four parts: a task to handle physical endurants P ED(x), a task to handle non-physical

77 Chapter 3. Verification of DOLCE 64 endurants NP ED(x), a task to handle perdurants P D(x), and a task to handle qualities Q(x). Collectively, P ED(x) and N P ED(x) make up endurants ED(x), but since they are disjoint constructs 27, we created two sets of translation definitions, 1 and 4, to handle these endurant subcategories. The translation definitions for P D(x) can be found in 2, and the translation definitions for Q(x) are in 3. Similar to the reduction of T dolce present, we hypothesized that the primitive P RE(x, y) relation in DOLCE is equivalent to the incidence relation in(x, y) found in mereology with sort restrictions on its parameters: a point x which is incident on a line y is equivalent to either a physical endurant P ED(x), non-physical perdurant N P ED(x), or perdurant P D(x) or quality Q(x) that is present during a time interval T (x). Lemma Let 1 be the set of translation definitions ( x, y) part 1 (x, y) P (x, y) T (x) T (y) ( x, y)(in 1 (x, y) ((P RE(x, y) T (y) P ED(x)) (P RE(y, x) T (x) P ED(y)) ((x = y) (ED(y) T (y)))) ( x) point 1 (x) T (x) ( x) line 1 (x) P ED(x) ( x, y, z) tpart 1 (x, y, z) tp (x, y, z) P ED(x) P ED(y) T (z) ( x, y, z) tppart 1 (x, y, z) tp (x, y, z) (x y) P ED(x) P ED(y) T (z) ( x, y, z) tlt 1 (x, y, z) K(x, y, z) P ED(x) P ED(y) T (z) ( x, y, z)tleq 1 (x, y, z) (K(x, y, z) (P RE(x, z) (x = y))) P ED(x) P ED(y) T (z) ( x) poset element 1 (x) P ED(x) ( x) mereo element 1 (x) P D(x) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) 27 Recall Axioms to in T dolce taxonomy ).

78 Chapter 3. Verification of DOLCE 65 ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce constitution 1 = T 1 ideal cem lower reflect down foliation T taxonomy Lemma Let 2 be the set of translation definitions ( x, y) part 2 (x, y) P (x, y) T (x) T (y) ( x, y)(in 2 (x, y) ((P RE(x, y) T (y) P D(x)) (P RE(y, x) T (x) P D(y)) ((x = y) (P D(y) T (y))) ( x) point 2 (x) T (x) ( x) line 2 (x) P D(x) ( x, y, z) tpart 2 (x, y, z) (K(x, y, z) (P RE(x, z) (x = y))) P D(x) P D(y) T (z) ( x, y, z) tppart 2 (x, y, z) K(x, y, z) P D(x) P D(y) T (z) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce constitution 2 = T 2 ideal cem downward m foliation T taxonomy Lemma Let 3 be the set of translation definitions ( x, y)(in 3 (x, y) ((P RE(x, y) T (y) Q(x)) (P RE(y, x) T (x) Q(y)) ((x = y) (Q(y) T (y))))) ( x) line 3 (x) Q(x)

79 Chapter 3. Verification of DOLCE 66 ( x) point 3 (x) T (x) ( x, y) part 3 (x, y) P (x, y) T (x) T (y) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x) T dolce constitution 3 = T 3 ideal cem wmg T taxonomy Lemma Let 4 be the set of translation definitions ( x, y) part 4 (x, y) P (x, y) T (x) T (y) ( x, y)(in 4 (x, y) ((P RE(x, y) T (y) NP ED(x)) (P RE(y, x) T (x) NP ED(y)) ((x = y) (NP ED(y) T (y)))) ( x) point 4 (x) T (x) ( x) line 4 (x) NP ED(x) ( x, y, z) tpart 4 (x, y, z) tp (x, y, z) NP ED(x) NP ED(y) T (z) ( x, y, z) tppart 4 (x, y, z) tp (x, y, z) (x y) NP ED(x) NP ED(y) T (z) ( x, y, z) tlt 4 (x, y, z) K(x, y, z) NP ED(x) NP ED(y) T (z) ( x, y, z)tleq 4 (x, y, z) (K(x, y, z) (P RE(x, z) (x = y))) NP ED(x) NP ED(y) T (z) ( x) poset element 4 (x) NP ED(x) ( x) mereo element 4 (x) P D(x) ( x) L 1 (x) ED(x) ( x) L 2 (x) P D(x) ( x) L 3 (x) Q(x) ( x) L 4 (x) P ED(x) ( x) L 5 (x) NP ED(x)

80 Chapter 3. Verification of DOLCE 67 T dolce constitution 4 = T 4 ideal cem lower reflect down foliation Lemma Let Π be the set of translation definitions ( x, y, z) K(x, y, z) (tlt 1 (x, y, z) tlt 4 (x, y, t) tppart 2 (x, y, t)) ( x, y, z) tp (x, y, z) (tpart 1 (x, y, z) tpart 4 (x, y, z)) ( x, y) P RE(x, y) (in 1 (y, x) point 1 (y) line 1 (x)) (in 2 (y, x) point 2 (y) line 2 (x)) (in 3 (y, x) point 3 (y) line 3 (x)) (in 4 (y, x) point 4 (y) line 4 (x)) ( x, y) P (x, y) part 1 (x, y) ( x, y) P (x, y) part 2 (x, y) ( x, y) P (x, y) part 3 (x, y) ( x, y) P (x, y) part 4 (x, y) ( x) P ED(x) poset element 1 (x) ( x) NP ED(x) poset element 4 (x) ( x) P D(x) mereo element 1 (x) ( x) P D(x) mereo element 4 (x) ( x) T (x) point 1 (x) ( x) T (x) point 2 (x) ( x) T (x) point 3 (x) ( x) T (x) point 4 (x) ( x) ED(x) line 1 (x) line 4 (x) ( x) P ED(x) line 1 (x) ( x) NP ED(x) line 4 (x) ( x) P D(x) line 2 (x) ( x) Q(x) line 3 (x) ( x) ED(x) L 1 (x) ( x) P D(x) L 2 (x) ( x) Q(x) L 3 (x) ( x) P ED(x) L 4 (x) ( x) NP ED(x) L 5 (x)

81 Chapter 3. Verification of DOLCE 68 T 1 ideal cem lower reflect down foliation T 4 ideal cem lower reflect down foliation T 2 ideal cem downward m foliation T 3 ideal cem wmg T taxonomy Π = T dolce constitution Theorem T dolce constitution is definably equivalent to T 1 ideal cem lower reflect down foliation T 2 ideal cem downward m foliation T 3 ideal cem wmg T 4 ideal cem lower reflect down foliation Proofs for this theorem can be found in COLORE Summary of DOLCE Modules From what we have seen in this chapter, our modularization makes distinctions between endurants and perdurants, especially in the T dolce temporary parthood and T dolce constitution modules. We have provided the axioms of each module in first-order logic and in CLIF, and have utilized the modularization technique presented in [29]. From our modularization, the following observations have been made: Our modularization of DOLCE is coarser-grained than the modules presented in [48]. Every module in our modularization is a module of DOLCE. Every module in [48] is a module of the modules we have presented in this work. We divided the reduction for each module based on whether or not the axioms involved endurants or perdurants while preserving the taxonomic structure found in the original DOLCE axioms constitution/interprets/output/

82 Chapter 4 Ontology Composition: Interpretations Between DOLCE & COLORE Recall from the previous chapter that DOLCE is built up of modules shown in Figure 3.2. In this chapter, we examine how T dolce participation and T dolce present can be mapped with T psl core and other mathematical theories found in COLORE, and discuss the steps needed to bridge these theories together. As discussed in Chapter 2, the process of verification involves finding all possible models of a given ontology. This means that we map the DOLCE ontology with mathematical theories found in COLORE. In the introductory section of this thesis, we had discussed our motivations and interest in examining how DOLCE is related to other ontologies; DOLCE is known as an ontology of endurants and perdurants, but we can also say that it is an ontology of processes and objects. Thus, we were curious in examining how DOLCE is related to other ontologies that describe processes and objects. Current process ontologies include the Suggested Upper Merged Ontology (SUMO), OpenCyc, Basic Formal Ontology (BFO), and PSL; we had considered analyzing the first three 69

83 Chapter 4. Interpretations Between DOLCE & COLORE 70 ontologies, but due to the large number of axioms found in these ontologies 1 and different logic languages in which they are written 2, we opted to analyze an ontology of comparable size that was already defined in first-order logic. Due to prior familiarity with PSL and that it is already available in COLORE, we opted to use PSL to identify any relationships it may have with DOLCE, and whether DOLCE makes additional ontological commitments with these process-related concepts and to analyze the relationship between them. 4.1 Relationship with PSL and COLORE Theories From what we have seen with DOLCE, time intervals are used to describe temporal objects in T dolce temporary parthood, T dolce constitution, and T dolce present, all of which contain T dolce time mereology. DOLCE does not contain an ordering on time, but has a time mereology. In contrast, the PSL ontology uses timepoints to describe the temporal aspects of objects and activity occurrences, as well as uses an ordering on time, but does not contain a time mereology. From this observation, both ontologies appear to have intuitions of perdurants/endurants and activity occurrences/objects being present and participating in some time construct. We explore these intuitions further by bridging these two ontologies together. We note that T dolce participation contains the following axiom (Ad35 in [51]) which indicates every endurant participates in some perdurant at a given time object: x ED(x) (x, t) P C(y, x, t) A similar axiom is found in T psl core that indicates activity occurrences require an object to participate in them. From these observations, we hypothesized that perdurants and 1 As of writing, SUMO contains approximately 25,000 terms and 80,000 axioms [2], OpenCyc contains approximately 239,000 terms [18], whereas BFO is smaller in size [58]. 2 SUMO, OpenCyc, and BFO are axiomatized in SUO-KIF, Lisp, and OWL, respectively.

84 Chapter 4. Interpretations Between DOLCE & COLORE 71 endurants from DOLCE are equivalent to activity occurrences and objects in PSL, respectively. We can say that the notion of participation P C(x, y, z) in DOLCE is equivalent to the participates in(x, y, t) in PSL: for any object x, activity occurrence y, and time interval z, there exists a time construct t that is equivalent to the time interval z, where x participates in y during t. We write these equivalences as the following translation definitions: x P D(x) activity occurrence(x) (4.1.1) x ED(x) object(x) (4.1.2) x T (x) timeinterval(x) (4.1.3) x y z t (P C(x, y, z) object(x) activity occurrence(y) timeinterval(z) (bef oreeq(beginof(z), t) bef oreeq(t, endof(z)) participates in(x, y, t))). (4.1.4) Based on these equivalences, we realized that there was a need to create new theories that combine and utilize timepoints and time intervals with the PSL ontology. In order to identify a concrete relationship between the two ontologies, we hypothesized that if we added a mereology of time intervals to PSL, or added an ordering to DOLCE, we would be able to determine whether theories from DOLCE could faithfully interpret theories found in PSL. Since PSL has a mereology and ordering on timepoints, but DOLCE only has a mereology on time intervals, we could not say that the theories between these ontologies are definably equivalent. In order to examine this interpretation of theories, a time ontology that contained both timepoints and time intervals was required in order to be strong enough to interpret a mereology on timepoints and time intervals. COLORE contains numerous mathematical theories that aided us in this regard: the Combined Time hierarchy, H combined time, in COLORE contains time theories utilize both timepoint

85 Chapter 4. Interpretations Between DOLCE & COLORE 72 and time interval constructs, and are able to interpret a mereology on timepoints and time intervals. Figure 4.1 illustrates how we bridged the PSL and DOLCE ontologies together, but we will first discuss the temporaly hierarchies in more detail below. interval mandatory dolce constitution dolce temporary parthood dolce participation interval psl core Interval PSL Hierarchy mandatory psl core psl core root PSL Hierarchy dolce dependence dolce present endpoints interval with endpoints dolce mereology dolce time mereology sim vc end finite sim vc end DOLCE Hierarchies dolce taxonomy finite periods Combined Time Hierarchy cem periods periods linear point lp infinite end Periods Hierarchy periods root lp ordering Timepoints Hierarchy Figure 4.1: Relationships between DOLCE modules and theories in COLORE. Solid lines indicate conservative extensions, dashed lines indicate non-conservative extensions, and the bolded dash-dot-dotted lines indicate faithful interpretations between theories. 4.2 Temporal Theories in COLORE Existing temporal theories found in COLORE were utilized to analyze the interpretations between the DOLCE and COLORE theories in this chapter. Here we briefly outline the timepoint and time interval theories used. We make a note here regarding the convexity of

86 Chapter 4. Interpretations Between DOLCE & COLORE 73 time intervals in DOLCE. Intuitively, convex intervals are those which have no gaps [49] 3. The convexity of time intervals requires an ordering over time intervals and a mereology. However, we reiterate that DOLCE only has a mereology over its time intervals, so it cannot define convexity The Timepoints Hierarchy (H timepoints ) Within this hierarchy are theories that describe time in terms of timepoints. We were interested in the in the weakest theory of this hierarchy, T linear point, since it is used by T endpoints which is described in Section 4.2.3, and T lp infinite end. The linear point theory, T 4 linear point, derived from axioms found in [35], is a simple ontology representing timepoints on a line. It contains a binary relation, bef ore(x, y), that is transitive and irreflexive, and axioms that state that timepoints infinitely extend a timeline in both forward and backward directions. The linear timepoints with endpoints at infinity theory, T 5 lp infinite end, derived from axioms found in [35], is a simple ontology representing timepoints on a line. It contains axioms that infinitely extend a timeline in both forward and backward directions, and that there exist endpoints at infinity in both directions The Periods Hierarchy (H periods ) The axioms for the periods hierarchy, H periods, were provided in [62]; additional information about other theories in this hierarchy can be found in [29]. We were interested in the in the weakest theory of this hierarchy, T periods, since it is used by T endpoints, which is described in Section Additional information about the various relations found in convex and non-convex intervals can be found in [49] and [45]. 4 timepoints/linear_point.clif 5 timepoints/lp_infinite_end.clif

87 Chapter 4. Interpretations Between DOLCE & COLORE 74 The Minimal Theory of Periods, T periods, constitutes the minimal set of conditions that must be met by any period structure [62]. It contains two relations, precedence(x, y) and inclusion(x, y), and two conservative definitions, glb(x, y, z) and overlaps(x, y), as its non-logical lexicon. Every element in the domain is considered a time interval, and there are transitivity and irreflexivity axioms for the precedence(x, y) relation, making it a strict partial order; similarly, the transitivity, reflexivity, and anti-symmetry axioms for the inclusion(x, y) relation make it a partial order. As well, the axiom, glb(x, y, z), guarantees the existence of greatest lower bounds between overlapping intervals defined by overlaps(x, y) The Combined Time Hierarchy (H combined time ) Hybrid-time theories are those that include both timepoints and time intervals as primitives, and define a set of functions and relations specifying the interactions between them. These time theories in COLORE are derived from the time ontologies presented in [35], and have been modified and verified in [32]; Figure 4.2 below shows the relationships between all of the theories in this hierarchy. Depending on the relations and functions used, these theories can represent time in very different ways. For example, the theory of endpoints, T endpoints, defines timepoints only as the boundary of time intervals, where every interval is associated with exactly two timepoints: the begin of and end of the interval. In contrast, the theory of timepoint continuum, T point continuum, defines intervals by the set of adjacent timepoints in which they are contained; another theory, T vector continuum introduces the concept of directionality by allowing backward intervals where the end of point is before the begin of point in the timeline. With such varied models for each hybrid-time theory, we briefly discuss them individually below, and refer the reader to [32] and COLORE 6 for the axiomatizations of these theories. 6 time/

88 Chapter 4. Interpretations Between DOLCE & COLORE 75 linear_point lp_ordering lp_infinite_end moment_with_endpoints interval_with_endpoints endpoints mo_endpoints mo_continuum vectorcontinuum no_backwards no_moment moment sim_vc_end finite_endpoints finite_mo_endpoints finite_mo_continuum finite_vc finite_no_backwards finite_no_moment finite_moment finite_backwards finite_sim_vc_end backwards Figure 4.2: Relationships between theories found in the Combined Time hierarchy, H combined time. Solid lines indicate conservative extensions and dashed lines indicate nonconservative extensions.

89 Chapter 4. Interpretations Between DOLCE & COLORE 76 The theory of endpoints, T 7 endpoints, combines the language of intervals and points by defining the beginof, endof, and between functions to relate intervals to timepoints and vice-versa. From Figure 4.2, we see that this theory imports axioms from T linear point that define a binary bef ore(x, y) relation between timepoints as transitive and irreflexive, and asserts that all timepoints are linearly ordered and infinite in both directions. As well, this theory includes axioms that define the meets at(i, x, j) relation as one between two intervals and the point at which they meet along, restrict beginof(i) to always come before the endof(i) function, and states that intervals are between two points if they are properly ordered. The vector continuum theory, T 8 vector continuum, introduces the notion of orientation of intervals, and also imports T linear point. It contains the same three functions (beginof(i), endof(i), and between(x, y)) that transform intervals into timepoints and vice-versa, but differs in its definition of between(x, y) by allowing the formation of intervals whose endof point is equal to or before its beginof. Thus, every interval in T vector continuum has a reflection in the opposite direction via the back(i) function; intervals oriented in the forward direction are defined normally where beginof(i) is before endof(i). As well, single-point intervals, known as moments, are defined as intervals whose beginof(i) and endof(i) points are the same. In this work, we utilized the theory of similarity of vector continuums T 9 sim vc end. Similar to T vector continuum, this theory contains axioms that define the notion of orientation of intervals, but also contains an axiom that describes the notion of similarity, as adopted from [32]: Definition Let T 1 and T 2 be theories with the language L. The similarity of T 1 and T 2 is the strongest subtheory of T 1 and T 2, so that for all σ, φ L if T 1 = σ and 7 time/endpoints.clif 8 time/vector_continuum.clif 9 time/sim_vc_end.clif

90 Chapter 4. Interpretations Between DOLCE & COLORE 77 T 2 = φ, and T = σ and T = φ, then either σ φ is independent of T or it is a tautology. This theory is used to examine the relationships between T endpoints and T vector continuum since both theories have the same primitive non-logical lexicon, and can be compared using the notions of satisfiability, extension, and independence [32] Composing the Theory of Intervals with Endpoints (T interval with endpoints ) The Combined Time hierarchy contains theories that relate timepoints and time intervals together. These theories were originally proposed by Pat Hayes in [35], and assume an import of the T endpoints theory, where every time interval is associated with two timepoints. However, since T psl core contains a timepoint ontology that contains a linear ordering with endpoints at infinity 10, the theory becomes inconsistent with T endpoints since time intervals cannot be described with this temporal theory. Consequently, we needed to remove the time ontology from T psl core and specify a new time theory, T interval with endpoints, to make T psl core compatible with time intervals. In H combined time, we created T interval with endpoints to contain the time interval axioms of T endpoints with a different timepoint ontology. This new Intervals with Endpoints theory, T interval with endpoints, imports axioms from T finite sim vc end from H combined time and T lp infinite end from H timepoints. The primary difference between the T finite sim vc end and T sim vc end theories within H combined time is that different timepoint ontologies are used in each theory; while both theories have a common theory, T lp ordering, additional axioms in T linear point make T sim vc end different from T finite sim vc end, as depicted in Figure 4.1. Consequently, T interval with endpoints non-conservatively extends T finite sim vc end since it contains the same time interval axioms as T finite sim vc end, but different timepoint axioms from T lp infinite end. The axioms of T interval with endpoints can be found in COLORE Refer to Axioms A.1.6 to A.1.9 in Appendix A time/interval_with_endpoints.clif

91 Chapter 4. Interpretations Between DOLCE & COLORE 78 The DOLCE ontology has no ordering on time intervals, but a mereology; combined time theories have an explicit ordering over time intervals and a mereology can be defined on them. The Periods hierarchy bridges DOLCE and combined time hierarchies together since T periods is the common theory between them. We note that the dash-dot-dotted arrows in Figure 4.1 outline the faithful interpretations between H dolce and H periods, and H periods and H combined time ; however, these are faithful interpretations are proposed and proofs have not been carried out 12. We only discuss the composition of theories needed to prove the faithful interpretations between DOLCE and PSL. 4.3 Extending T psl core Within PSL, activity occurrences are considered to be occurrents, while objects are represented by continuants [22]. The relation participates in(x, o, t) is used to specify that an object x participates in activity occurrence o at timepoint t. Since DOLCE does not utilize timepoints but time intervals in its time mereology, an extension of T 13 psl core was created in order to utilize the participates in(x, o, t) relation with time intervals Theory of PSL-Core Root (T psl core root ) Furthermore, a subset of the axioms in T psl core were extracted to create the T psl core root theory. The following closure axiom from T psl core was removed because it was too strong and contained the timepoint(x) construct: ( x (activity(x) activity occurrence(x) timepoint(x) object(x))). This theory is later used in the Interval PSL hierarchy (H interval psl ), which is described in the next section. 12 These will be addressed in future work. 13 We could not modify the axioms found in T psl core since the axioms are standardized in ISO :2005.

92 Chapter 4. Interpretations Between DOLCE & COLORE 79 ( x (object(x) ( o t participates in(x, o, t)))). (4.3.1) ( o t (activity occurrence(o) is occurring at(o, t) ( x participates in(x, o, t)))). (4.3.2) Figure 4.3: Axioms found in T mandatory Theory of Mandatory Participation (T mandatory ) We defined a new non-conservative extension of T psl core called T mandatory to take into account the mandatory participation of PSL objects in a temporal construct. In this extension, we did not commit to a specific temporal object, so t may be timepoints or time intervals. The axioms found in this extension import T psl core root and do not include the between(x, y, z) and before(x, y, z) relations found in T psl core since they involve the usage of timepoints, not time intervals, to describe the participation of objects in activity occurrences and time objects. Figure 4.3 lists all of the axioms found in T mandatory, and the axioms can be found in COLORE 14. Axiom indicates that every object x has to participate in some activity occurrence o at a time object t, and Axiom indicates that, for every activity occurrence o that occurs during the time object t, there exists an object that also participates in that time object. mandatory psl core psl core root PSL Hierarchy Figure 4.4: Relationships between theories found in the PSL hierarchy. Solid arrows denote conservative extensions and dashed arrows denote non-conservative extensions mandatory.clif

93 Chapter 4. Interpretations Between DOLCE & COLORE 80 In T mandatory, we did not commit to a specific type of temporal object for object participation, but we did note that there needs to be a bridge of sorts to connect the DOLCE and PSL ontologies together. Consequently, we were interested in creating a new bridge ontology that contains the PSL constructs that are used with time intervals. We discuss this new H interval psl hierarchy in the next section. 4.4 The Interval PSL Hierarchy (H interval psl ) Since the PSL ontology only describes object and activity occurrences with respect to timepoints, we needed to create a time interval version of the PSL ontology. A new hierarchy, H interval psl, was created in COLORE with T interval psl core as its root theory. This hierarchy contains the time interval versions of the T psl core and T mandatory theories which are named T interval psl core and T interval mandatory, respectively, and are depicted in Figure 4.7. Each of these theories is briefly described below, and can be found in COLORE Theory of PSL-Core with Intervals (T interval psl core ) This theory imports axioms from T psl core root and T interval with endpoints. In order to ensure that the time interval version of T psl core root contains axioms that describe time intervals, and not timepoints T interval with endpoints is used to describe the time objects found in this compiled theory. Three axioms are added to T interval psl core in addition to the imported theories and are outlined in Figure 4.5. Axiom indicates that a time interval is not an activity, activity occurrence, object, or timepoint. In Axiom 4.4.2, the relation, psl interval(x, y), is introduced to relate a time interval with the begin of and end of an activity occurrence or object. Finally, the overlay(x, y, z) relation is introduced in Axiom to describe 15 psl

94 Chapter 4. Interpretations Between DOLCE & COLORE 81 ( x (timeinterval(x) (activity(x) activity occurrence(x) timepoint(x) object(x)))). (4.4.1) ( x y (psl interval(x, y) (activity occurrence(x) object(x)) timeinterval(y) beginof(x) = beginof(y) endof(x) = endof(y))). (4.4.2) ( x y z (overlay(x, y, z) ( i 1 i 2 (psl interval(x, i 1 ) psl interval(y, i 2 ) beginof(i 2 ) = beginof(z) endof(i 1 ) = endof(z))))). (4.4.3) Figure 4.5: Axioms of T interval psl core. a time interval z that overlays 16 activity occurrences x and y. However, it may not necessarily be the case that both activity occurrence/object y overlays an activity occurrence/object x, or vice versa. This axiom is included in case such overlaying of intervals does occur. Figure 4.6 graphically depicts this relationship between two overlaying time intervals. x i 1 y i 2 z Figure 4.6: Graphical depiction of the overlay(x, y, z) relation. 16 We chose not to use the terms overlap and intersect because they are used in mereology ontologies. To be consistent with PSL, we decided to use the term overlay to describe the relationship where time intervals may overlay one another.

95 Chapter 4. Interpretations Between DOLCE & COLORE Theory of Mandatory Intervals (T interval mandatory ) Finally, we have the theory of mandatory intervals which imports axioms from T interval psl core and T mandatory. Since we would like to show that T dolce participation can faithfully interpret the time interval versions of PSL theories from T interval psl core, we extended T interval psl core to include the time interval versions of the axioms from T mandatory. No additional axioms are included in this theory and it can be found in COLORE 17. Essentially this theory assigns time intervals 18 to T interval psl core to indicate the mandatory participation of PSL over a time interval. Figure 4.7 summarizes the relationships between the Interval PSL, PSL, and Combined Time hierarchies. 4.5 Interpretations Between DOLCE and Theories in COLORE In order to determine whether DOLCE theories are able to faithfully interpret the theories in COLORE, we needed to modify T dolce present. To preserve the original DOLCE axioms, a copy of T dolce present was created with all references of qualities Q(x) removed and this new theory was named as T dolce present. This is due to the fact that T psl core root is unable to define what a quality is due to the following translation definitions used in our verification: x ED(x) object(x) x Q(x) object(x) Since T psl core root is unable to discern which object(x) is an endurant ED(x) or a quality Q(x), it was necessary to create a subtheory of T dolce present that did not include qualities for this portion of the interpretation. The axioms of T dolce present can be found in Ap psl/interval_mandatory.clif 18 Recall that we did not commit to a particular temporal construct in T mandatory.

96 Chapter 4. Interpretations Between DOLCE & COLORE 83 Interval PSL Hierarchy interval mandatory interval psl core mandatory psl core psl core root PSL Hierarchy interval with endpoints finite sim vc end Combined Time Hierarchy Figure 4.7: Relationships between the Interval PSL, PSL, and Combined Time hierarchies. Solid lines indicate conservative extensions and dashed lines indicate nonconservative extensions between theories.

97 Chapter 4. Interpretations Between DOLCE & COLORE 84 pendix B.2.1 and in COLORE 19. This creation of T dolce present does not affect any of the modules verified in the previous chapter since the modularization of DOLCE includes the quality axioms. The DOLCE theories for T dolce participation and T dolce time mereology are able to interpret the T interval mandatory and T interval psl core theories in H interval psl, respectively. Figure 4.8 illustrates these graphically, where 1 and 2 are interpretations from the DOLCE theories to the Interval PSL theories. We discuss each interpretation below. Interval PSL Hierarchy dolce participation 2 interval mandatory dolce present dolce present* 1 interval psl core dolce time mereology dolce taxonomy DOLCE Hierarchy Figure 4.8: Interpretations between DOLCE modules and theories in COLORE. Solid lines indicate conservative extensions, dashed lines indicate non-conservative extensions, and the bolded dash-dot-dotted lines indicate faithful interpretations between theories Interpretations Between T interval psl core and T dolce present From our brief discussion of the theories found in COLORE, we make the observation that the concept of parthood in DOLCE is equivalent to the inclusion of time intervals 19 present/dolce_present_star.clif

98 Chapter 4. Interpretations Between DOLCE & COLORE 85 in T interval psl core : ( t 1 t 2 (P (t 1, t 2 ) timeinterval(t 1 ) timeinterval(t 2 ) beforeeq(beginof(t 2 ), beginof(t 1 )) beforeeq(endof(t 1 ), endof(t 2 )))). (4.5.1) We graphically depict this relationship in Figure 4.9; the time interval t 1 is part of time interval t 2 : the beginning of t 2 can either be before or equal to the beginning of t 1, and the end of t 1 can either be before or equal to the end of t 2. t 2 t 1 Figure 4.9: Graphical depiction of the P (x, y) translation definition for T interval psl core and T dolce present. Furthermore, we can state that the concept of being present in DOLCE is equivalent to the concept of an object or activity occurrence that exists in a given time interval, where the beginning of the time interval is the timepoint in which an object or activity occurrence starts, and that the end of the time interval is the timepoint in which the object or activity occurrence ends. ( x y t (P RE(x, t) (object(x) activity occurrence(x)) timeinterval(t) bef oreeq(beginof(x), beginof(t)) bef oreeq(endof(t), endof(x)))). (4.5.2) We note that, in psl interval(x, y), an unique maximal time interval is associated with an object or activity occurrence in PSL. On the other hand, the time interval associated in P RE(x, t) in DOLCE needs not be the maximal interval at which an endurant or perdurant is present. Thus, we define that a time interval z is the sum of the time

99 Chapter 4. Interpretations Between DOLCE & COLORE 86 intervals of two activity occurrences x and y as follows: x y z(su M(z, x, y) (timeinterval(x) timeinterval(y) timeinterval(z) (((beginof(z) = beginof(x)) (endof(z) = endof(y))) ((beginof(z) = beginof(y)) (endof(z) = endof(x)))))). (4.5.3) Consequently, the translation definition for SUM(z, x, y) reflects the idea that the sum of two time intervals in DOLCE can be the minimal sum or the maximal sum, as depicted in Figure x i 1 y i 2 z minimal sum of intervals z maximal sum of intervals Figure 4.10: Graphical depiction of the SU M(z, x, y) translation definition. Theorem T interval psl core interprets T dolce present. Proof Let 1 be the set of translation definitions x((ed(x) object(x))). x((q(x) object(x))). x((p D(x) activity occurrence(x))). x((t (x) timeinterval(x))). t 1 t 2 ((P (t 1, t 2 ) timeinterval(t 1 ) timeinterval(t 2 ) beforeeq(beginof(t 2 ), beginof(t 1 )) beforeeq(endof(t 1 ), endof(t 2 )))). x y t(p RE(x, t) ((object(x) activity occurrence(x))

100 Chapter 4. Interpretations Between DOLCE & COLORE 87 timeinterval(t) bef oreeq(beginof(x), beginof(t)) beforeeq(endof(t), endof(x)))). x y z(su M(z, x, y) (timeinterval(x) timeinterval(y) timeinterval(z) (((beginof(z) = beginof(x)) (endof(z) = endof(y))) ((beginof(z) = beginof(y)) (endof(z) = endof(x)))))). T interval psl core 1 = T dolce present Thus, we can say that T interval psl core faithfully interprets T dolce present. The proofs for these experiments can be found in COLORE Interpretations Between T interval mandatory and T dolce participation For the interpretation of T interval mandatory and T dolce participation, we reuse the set of translation definitions, 1, from the previous section, along with the additional translation definition described below. 1 is reused because T interval mandatory imports T interval psl core, so 1 is used in conjunction with 2. Since the DOLCE ontology contains axioms for participation 21, we make the observation that the participation relation, P C(x, y, z), is similar to the participates in(x, y, t) relation found in PSL. Thus, we can state that any x and y that participate in z in DOLCE is equivalent an object x that participates in an activity occurrence y in a given time interval z and, at every timepoint in that interval, x participates in y. ( x y z t (P C(x, y, z) 20 dolce_present/interprets/output 21 Recall that our verification of DOLCE is a partial modularization of the ontology. The modules of our verification were presented in Chapter 3, but we did not include T dolce participation, so it will be verified in future work.

101 Chapter 4. Interpretations Between DOLCE & COLORE 88 object(x) activity occurrence(y) timeinterval(z) (bef oreeq(beginof(z), t) bef oreeq(t, endof(z)) participates in(x, y, t)))). (4.5.4) Theorem T interval mandatory interprets T dolce participation. Proof Let 2 be the set of translation definitions x y z t((p C(x, y, z) object(x) activity occurrence(x) timeinterval(z) bef oreeq(beginof(z), t) bef oreeq(t, endof(z)) participates in(x, y, t)))). T interval mandatory 1 2 = T dolce participation Thus, we can say that T interval mandatory faithfully interprets T dolce participation. The proofs for these experiments can be found in COLORE Insights Faithful interpretations between the DOLCE and COLORE theories in this chapter have shown that there multiple bridges were needed before any analyses with the T dolce participation and T dolce present theories could be carried out with theories in COLORE. Firstly, we saw that the Combined Time hierarchy bridges the Periods and Timepoints hierarchies together to have ontologies of time that contain both timepoints and time intervals. Secondly, the Interval PSL hierarchy bridges both the PSL and DOLCE hierarchies together to allow the faithful interpretations of mereology and orderings in both timepoints and time intervals. This exercise in bridging ontologies together proves to be rewarding since it demonstrates how we can axiomatize the relationships between theories and outline the composition of theories that are required for the bridging task dolce_participation/interprets/output

102 Chapter 5 Semantic Augmentation: The CIMOSA Process Ontology In this chapter, we outline a case study where semantic augmentation is required to provide an ontology with semantics. With Enterprise Modelling (EM) formalisms, there currently do not exist ontologies that explicitly define the terms utilized in their syntactic constructs. An ontology is a formal specification of the knowledge, concepts, and relationships found within a domain. Without such specifications in EM languages, it makes it difficult for users of the language to understand how the constructs can be used. With an explicit definition of these terms, users and software applications will then be able to use the constructs correctly and appropriately. 5.1 Background & Motivation Enterprises & Ontologies During the mid 1990s, enterprise modelling (EM), enterprise engineering (EE), and enterprise integration (EI) had become a focal point in the manufacturing industry. The overall goal of enterprise modelling is to better understand, represent, and design enter- 89

103 Chapter 5. The CIMOSA Process Ontology 90 prise operations [63], and is considered the first step to achieving enterprise integration. Enterprise engineering, on the other hand, is concerned with (re)designing business entities that are involved in an enterprise s lifecycle to optimize the cost, time, and resource aspects of the enterprise [63]. Finally, the goal of enterprise integration is to break down any organizational barriers within the enterprise, such as humans, machines, and applications, to facilitate improved communication, co-operation, and co-ordination [63, 61]. Consequently, the interest in these three aspects of enterprises has led the way for enterprise ontologies to be introduced and applied in practice. An enterprise ontology is a collection of terms and definitions that are relevant to business enterprises [61]. Intended to be sets of terms and definitions that adequately and correctly covers concepts found in the enterprise domain, the Edinburgh Enterprise and TOronto Virtual Enterprise (TOVE) ontologies described in [61] and [31], respectively, are intended to resolve any misunderstandings where terms are used differently. Acting as a communication medium between people and computational system, the Edinburgh Enterprise Ontology (EEO) assists users with the representation of basic and core enterprise concepts, along with structuring and organizing libraries of knowledge [61]. As such, it outlines five different classes for describing the various aspects of an enterprise (Activities and Processes, Organization, Strategy, Marketing, and Time). Activities and Processes consist of the activities and resources in the enterprise, while the Organization class covers the organizational constraints for the enterprise. Similarly, the Strategy class contains all of the goals, policies, and relationships to the activities performed by the enterprise and its agents. The Marketing class covers the external relationships between the enterprise, its customers, suppliers, and partners. The EEO does not, however, cover nor describe an enterprise s products and services in detail. The TOVE project is an integrated suite of ontologies that is designed to provided a shared terminology for the enterprise that can be jointly understood and used by applications [17, 31]. The suite is divided into three groups: Core, Derivative, and Enterprise

104 Chapter 5. The CIMOSA Process Ontology 91 ontologies. The Core ontologies capture the generic characteristics of an enterprise, while the Derivative ontologies are specializations of classes found in the Core category. From there, the Enterprise ontologies are used to define classes of enterprises through the identification of classes of processes, resources, products, services, and organization constraints found in enterprises. With this in mind, ontologies for enterprise modelling formalisms have not been established to alleviate any of the previously discussed communication barriers. We have chosen to study and develop a process ontology the CIMOSA framework, which will be further discussed in Section 5.2. The Process Specification Language (PSL) Since we have already described PSL in Section 2.1.5, we remind the reader that PSL contains axioms that have been well-defined and standardized in ISO :2004, so it was appropriate to utilize this ontology to semantically augment CIMOSA concepts. IAOA s Standardization Coordination Efforts Within the International Association of Ontology and its Applications (IAOA), the Standardization Coordination Committee fosters the harmonization between the ontology and standards communities. As well, the committee works with the Ontology Integration and Interoperability (OntoIOp) group to facilitate the application of ontologies and ontological analysis to existing and emerging standards. Currently, the committee is looking into methodologies for evaluating standards ontologically to assist people in developing and evaluating standards. Consequently, this work aids the committee in their interest to ontologically evaluate a semantically-weak standard such as CIMOSA.

105 Chapter 5. The CIMOSA Process Ontology The Computer Integrated Manufacturing Open System Architecture (CIMOSA) The focus of this case study was to examine the Computer Integrated Manufacturing Open System Architecture (CIMOSA), which was developed in 1992 and has been standardized by the International Organization for Standardization (ISO) since Its construct specification can be found in [39] and [40], which forms the basis of the work done in this case study. ISO 19439:2006 and ISO 19440:2007 define generic concepts that are used in enterprise models and frameworks with the intention of being integrated in computer (manufacturing) systems. CIMOSA defines an integrated methodology to support all phases of a CIM system life cycle from the requirements specification through to the system design, implementation, operation, and maintenance phases [17]. This methodology is used to plan, design, and optimize the environment in which the enterprise operates. Furthermore, CIMOSA provides industry with an enterprise modelling framework (EMF) and an integrating infrastructure (IIS) [46, 63]. The modelling framework represents the business operations in the form of processes and allows the creation of executable enterprise models in CIM programs. The IIS is used to support the integration of business and applications, as well as the execution and implementation of models to control and monitor enterprise operations. This infrastructure provides a set of generic services that process the implementation model, provide access to information, and connect to resources. For the purposes of this case study, only the modelling framework will be discussed in detail in the sections that follow. CIMOSA Modelling Framework The CIMOSA modelling framework supports the explicit description of enterprise processes at different levels of abstraction. The CIMOSA cube shown in Figure 5.1 outlines

106 Chapter 5. The CIMOSA Process Ontology 93 the ability to model different aspects and views of an enterprise. This three-dimensional framework has the following dimensions: Dimension of genericity: the degree of particularization that spans generic building blocks to their aggregation into a model of a specific enterprise domain, Dimension of modelling: provides the modelling support for the system life cycle, starting from statements of requirements to a description of the system implementation, Dimension of views: offers the possibility to work with sub-models representing different aspects of the enterprise. Figure 5.1: The CIMOSA modelling approach, adapted from Figure 1 in [46]. Dimension of Genericity CIMOSA categorizes manufacturing operations with respect to Generic and Specific (Partial and Particular) functions. Generic functions are found in Reference Architectures, and can be considered to be a catalogue of reusable building blocks that are applicable to specific needs in an enterprise. Particular Architectures serves the use of specific cases in process modelling which are not intended to be reusable for other models (hence the name partial and particular ).

107 Chapter 5. The CIMOSA Process Ontology 94 Dimension of Modelling CIMOSA facilitates a system life cycle which guides the user through model engineering and model execution. The life cycle does not represent a time sequence, but identifies a set of activities, which may be carried out in any sequence appropriate for the particular enterprise engineering tasks at hand [46]. The life cycle consists of collecting business requirements (Requirements Definition), translating the requirements into a model, and developing a description of the CIM system (Design Specification). These phases are followed by the implementation of the model for controlling and monitoring purposes (Implementation Description). Dimension of Views To model the specific aspects of the enterprise, CIMOSA defines four different views of the enterprise which are described below. 1. Function View: describes the work flows required to satisfy the enterprise s objectives. 2. Information View: describes the inputs and outputs required by each function. 3. Resource View: describes the structure of resources (humans, machines, information systems) and how they relate to functional and control aspects of the enterprise. 4. Organization View: describes and defines the responsibilities assigned to individuals. Types of Flows In addition to the modelling views, three separate types of flows within an enterprise are identified in CIMOSA [63]: The control flow is a work flow and describes the enterprise behaviour The material flow describes the flow of products and physical components The information flow describes the flow of information objects and decisions

108 Chapter 5. The CIMOSA Process Ontology 95 Basic CIMOSA Constructs In addition to the modelling framework, the CIMOSA Reference Architecture provides a basic set of building blocks for modelling enterprises [47]: Processes, Events, and Enterprise Activities are object classes that describe the functionality and behaviours of the enterprise s operations. Inputs and outputs of Enterprise Activities define the information (Enterprise Object) and the resources needed. Organizational aspects of the enterprise are defined in terms of responsibilities and authorisation (Organization Elements) for functionalities, information, resources and organization, and are structured into Organisational Units or Cells. These constructs are graphically outlined in Figure 5.2. Figure 5.2: The CIMOSA modelling constructs, adapted from Figure 2 in [47]. Process-Based Enterprise Modelling The CIMOSA modelling paradigm is based on an event-driven process-based modelling approach. CIMOSA distinguishes between processes and resources as the things to be done and the doers of the activities, respectively. A business process is a collection of related activities or tasks defined by the business to fulfil some goals of the enterprise and/or customer.

109 Chapter 5. The CIMOSA Process Ontology 96 In the context of CIMOSA, business processes are defined in terms of the work flow required by the enterprise, where enterprise activities are elementary steps in a process. As outlined in [39] and [40], business processes can be further decomposed into constituent business processes or enterprise activities, or both, along with their interconnections, and can be arranged by ordering relationships and dependencies that are described by behavioural rules [39, 40]. Behavioural rules describe the logical sequence of relationships found within enterprise activities, and identify the start of the business process [39, 40]. Logical sequencing of processes outlined in [40] consists of: Well-structured processes: the sequence of business processes or enterprise activities are completely defined (deterministic), and the expected outcome is known. Semi-structured processes: the sequence of business processes or enterprise activities is only known at run-time (semi-deterministic), and the expected outcome is known. Ill-structured processes: the sequence of business processes and the expected outcome are not completely known (non-deterministic). In CIMOSA, behavioural rules have the following form: W HEN (condition) DO action Several work flow situations that may occur and its language syntax, in Backus-Naur form, are presented in [63]. The behavioural rules are summarized in Table 5.1, and the language syntax for CIMOSA s Behavioural Rule Set (BRS) is shown below. Grammar 5.1: Behavioural Rule Set (BRS) for well-structured processes specified in Backus-Naur Form in [63]. b e h a v i o u r a l r u l e s e t ::= <s t a r t i n g r u l e s > <b e h a v i o u r a l r u l e s > <s t a r t i n g r u l e s > ::= <s i m p l e s t a r t i n g r u l e > <e v e n t d r i v e n r u l e s > <s i m p l e s t a r t i n g r u l e > ::= WHEN (START) DO <action > <e v e n t d r i v e n r u l e s > ::= <e v e n t d r i v e n r u l e > <e v e n t d r i v e n r u l e > <n e x t e v e n t d r i v e n r u l e s > <n e x t e v e n t d r i v e n r u l e s > ::= <e v e n t d r i v e n r u l e s > n i l

110 Chapter 5. The CIMOSA Process Ontology 97 <e v e n t d r i v e n r u l e > ::= WHEN ( <e v e n t c o n d i t i o n > ) DO <action > <e v e n t c o n d i t i o n > ::= START WITH <e v e n t l i s t > <e v e n t l i s t > ::= event id <next event > <next event > ::= AND event id <next event > n i l <b e h a v i o u r a l r u l e s > ::= <b e h a v i o u r a l r u l e > < n e x t b e h a v i o u r a l r u l e s > <n e x t b e h a v i o u r a l r u l e s > ::= <b e h a v i o u r a l r u l e s > n i l <b e h a v i o u r a l r u l e > ::= WHEN ( <t r i g g e r i n g c o n d i t i o n s > ) DO < action > <t r i g g e r i n g c o n d i t i o n s > ::= <t r i g g e r i n g c o n d i t i o n > < n e x t t r i g g e r i n g c o n d i t i o n > <n e x t t r i g g e r i n g c o n d i t i o n > ::= AND <t r i g g e r i n g c o n d i t i o n > < n e x t t r i g g e r i n g c o n d i t i o n > AND event id <n e x t t r i g g e r i n g c o n d i t i o n > n i l <t r i g g e r i n g c o n d i t i o n > ::= ES ( p r o c e s s s t e p id ) = <Esvalue> <Esvalue> ::= ending status id ANY <action > ::= process step id <asynchronous spawning> < synchronous spawning > FINISH <asynchronous spawning> ::= process step id <o t h e r s t e p s > <o t h e r s t e p s > ::= & process step id <o t h e r s t e p s > n i l <synchronous spawning > :: = SYNC ( <asynchronous spawning > ) The condition part of the rule outlines the circumstances in which the next step in a process can be started; these include the occurrence of one or more events, end of a process step, or combination of these [63, 47, 1]. The action part indicated the step that is activated next when the condition part becomes true. If one or more steps need to be performed in parallel, the & operator is used. The flow of control in a process is determined by state changes and transitions. It is of great interest to axiomatize these behavioural rules as first-order sentences by using axiomatized concepts, such as objects, activities, subactivities, activity occurrences, and participation, from PSL. Each of these behavioural rules are further discussed in the sections that follow.

111 Chapter 5. The CIMOSA Process Ontology 98 Table 5.1: CIMOSA behavioural rules, adapted from [63] and [1]. Type Process Triggering Rules Forced Sequential Rules Sequential Rules Conditional Sequential Rules Spawning Rules Rendezvous Rules (Logical AND) Convergence Rules (Logical OR) Loop Rules Process Completion Rules Syntax WHEN (START WITH event 1) DO EF1 WHEN (ES(EF1)=any) DO EF2 WHEN (ES(EF1)=end stat 1) DO EF1 WHEN (ES(EF1)=end stat 1) DO EF2 WHEN (ES(EF2)=end stat 2) DO EF3 WHEN (ES(EF3)=end stat 3) DO EF4 WHEN (ES(EF1)=value 1) DO EF1 & EF2 & EF3 WHEN (ES(EF1)=value 1 AND ES(EF2) =value 2 AND ES(EF3)=value 3) DO EF4 WHEN (ES(EF1) = value 1 OR ES(EF2) = value 2 OR ES(EF3)=value 3) DO EF4 WHEN ES(EF1)=loop value DO EF1 WHEN ES(EF2)end stat 1 DO FINISH Behavioural Rules for Well-Structured Processes This section outlines the behavioural rules for deterministic processes that have expected outcomes. Process Triggering Rules Process triggering rules come in two forms: Initiating a Business Process by calling one or more enterprise functions (EF s); for example, event 1 and event 2): W HEN (ST ART W IT H event 1 AND event 2) DO EF 1 Initiating one or more EF s following the occurrence of a designated start event: W HEN (ST ART ) DO EF 1

112 Chapter 5. The CIMOSA Process Ontology 99 Forced Sequential Rules These rules are used when a process step must follow another step regardless of the ending status of the previous step. In the example below, EF y follows EF x regardless of the ending status of EF x. The reserved word ANY is used by the author of [63] to illustrate the disregard for the ending status. They are of the form: W HEN (ES(EF x) = ANY ) DO EF y Conditional Sequential Rules Unlike the forced sequential rules, these rules are used to represent branching conditions. These rules cause the activation of one of a defined number of Enterprise Activities or Business Processes according to the value of an ending status. For example, if EF 1 had three different ending statuses, we can write: W HEN (ES(EF 1) = end stat 1) DO EF 2 W HEN (ES(EF 1) = end stat 2) DO EF 3 W HEN (ES(EF 1) = end stat 3) DO EF 4 This indicates that EF 2, EF 3, and EF 4 are the different branches that are enabled depending on the ending status of EF 1. Spawning Rules These rules are used to represent the parallel execution of process steps. Two types of spawning rules are defined in [63] and [40]: Asynchronous spawning: For instance, when EF 1 finishes with status value, EF 2, EF 3 and EF 4 will all be requested to start as soon as they are enabled, i.e. when

113 Chapter 5. The CIMOSA Process Ontology 100 their preconditions are satisfied (& is the parallel operator). W HEN (ES(EF 1) = value) DO EF 2 & EF 3 & EF 4 Synchronous spawning: For instance, when EF 1 finishes with status value, EF 2, EF 3 and EF 4 will all be requested to start exactly at the same time assuming that they are all enabled (SYNC indicates the synchronisation). W HEN (ES(EF 1) = value) DO SY NC (EF 2 & EF 3 & EF 4) Rendezvous Rules Rendezvous rules are used to synchronize the end of spawning rules. For example, if EF 5 starts after EF 2 finishes with a status of value 24, EF 3 finishes with a status of value 3, and EF 4 finishes with a status of value 4, then the rendezvous rule is written as: W HEN (ES(EF 2) = value 2 AND ES(EF 3) = value 3 AND ES(EF 4) = value 4) DO EF 5 Loop Rules Loop rules repeat a process step (or several) as long as a given condition holds, or for a defined number of iterations. In the example below, EF 1 repeats until it continues to have a status of loop value. W HEN (ES(EF 1) = loop value) DO EF 1 Process Completion Rules Process completion rules indicate the end of an execution of a set of rules. In [63], a process behaviour is declared to be consistent if FINISH can be reached from all STARTs and all process steps used in the rules belong to at least one path from START

114 Chapter 5. The CIMOSA Process Ontology 101 to FINISH (no isolated process steps and no dead-ends are allowed) in the control flow. W HEN (ES(EF 1) = end stat x AND ES(EF 2) = end stat y) DO F INISH Behavioural Rules for Semi-Structured Processes In [63], two additional rules have been added to model semi-structured processes. In these rules the action refers to a compound action, denoted by the set S, which indicates that it is considered as a whole in order to define its ending status. The exclusive choice, XOR, operator is used The grammar is defined as follows: Grammar 5.2: Behavioural Rule Set (BRS) for semi-structured processes specified in Backus-Naur Form in [63]. <action > ::= <r u n t i me choice > <unordered set > <run t i m e c h o i c e > ::= compound action id = ( process step id XOR process step id <o t h e r r u n t i m e s t e p s > ) <o t h e r r u n t i m e s t e p s > ::= XOR process step id < o t h e r r u n t i m e s t e p s > n i l <unordered set > ::= compound action id = { process step id, process step id <o t h e r u n o r d e r e d s e t s t e p s > } <o t h e r u n o r d e r e d s e t s t e p s > ::= process step id < o t h e r u n o r d e r e d s e t s t e p s > n i l Run-Time Choices Rules These rules are used when there is an exclusive choice among several alternatives. Exactly one process step in the list will be executed as decided by the resource at run-time, which must be common to all steps in the list. W HEN (ES(EF 1) = end stat 1) DO S = (EF 2 XOR EF 3 XOR EF 4)

115 Chapter 5. The CIMOSA Process Ontology 102 Unordered Set Rules They are used to indicate that a set of process steps must be executed, but the order of execution is unknown. W HEN (ES(EF 1) = end stat 1) DO S = {EF 2, EF 3, EF 4} As a whole, CIMOSA defines a model-based enterprise engineering method that categorizes manufacturing operations into generic and specific functions. These functions can be combined to create a model that can be used for simulation and analysis, scheduling, dispatching, monitoring, and providing process information. While [40] provides templates and behavioural rules for its constructs, it does not explicitly define, nor axiomatize, the CIMOSA terminology in a computer-interpretable manner. 5.3 Methodology In order to axiomatize CIMOSA s constructs and behavioural rules in first-order logic, various approaches were taken in order to understand the framework s implicit semantics. The subsequent sections that follow outline the methodologies taken to axiomatize the concepts and behavioural rules found in CIMOSA, which include: Identifying competency questions that the ontology should answer. Matching the syntactic grammar found in CIMOSA and PSL. Identifying keywords to develop a lexicon of CIMOSA terminology. Axiomatizing the behavioural rule set through identification of similar PSL constructs. In summary, the methodology taken is ad-hoc in nature: there was no real process with developing the axioms. Once the competency questions were identified, it was appropriate to try to utilize, as much as possible, the available materials on CIMOSA s behavioural rule set. In this case, this involved attempting to match the syntactic grammars provided

116 Chapter 5. The CIMOSA Process Ontology 103 in [63] and to develop a list of terminology used in [40] and [1]. Once matching the grammars proved to be difficult and unfruitful, we then attempted to develop axioms to describe the rules. Thus, there was no real nor structured process taken to go from one step to another, so it would not be appropriate to depict the steps graphically in a flowchart Identification of Competency Questions Competency questions are used to determine the scope of the ontology to be designed and are essentially questions that a knowledge base, based on the ontology, should answer [27]. Thus, these questions aid ontology designers in determining whether or not the ontology contains information to answer these types of questions, and whether a particular level of detail or representation is needed for the ontology. Since we have limited our scope to axiomatize only the CIMOSA behavioural rules, the competency questions have been restricted to ask process-related questions. As such, the following competency questions were developed to help guide the ontology design process: 1. Which enterprise function starts the domain process? 2. What ending status triggers the following enterprise function? 3. When does this enterprise function or domain process terminate? 4. Does this enterprise function repeat itself? 5. Are these enterprise functions done in parallel? Utilizing CIMOSA s Grammar CIMOSA s modelling constructs are outlined in Grammar 5.1 and can be used to examine the relationship between states and activities in PSL. By mapping the CIMOSA and PSL grammars for state-based activities, this allows the further examination of the CIMOSA behavioural rules and the discovery of any relationships between PSL and CIMOSA, such as the identification of corresponding activity classes between the two languages.

117 Chapter 5. The CIMOSA Process Ontology 104 We examine the grammar found in the State-based Conditional Activity Axioms section of the PSL ontology 1, which are given below. Grammar 5.3: Grammar for process descriptions in PSL. ( c o n d i t i o n a l?a ) < c o n d i t i o n a l a c t i v i t y > ::= ( f o r a l l (? s? s2 ) ( i f f (do?a? s? s2 ) < s i m p l e c o n d i t i o n a l >)) ( p a r t i a l c o n d i t i o n a l?a ) < p a r t i a l c o n d i t i o n a l > ::= ( f o r a l l (? s? s2 < v a r i a b l e >+) ( i f f (do?a? s? s2 ) < c o n d i t i o n a l f o r m u l a >)) Grammar 5.4: Grammar for auxiliary rules in PSL. < s i m p l e c o n d i t i o n a l > ::= ( i f < s i m p l e s t a t e a x i o m > < v a r i a t i o n f o r m u l a >) < c o n d i t i o n a l f o r m u l a > ::= ( i f < state axiom > < v a r i a t i o n f o r m u l a >) Direct mappings between the grammars could not be determined, so it was decided to move onto the next method of identifying keywords found in [39], [40], and [1] to develop a lexicon for CIMOSA. In future revisions of the ontology, we will revisit this idea to match the grammars Identifying Keywords to Piece Together Behavioural Rules Another approach taken was to identify the frequently used key terms in [39], [40], [1], and [63]. To this effect, a lexicon for CIMOSA was developed to capture process-related terminology used in the descriptions of CIMOSA s behavioural rule set. By developing a lexicon, it provided a starting point for creating the ontology and allowed the distinction 1 The grammar for the State-based Conditional Activity axioms in BNF form can be accessed via: variation.bnf.html

118 Chapter 5. The CIMOSA Process Ontology 105 between relations and functions needed to semantically augment the CIMOSA constructs with terminology from PSL. A lexicon is essentially the vocabulary of a language that contains some knowledge of how each word is used [38]. For technical domains, such as that in CIMOSA, if an explicit vocabulary of terms exist, then it is possible that an ontology exists within the vocabulary [38]. A lexicon that is structured with semantic hierarchies can serve as a basis for an ontology, and that an ontology gives way for lexical classifications. It remains debatable whether a lexicon is considered as an ontology 2, but for the purposes of this case study, the development of a lexicon of terms was determined to be the best way to approach the ontology design process. A lexicon allowed the determination of terms that were potentially equivalent to concepts defined in the PSL lexicon found in [22]. By examining [39], [40], [1], and [63], key words that captured the intended the semantics of the CIMOSA framework were identified and are further discussed in Section A drawback of this method to determine keywords is that not all of the keywords identified were used in the axiomatizations with PSL constructs; this was due to the fact that some CIMOSA constructs could not be directly mapped with PSL constructs Axiomatizing the Behavioural Rule Set Through Identification of Similar PSL Constructs Another approach taken was to axiomatize the behavioural rule set without any keywords, but to go straight ahead with identifying PSL constructs that could be used to represent the rules. Since CIMOSA s process descriptions involve complex activities, we can utilize the constructs found in the PSL ontology to map CIMOSA expressions into sentences that contain these PSL constructs. psl core The constructs that are used are of those found in the PSL-CORE hierarchy H 2 Additional notes about the relationships between lexicons and ontologies can be found in [56], [5], and [64].

119 Chapter 5. The CIMOSA Process Ontology 106 in COLORE 3. Activity trees characterize the occurrences of complex activities and consists of all possible sequences of atomic subactivity occurrences beginning from a root subactivity occurrence. Possible sequences of subactivity occurrences of the complex activity correspond to branches within the activity tree. The following relations are used to describe complex activities within PSL [21] and their axiomatizations can be found in Appendix C.1: root(o, a) specifies that the atomic subactivity occurrence o is the root of the activity tree. leaf(s, a) specifies the leaf of an activity tree if and only if there exists an earlier atomic subactivity occurrence but there does not exist a later atomic subactivity occurrence. min precedes(s 1, s 2, a) is the ordering relation over the atomic subactivity occurrences in the activity tree. precedes(o 1, o 2 ) specifies that o 1 is earlier than o 2 within the occurrence tree. The axiomatized behavioural rules can be found in Sections and The Proposed CIMOSA Process Ontology This section outlines and describes the CIMOSA process ontology written in first-order logic Lexicon In [40], the standards document makes a major distinction between business processes and enterprise activities. Business Processes do not have an ending status; instead, process completion is signalled by the behavioural rule F IN ISH action and possible exception. In addition, business processes have observable and/or quantifiable results, such as material entities, information entities, new processes, or achievements of one or 3

120 Chapter 5. The CIMOSA Process Ontology 107 more enterprise objectives [40]. Table 5.2 outlines the general terminology found in the following CIMOSA documentation: [63], [47], [66], [39], and [40]. In the PSL ontology, a lexicon is defined in [22] to indicate the core theories within the ontology (refer to Appendix A.2). Similarly, we define a first-order lexicon for CIMOSA s various constructs in Table 5.3, with definitions adapted from [47], [66], [39], and [40]. This lexicon includes potential entities, relations, and functions that were considered when developing the process ontology for CIMOSA. To semantically augment these CIMOSA constructs with the PSL constructs found in [22], we attempted to do a one-to-one mapping between the terminology in both lexicons. In Table 5.4, we have attempted to compare the lexicons and, where possible, have determined that the following terms are similar, if not potentially equivalent, to each other Behavioural Rules for Well-Structured Processes The following section discusses the possible axiomatizations of the well-structured CIMOSA behavioural rules that were outlined and discussed in Table 5.1 and Section 5.2. The Common Logic versions of the axioms described below can be found in Appendix C.2 and in COLORE 4. From Table 5.4, we are able to write the following axioms: A business process in CIMOSA is an activity in PSL. x ((business process(x) activity(x))). (5.4.1) An enterprise activity in CIMOSA is an activity in PSL. x ((enterprise activity(x) activity(x))). (5.4.2) An enterprise function in CIMOSA is an activity in PSL. x ((enterprise f unction(x) activity(x))). (5.4.3) 4 cimosa.clif

121 Chapter 5. The CIMOSA Process Ontology 108 Table 5.2: Definition of Terms Found in CIMOSA, adapted from [63], [47], [66], [39], and [40]. CIMOSA Term Behavioural Rule Business Processes (BP) Domain Ending Status (ES) Enterprise Activities (EA) Enterprise Function (EF) Enterprise Model Enterprise Object Event Occurrence Definition Description of the sequencing relationships of constituent activities used in the specification of Business Process behaviour. Partially ordered set of enterprise activities that can be executed to achieve some desired end-result in pursuit of a given objective of an enterprise or a part of an enterprise. Part of the enterprise relevant to a set of business objectives and constraints for which a model is created. The termination status of the execution of an occurrence of the activity (such as successful execution, aborted, done or less than 100 items produced ). All, or part, of process functionality that consists of elementary tasks performed in the enterprise that consume inputs and allocate time and resources to produce outputs. A business process or enterprise activity. A representation of what an enterprise is composed of, what it intends to accomplish and how it operates in accordance. Construct that represents a piece of information in the domain of the enterprise that describes a generalized or a real or an abstract entity, which can be conceptualized as being a whole. A solicited or unsolicited fact indicating a state change in the enterprise. A single, actual realization of an entity in the real world.

122 Chapter 5. The CIMOSA Process Ontology 109 Table 5.3: Lexicon for CIMOSA in first-order logic. Term begin(x) business process(x) ending status(x) enterprise activity(x) enterprise f unction(x) enterprise object(x) event(x) occurrence(x) Description Performs an action (such as carrying out a business process or enterprise activity) when invoked. Partially ordered set of enterprise activities that can be executed to achieve the enterprise s objective. Provides information on the completion or termination of an Enterprise Activity. Elementary tasks performed in the enterprise that consume inputs and allocate time and resources to produce outputs. A business process or enterprise activity. A generalized or a real or an abstract entity in the enterprise. A solicited or unsolicited fact indicating a state change in the enterprise or environment. An occurrence of an enterprise function. Table 5.4: Comparison between CIMOSA and PSL s lexicons. CIMOSA Term PSL Term business process(x) is potentially equivalent to activity(x) enterprise activity(x) is potentially equivalent to activity(x) enterprise function(x) is potentially equivalent to activity(x) event(x) is potentially equivalent to activity(x) occurrence(x) is potentially equivalent to activity occurrence(x) enterprise object(x) is potentially equivalent to object(x)

123 Chapter 5. The CIMOSA Process Ontology 110 An enterprise object in CIMOSA is an object in PSL. x ((enterprise object(x) object(x))). (5.4.4) An event in CIMOSA is an activity occurrence in PSL. x ((event(x) activity(x))). (5.4.5) An occurrence in CIMOSA is an activity occurrence in PSL. x ((occurrence(x) activity occurrence(x))). (5.4.6) All enterprise functions are business processes or enterprise activities x ((enterprise f unction(x) business process(x) enterprise activity(x))). (5.4.7) We can define the Ending Status (ES) values as a constant named end stat 1. o x ((occurrence of(o, enterprise function(x)) holds( end stat 1, o))). (5.4.8) These ending statuses are values that are specified by the ontology user, depending on the context and the domain(s) of use. Process Triggering Rules Recall that the rule indicates that a domain process can be started by one or more events. W HEN (ST ART W IT H event i AND event j) DO EF 1 Thusly, we can write the following rule using the PSL constructs of occurrence of(o, a) and precedes(o1, o2): o 1 o 2 x f ((occurrence of(o 1, domain process(x))

124 Chapter 5. The CIMOSA Process Ontology 111 root(o 2, o 1 ) occurrence of(o 2, enterprise function(f)) o 3 o 4 i j (precedes(o 3, o 2 ) precedes(o 4, o 2 ) occurrence of(o 3, activity(i)) occurrence of(o 4, activity(j))))). (5.4.9) For rules where a business process is started from a parent process, recall that the original rule is stated as: W HEN (ST ART ) DO EF 1 We can use the PSL construct for root notes in an occurrence tree to write the following: o 1 x ((occurrence of(o 1, business process(x)) o y(root(o, o 1 ) occurrence of(o, business process(y)) precedes(o, o 1 )))). (5.4.10) Forced Sequential Rules With forced sequential rules, a process step must follow another step regardless of the ending status of the previous step. The reserved word ANY is used by the author of [63] to illustrate the disregard for the ending status. They are of the form: W HEN (ES(EF x) = ANY ) DO EF y We can write this as follows: o 1 x ((holds(any, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 y(occurrence of(o 2, enterprise function(y)) precedes(o 1, o 2 )))). (5.4.11)

125 Chapter 5. The CIMOSA Process Ontology 112 Conditional Sequential Rules Recall that the original rule is stated as: W HEN (ES(EF 1) = end stat 1) DO EF 2 W HEN (ES(EF 1) = end stat 2) DO EF 3 W HEN (ES(EF 1) = end stat 3) DO EF 4 If the enterprise function x has an ending status value of end stat 1, and o 1 is an occurrence of x, then there exists an o 2 which is an occurrence of enterprise function y that occurs after o 1. We assume end stat 1, end stat 2, etc. are specific ending status values. Thus, we are able to write the above three rules as follows: o 1 x ((holds( end stat 1, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 y(occurrence of(o 2, enterprise function(y)) precedes(o 1, o 2 )))). (5.4.12) o 2 x ((holds( end stat 2, o 2 ) occurrence of(o 2, enterprise function(x)) o 3 y(occurrence of(o 3, enterprise function(y)) precedes(o 2, o 3 )))). (5.4.13) o 3 x ((holds( end stat 3, o 3 ) occurrence of(o 3, enterprise function(x)) o 4 y(occurrence of(o 4, enterprise function(y)) precedes(o 3, o 4 )))). (5.4.14) Spawning Rules Recall that spawning rules come in two different forms: asynchronous and synchronous. The asynchronous form is defined in such a way that EF 2, EF 3 and EF 4 will all be

126 Chapter 5. The CIMOSA Process Ontology 113 requested to start as soon as they are enabled after EF 1 finishes with a status value: W HEN (ES(EF 1) = value) DO EF 2 & EF 3 & EF 4 We can write this in first-order logic, where value is the specific ending status required for spawning to occur, as shown below. We do not know in which order EF 2, EF 3 and EF 4 occurs, so the axiom can be defined as follows: o 1 x ((holds( value, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 o 3 o 4 t y z (occurrence of(o 2, enterprise function(t)) occurrence of(o 3, enterprise function(y)) occurrence of(o 4, enterprise function(z)) precedes(o 1, o 2 ) precedes(o 1, o 3 ) precedes(o 1, o 4 )))). (5.4.15) The precedence constraint that EF 1 occurs before EF 2, EF 3 and EF 4 is preserved through the use of the precedes(o 1, o 2 ), precedes(o 1, o 3 ), and precedes(o 1, o 4 ) relations, respectively. Similarly, for synchronous spawning, EF 2, EF 3 and EF 4 will all be requested to start exactly at the same time assuming that they are all enabled (SYNC indicates the synchronization): W HEN (ES(EF 1) = value) DO SY NC (EF 2 & EF 3 & EF 4) To write this in first-order logic, we can assume that EF 2, EF 3 and EF 4 start at the same time point. Thus, we use the beginof(o) function in PSL to indicate that the

127 Chapter 5. The CIMOSA Process Ontology 114 starting time points of EF 2, EF 3 and EF 4 are the same: o 1 x ((holds( value, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 o 3 o 4 t y z (occurrence of(o 2, enterprise function(t)) occurrence of(o 3, enterprise function(y)) occurrence of(o 4, enterprise function(z)) precedes(o 1, o 2 ) precedes(o 1, o 3 ) precedes(o 1, o 4 ) (beginof(o 2 ) = beginof(o 3 )) (beginof(o 2 ) = beginof(o 4 ))))). (5.4.16) Rendezvous Rules Recall these rules synchronize the end of spawning rules; in this case, EF 5 starts only when EF 2 finishes with a status of value 2, EF 3 finishes with a status of value 3, and EF 4 finishes with a status of value 4. W HEN (ES(EF 2) = value 2 AND ES(EF 3) = value 3 AND ES(EF 4) = value 4) DO EF 5 Since the ending time points for the enterprise functions EF 2, EF 3 and EF 4 are unknown, and that these functions may not end at the same time, we do not use the endof(o 1 ) function in PSL in the axiomatization of this behavioural rule. If we treat value 2, value 3, and value 4 as constants, then we can write the following rule where the precedence constraint is conserved: o 2 o 3 o 4 x y z ((holds( value 2, o 2 )

128 Chapter 5. The CIMOSA Process Ontology 115 holds( value 3, o 3 ) holds( value 4, o 4 ) occurrence of(o 2, enterprise function(x)) occurrence of(o 3, enterprise function(y)) occurrence of(o 4, enterprise function(z)) o 5 t (occurrence of(o 5, enterprise function(t)) precedes(o 2, o 5 ) precedes(o 3, o 5 ) precedes(o 4, o 5 )))). (5.4.17) Loop Rules Loop rules repeat a process step (or several) as long as a given condition holds, or for a defined number of iterations. In the example below, EF1 repeats until it continues to have a status of loop value. W HEN (ES(EF 1) = loop value) DO EF 1 We can axiomatize this trivially in first-order as: o 1 x ((holds( loop value, o 1 ) occurrence of(o 1, enterprise function(x)) occurrence of(o 1, enterprise function(x)))). (5.4.18) It is uncertain whether this is the correct axiomatization of this behavioural rule because occurrence of(o 1, enterprise function(x)) only occurs once based on the implication. Another potential way of axiomatizing this would be to take a look at the subactivity

129 Chapter 5. The CIMOSA Process Ontology 116 occurrence ordering theory, T soo 5, in PSL and attempt to use the soo(s, a) relation 6 in a revision to this axiomatization. Process Completion Rules Process completion rules indicate the end of an execution of a set of rules. If FINISH can be reached from all STARTs and all process steps used in the rules belong to at least one path from START to FINISH, then the rule is considered consistent, according to [63]. W HEN (ES(EF 1) = end stat x AND ES(EF 2) = end stat y) DO F INISH This can be written in first-order as follows: s a o 1 o 2 b f ((leaf occ(o 2, o 1 ) occurrence of(o 2, enterprise function(f) occurrence of(o 1, business process(f)) o 3 o 4 g i j (precedes(o 3, o 2 ) precedes(o 4, o 2 ) occurrence of(o 3, enterprise function(f)) occurrence of(o 4, enterprise function(g)) holds( end stat x, o 3 ) holds( end stat x, o 4 )))). (5.4.19) 5 soo.clif 6 The lexicon for this subactivity occurrence ordering theory can be accessed via:

130 Chapter 5. The CIMOSA Process Ontology Behavioural Rules for Semi-Structured Processes The following section discusses the possible axiomatizations of the semi-structured CIMOSA behavioural rules that were outlined and discussed in Table 5.1 and Section 5.2. The Common Logic versions of the axioms described below can be found in Appendix C.2 and in COLORE 7. Run-Time Choice Rules Recall that these rules are used when there is an exclusive choice among several alternatives. Exactly one process step will be executed as decided by the resource at run-time: W HEN (ES(EF 1) = end stat 1) DO S = (EF 2 XOR EF 3 XOR EF 4) In first-order logic, the exclusive or (XOR) operator is represented as one or the other, but not both : p q (p q) (p q) Thus, we adopt this format to axiomatize this rule, but assume there is an alternative between two different enterprise functions. If there are three listed, the axiom would be very complex. o 1 x ((holds( end stat 1, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 o 3 y (occurrence of(o 2, enterprise function(y)) precedes(o 1, o 2 ) (occurrence of(o 3, enterprise function(y)) precedes(o 1, o 3 )) occurrence of(o 3, enterprise function(y)) precedes(o 1, o 3 ) 7 cimosa.clif

131 Chapter 5. The CIMOSA Process Ontology 118 (occurrence of(o 2, enterprise function(y)) precedes(o 1, o 2 ))))). (5.4.20) Unordered Set Rules They are used to indicate that a set of process steps must be executed, but the order of execution is unknown. W HEN (ES(EF 1) = end stat 1) DO S = {EF 2, EF 3, EF 4} Since the unordered set rule in the CIMOSA documentation does not indicate whether all of these process steps need to be executed, compared to some of the process steps, we make the assumption that the AND operator is used. This means that every process step in the set S must be executed at least once. We represent this in first-order logic as follows: o 1 x ((holds( value, o 1 ) occurrence of(o 1, enterprise function(x)) o 2 o 3 o 4 t y z (occurrence of(o 2, enterprise function(t)) occurrence of(o 3, enterprise function(y)) occurrence of(o 4, enterprise function(z)) precedes(o 1, o 2 ) precedes(o 1, o 3 ) precedes(o 1, o 4 )))). (5.4.21) 5.5 Discussion The following section discusses the limitations of the applied methodologies in providing CIMOSA with semantics, and the general limitations with the developed ontology.

132 Chapter 5. The CIMOSA Process Ontology Limitations of the Ontology The proposed CIMOSA ontology only covers the process specifications found in enterprise modelling. In the appendices of [40], there are metamodels that have not been formalized within this ontology. These metamodels describe how various CIMOSA concepts and constructs are related to each other via the different views (function, information, resource, and organization). As well, the proposed ontology does not axiomatize any of the different views and flows found in CIMOSA since they are not referred to, nor specified, in the behavioural rule set. Furthermore, the axiomatizations for loop rules, run-time choice rules, and unordered set rules need to be revised to accurately reflect the semantics behind the CIMOSA constructs. With the loop rules, it was indicated that the rule was trivialized to only have the activity occurrence repeat once after a desired ending status is attained. The run-time and unordered set rules will need to be re-examined since their axiomatizations depends on the number of enterprise functions contained within the set S. Consequently, as the number of elements in set S increases, the axiomatizations will be different for every size n of the set S. As well, for the unordered set rules, the documentation indicates that the enterprise functions in set S need to be enacted at least once, but the current axiomatization does not take into account the repetition of enterprise functions within the set. We are currently unsure of how to represent the dynamic characteristics of these behavioural rules Inability to Test and Verify Axioms for its Intended Semantics One of the critical questions with designing ontologies, or attributing ontologies, to already existing standards and frameworks is whether or not the axioms developed are indeed correct. One of the approaches discussed by Grüninger in [21] is to utilize a

133 Chapter 5. The CIMOSA Process Ontology 120 pre-existing software environment to hypothesize that the axiomatizations behave in accordance and make the same predictions as the software. However, since the CIMOSA software was developed in isolation in the late 1990s, we are unable to test our various axiomatizations for correctness since it utilizes its own descriptive language known as the CIMOSA Implementation Descriptive Language The Need for Ontology Design Best Practices Currently, there do not exist any generalized best practices when it comes to designing new ontologies. There have been discussions about the ontology lifecycle for theorem proving [43] and within biomedical informatics [54], but there do not exist any general best practices to create ontologies from standardized formalisms and frameworks such as the Integration DEFinition (IDEF) family of constructs and CIMOSA, respectively. With respect to the methodology for ontology verification described in [43], ontologies can be verified if the intended models of the ontology are known. In the circumstance with CIMOSA, we are not sure what the specification of the ontology s intended models are supposed to look like in the Requirements Phase, nor do we know how to axiomatize the models that are captured by the requirements in the Design Phase of the ontology design lifecycle. Since the initial two phases of this methodology cannot be carried out with respect to CIMOSA, we have identified that there is a need for a general methodology, or suggested best practices, for designing ontologies from established standards. 5.6 Challenges & Difficulties Encountered The following challenges and difficulties were encountered in this case study. 8 This implementation language is described in detail in [1].

134 Chapter 5. The CIMOSA Process Ontology 121 Lack of Ontology Design Methodologies To our knowledge, there have not been methodologies proposed for the ontology design process. While there are approaches to develop ontologies through natural-language processing (NLP) techniques, such as those found in [56], NLP search capabilities are often assumed to be limitless and provide unrealistic expectations of results for end-users. As well, they are costly to implement and may perform worse than simple, keyword-based search engines once their limits have been reached. Given these limitations, however, there is an implicit understanding within the ontology community that there exists a life cycle in which ontologies are created, evaluated, and fixed, similar to workflows and design patterns found in project management and software development. Since this case study required the creation of new axioms to describe CIMOSA s behavioural rules, the adopted methodology developed the proposed axioms has been ad-hoc. While we initially started off with competency questions and an collection of commonly-used terminology found in the behavioural rule set, we realized that the challenge lies in how the reader interprets the context and content of the CIMOSA documentation. Technical Jargon and Ambiguous Phrasing Hinder Understanding of Semantics With the two standards documents, there is a lot of legal writing, or legalese, used. Despite the fact that these standards are not government standards and are not legally binding, the intent of the documents is to ensure that the CIMOSA framework is used in a consistent manner. Regardless of this fact, the wording in certain parts of the standards documents is ambiguous and prevents the reader from fully understanding the intent of the writing. For example, in the Compliance Principles section of [40], the following is specified: A model can also claim compliance to this standard if it is (i) a valid construc-

135 Chapter 5. The CIMOSA Process Ontology 122 tion of a modelling language that is itself compliant, or (ii) for a modelling language claiming qualified compliance, if the model uses only those modelling language constructs that are mappable to the constructs of this standard. Nowhere in [40] is a model specified for CIMOSA, or any of the other formalisms found within this standards document. The term model is defined ambiguously, in both [39] and [40], as: [an] abstract description of reality in any form (including mathematical, physical, symbolic, graphical, or descriptive) that presents a certain aspect of that reality. The ambiguous phrasing used in this definition makes it difficult for the reader to fully understand what a CIMOSA - or more generally, an enterprise - model should encompass. Uncertainty of the Role of CIMOSA Dimensions in Process Specification of the Behavioural Rule Set Part of the challenge with axiomatizing CIMOSA is that we are unsure of the role of the dimensions of genericity, views, and life cycle outlined in Section 5.2 have in the behavioural rule set. We were also unsure of how these constructs could be axiomatized in first-order logic. Similarly, we were uncertain as to how the different flows (control, material, information) could be represented in the proposed ontology. Describing CIMOSA s Looping Rules with PSL Constructs With respect to looping rules found in CIMOSA, the construct is similar to that of the graphical formalism found in the Integrated DEFinition for Process Description Capture Method (IDEF3) and the Unified Modelling Language (UML). IDEF3 allows cyclic orderings in its formalisms, so additional work will need to be done to determine how to represent these orderings axiomatically for CIMOSA; the soo(s, a) and soo precedes(s 1, s 2, a) relations from PSL, or other relations in other theories, may need to be created in order to axiomatize the looping rules.

136 Chapter 5. The CIMOSA Process Ontology Insights From this case study, we have gathered additional insight on the ontology design process, along with the difficulties of developing semantics for an area that lacks formalisms to properly describe commonly-used constructs within enterprise modelling. This case study has outlined potential research areas that may be of interest within the ontology, international standards, and enterprise engineering communities, as well as a starting point for ontologizing standards and frameworks found within the ISO.

137 Chapter 6 Ontology Mapping: ServicedAtHome In contrast to the previous chapters, here we describe a case study where rich sets of axioms were not provided nor used to map two ontologies together. This case study examines how two weak ontologies, with no semantics, can be mapped together in the e-commerce setting. ServicedAtHome is a website designed to integrate home product and service data intended to assist home owners, the users, to take better care of their homes. It integrates this data from various heterogeneous providers, but the semantic heterogeneity problem arises when different meanings of terms are used to describe the same products. The current challenge for ServicedAtHome is to integrate the data by the primary providers, Amazon and Sears, through the means of a semi-autonomous exchange of information; this means that there should be an automated mapping of data to reduce the amount of manual processing required. In order to do this, computer-interpretable ontologies are needed to provide a set of terms and the assigned meanings of these terms in a formal logical language. The development of ontologies assists with the semantic integration of software systems since ontologies contain a shared understanding of the terminology found within each provider. 124

138 Chapter 6. Serviced At Home Background & Motivation In this section, we outline our primary motivations for undertaking this case study with Hunch Manifest, Inc., and describe the data and infrastructure involved Hunch Manifest, Inc. Internationally, the home improvement industry is approximately a $500 billion USD industry: material and merchandise retail sales comprise approximately one third and home service providers two thirds [16]. Hunch Manifest, Inc. 1 is a privately owned company founded in 2011 with the goal of creating innovative, sustainable and practical resources for people, their residences, and their community. The company s first product, is Canada s only home service marketplace that retrieves quotes from providers that are trusted by friends and family. Today, the company is poised to redefine the home improvement industry using an intelligent suite of semantic web tools and design methods. This case study was carried out as an industry-research partnership project with Hunch Manifest, Inc. in the form of a Natural Sciences and Engineering Research Council of Canada (NSERC) Engage grant 2. The results of this project will help the industry take a step forward through the introduction of semantic technology into an online e-commerce application. By adding intelligence and extending semantic capability to its back-end infrastructure, ServicedAtHome brings much needed utility to consumers by improving the system s ability to organize resources given the definition of some home improvement work. The user on the front-end will utilize a tool that will intelligently aid them in planning as well as intelligently recommend resources to execute the work plan These grants are designed to give companies access to the knowledge and expertise available at Canadian universities, and are intended to foster the development of new research partnerships by supporting short-term research and development projects aimed at addressing a company-specific problem. Additional information about the NSERC Engage Partnership can be found via nserc-crsng.gc.ca/professors-professeurs/rpp-pp/engage-engagement_eng.asp.

139 Chapter 6. Serviced At Home 126 The purpose of this project was to utilize semantic data integration techniques to semantically map the service providers data together, along with providing any necessary mappings between ServicedAtHome s HomeServices Ontology and other ontologies from third-party product and service providers. This case study attempts to address the problems of generating and verifying such ontology mappings. ServicedAtHome ServicedAtHome.com is an online service which matches home owners with resources to help them carry out tasks within their home. Resources may include service providers (e.g., plumbers, contractors), material (e.g., bathroom fixtures), and tools (e.g., wrenches, power drills). When a home owner defines the work they intend to complete in their home, ServicedAtHome processes the request, consolidates information and makes recommendations of available resources. The HomeServices Ontology (HSO) In order to process requests, ServicedAtHome has developed the HomeServices Ontology (HSO) deconstruct the requests into terminology the system can understand. The ontology is currently written in OWL and organizes knowledge pertaining to the home domain; it is based on the gist ontology, a minimalist upper ontology 3 that describes typical business concepts. Since the Home Services Ontology (HSO) was already developed in OWL and Hunch Manifest, Inc. preferred using the OWL syntax, first-order logic and Common Logic were not used in this case study Semantic Integration of Product and Service Data ServicedAtHome.com integrates home product and service data from numerous heterogeneous providers, who distribute their information to publishers in order to sell on their 3 An upper ontology describes generic concepts that are the same across all knowledge domains and are designed with the intention to support broad semantic interoperability between other ontologies.

140 Chapter 6. Serviced At Home 127 behalf in exchange for a commission. A key consolidation challenge with disparate data sources, however, is semantic heterogeneity. For example, a hammer is a type of tool but may also refer to the hip-hop artist MC Hammer, a West Sussex location, or a comic book character. This clash over the meaning of the terms prevents the seamless exchange of information among the providers. Therefore, a challenge for the business is to integrate data in a manner that increases mapping automation and reduces manual processing (such as semi-autonomous data integration). The development of ontologies has been proposed as a key technology to support semantic integration [30]. Ontologies are logical theories that provide a set of terms together with a computer-interpretable specification of the meanings of the terms in some formal logical language. The semantic integration of software systems is supported through a shared understanding of the terminology in their respective ontologies. 6.2 Infrastructure of Mapping Services & Ontologies For the purposes of this case study, Hunch Manifest, Inc. was interested in integrating home improvement product information provided by Amazon and Sears. Access to the Amazon and Sears Application Programming Interfaces (APIs) was provided by the company to retrieve the necessary product information in the Extensible Markup Language (XML) format. From the raw product data, we were able to develop API response ontologies in OWL for each company based on how the XML tags were structured. However, part of the project requirements was to test the mappings between the HSO and the API ontologies using Franz, Inc. s AllegroGraph Data Store, which is a graph database that has reasoning and ontology modelling capabilities. In order to do this, the conversion of XML product data into the Resource Description Framework (RDF) format was required. The mappings are then expressed in RDF syntax to be used by AllegroGraph to return the desired results to the user.

141 Chapter 6. Serviced At Home 128 Figure 6.1 summarizes the relationships between the different API technologies and ontologies involved in this case study. The intent of the front-end ServicedAtHome web application is to receive queries from the users of the system (usually homeowners who wish to carry out some home renovation project) and to provide users with a response to their queries. Queries to the system were intended to be comparative in nature, such as asking for the cheapest product offered by both vendors or for the average price of a given product. At the back-end of the system, there are scripts which run queries against the corresponding vendor APIs and retrieves those results in XML form. Since this case study was intended to be a proof of concept for Hunch Manifest, Inc., we were instructed to develop ontologies derived from the XML API responses in the OWL syntax. However, as the case study progressed, these OWL ontologies were not utilized to their fullest nature to test the ontology mappings since Hunch Manifest, Inc. had preferred to utilize the AllegroGraph Data Store to store all of the product information and to reason with the mappings. As outlined in future subsections, what resulted was that RDF subtheories were extracted from the developed OWL ontologies, and all of the product data needed to be imported into the data store in the RDF format in order to test the vendor mappings using SPARQL Protocol and RDF Query Language (SPARQL) queries. From there, the mapped results of the queries are outputted by AllegroGraph back to the user. 6.3 Methodology In order to map the vendor product data together, an ad-hoc approach was taken in order to understand the framework s implicit semantics. The subsequent sections that follow outline the steps taken to develop the mappings between the two vendors, which include: Acquiring sample product data through the vendors APIs.

142 Chapter 6. Serviced At Home 129 ServicedAtHome Mapping Front-End Query from User Response to User ServicedAtHome Mapping Back-End API Queries Amazon.com Amazon.com API Response OWL Ontology Amazon.com API XML Response Allegrograph RDF Data Store Amazon.com API Response RDF Ontology Mapped Results Sears.com API Sears.com XML Response Sears.com Response RDF Ontology Sears.com API Response OWL Ontology Figure 6.1: Relationship between the different API technologies and ontologies.

143 Chapter 6. Serviced At Home 130 Developing the vendor API ontologies through the examination of sample product data. Identifying the product concepts to be mapped from the ontologies. Transforming the raw product data into a computer-interpretable format for semantic integration. Mapping the product data by querying a semantic data store. In summary, the methodology taken was ad-hoc in nature since we were uncertain of whether the product vendors leveraged any semantic technologies in their product information. Upon realizing that we would need to do an initial data collection to understand the underlying concepts found in the product information, we decided that the initial data sample would suffice to develop proof-of-concept mappings with the HSO ontology. Once the concepts were identified, we then had to determine which concepts were similar in meaning and could be mapped together to provide us with the expected results. After the initial set of mappings was determined, the raw product data needed to be converted into a usable format for the data store before testing out the mappings in the SPARQL Acquiring Sample Vendor Product Details Before we could develop the vendor ontologies, we needed to determine what kind of concepts are described in the raw product data. For the purposes of this project, we arbitrarily selected five different products that are offered by both Amazon and Sears: 1. Black & Decker LDX112C 12-Volt MAX Lithium-Ion Drill/Driver 2. Tajima Tool Corp - Rapid Pull TPI blade 3. Craftsman 16 oz. Rubber Mallet 4. Delta Faucet U4993-SS Universal Showering Components Shower Arm and Flange, Stainless 5. KNIPEX Comfort Grip Cable Shears In order to run queries to retrieve the five products information against the product vendors APIs, we utilized the following tools:

144 Chapter 6. Serviced At Home Amazon s Product Advertising API ScratchPad This tool is provided by Amazon for developers to easily query the Amazon API. We primarily used this tool to retrieve the Amazon product information in the form of a single line query. Refer to Appendix D.3 for the queries use to retrieve the Amazon product information. 2. Git for Windows (to utilize the curl tool) Since Sears only allows its API to be queried through curl commands, we were required to install this version of Git on Windows to query the Sears API. (Alternatively, the curl software is preinstalled on Linux environments.) Developing the Vendor API Ontologies To create the ontologies required to map the product tags used by both vendors, we created Web Ontology Language (OWL) versions of the metadata tags used in the XML result sets. The OWL ontologies were created using the Protégé Ontology Editor 4. The Amazon API Result Set Ontology For this ontology, we took the results that are generated from the API queries and extract the tags that we require for the mapping process. In this case, since the ItemSearch and ItemLookUp operations return similar metadata tags (refer to Appendix D.1), we were able to develop a rudimentary ontology from the XML output. The ItemLookup operations returns some or all of the attributes for one product, whereas the ItemSearch operation returns products that satisfy a given search criteria. The major difference between the two operations is that many search parameters can be specified in ItemSearch and it is possible to search products by keyword through ItemSearch. Example attributes returned by both operations include the ASIN number, ItemAttributes, Title, ProductGroup, Price, and Manufacturer of the product. Amazon categorizes its offerings in the form of spreadsheets through the Amazon Seller Central website 5. For the purposes of this case study, we only included the cate- 4 For this case study, Protégé version was used and can be found at stanford.edu/. 5

145 Chapter 6. Serviced At Home 132 gorization of the Tools & Home Improvement section of the spreadsheets. For each class of items, we drill down on the various types of items that Amazon has to offer in these categories and add them as subclasses in the API ontology. For example, if we look at the Drills category on Amazon, we find the following: Tools Drills Core Drills Hammer Drills Pistol-Grip Drills From the API results, we created datatype properties for all of the metadata tags that encapsulate a product s information. Some of these tags are outlined in Table 6.1. Object properties in the ontology were not created because of how the product metadata is structured. There were no indications within the returned XML responses whether a product class has object properties; all of the XML responses encapsulated information in strings/literals, integers, and/or doubles. The Sears API Result Set Ontology For this ontology, we took the results that were generated from the API queries and extract the tags that we require for the mapping process. In this case, since the ProductSearch and ProductDetails APIs return similar metadata tags (refer to Appendix D.2), we are able to develop a rudimentary ontology from the XML output. The ProductSearch API allows developers to search and browse the Sears.com, KMart.com, and mygofer.com catalogues for products; similarly, the ProductDetails API allows developers to retrieve product details from the aforementioned vendors. Example attributes returned by both APIs include the Sears PartNumber, MfgPartNumber (if applicable), BrandName, Price, and DescriptionName of the product. Unlike Amazon, Sears does not have any formal documents specifying their categorization of products and offerings. However, all of the Sears verticals (and subcategories)

146 Chapter 6. Serviced At Home 133 Table 6.1: Excerpt of metadata tags found in the Amazon XML result set, along with the names used in OWL relations. Amazon XML Tag OWL Relation Name Functional? ASIN ASIN Yes DetailPageURL DetailPageURL Yes ItemLink ItemLink Yes Description Description Yes URL URL Yes ItemAttributes ItemAttributes Yes Binding Binding Yes Brand Brand Yes CatalogNumberList CatalogNumberList Yes CatalogNumberListElement CatalogNumberListElement Yes EAN EAN Yes EANList EANList Yes EANListElement EANListElement Yes Feature Feature Yes ItemDimensions ItemDimensions Yes Height Height Yes Length Length Yes Weight Weight Yes Width Width Yes Label Label Yes ListPrice ListPrice Yes Amount Amount Yes CurrencyCode CurrencyCode Yes FormattedPrice FormattedPrice Yes Manufacturer Manufacturer Yes Model Model Yes MPN MPN Yes PackageDimensions PackageDimensions Yes PackageQuantity PackageQuantity Yes PartNumber PartNumber Yes ProductGroup ProductGroup Yes ProductTypeName ProductTypeName Yes Publisher Publisher Yes SKU SKU Yes Studio Studio Yes Title Title Yes UPC UPC Yes UPCList UPCList Yes UPCListElement UPCListElement Yes Warranty Warranty Yes

147 Chapter 6. Serviced At Home 134 are listed on a page on the Sears website 6. For the purposes of this case study, we only included the categorization of the Tools section in the API ontology. For example, if we look at the Air Compressors & Air Tools category on Sears, we find the following: Tools Air Compressors & Air Tools Air Compressor Accessories Air Compressors Air Hoses Air Tool Accessories...etc. From the API results, we created datatype properties for all of the metadata tags that encapsulated a product s information. Some of these tags are outlined in Table 6.2. Similar to Amazon, object properties were not created in the ontology because of how the product metadata is structured. There were no indications within the returned XML responses whether a product class has object properties; all of the XML responses encapsulated information in strings/literals, integers, and/or doubles. Table 6.2: Excerpt of metadata tags found in the Sears XML result set, along with the names used in OWL relations. Sears XML Tag OWL Relation Name Functional? PartNumber PartNumber Yes Name Name Yes CutPrice CutPrice Yes SkuPartNumber SkuPartNumber Yes BrandName BrandName Yes CutPrice CutPrice Yes DisplayPrice DisplayPrice Yes CatEntryId CatEntryId Yes MfgPartNumber MfgPartNumber Yes KsnValue KsnValue Yes 6

148 Chapter 6. Serviced At Home Identifying the Concepts to be Mapped Prior to mapping the ontologies together, product concepts that could be potentially mapped together needed to be identified. The following steps were carried out to gain a better understanding of the relations utilized in the ontologies involved: 1. Examination of the XML tags used by Amazon and Sears to determine whether there was any product information that was the same. Where there were similarities, the XML tags were listed side-by-side in a table. 2. Examination of any similar tags found in the GoodRelations and gist ontologies with the product data to determine any similarities across all of the ontologies Preliminary Mappings Between Amazon and Sears Due to the uncertainty of which concepts could be mapped together, the raw XML data were examined and the vendor ontologies were developed to gain a better understanding of the possible concepts that could be mapped. In Table 6.3, we list the direct 1:1 mappings between Amazon and Sears (empty cells indicate that there was no mapping possible). Mapping Brand, Publisher, Manufacturer Tags Due to the limited number of metadata tags used by Sears, we could only map a small subset of their tags with Amazon. For example, Amazon has XML tags to describe the Publisher, Brand, and Manufacturer, whereas Sears only has the BrandName tag to describe the producer of the product. While there are circumstances where the manufacturer of a product is not the same as the brand, we decided to map these concepts together to ensure greater overlap between the different product information. Amazon : P ublisher Sears : BrandN ame (6.3.1) Amazon : Brand Sears : BrandN ame (6.3.2)

149 Chapter 6. Serviced At Home 136 Amazon : M anuf acturer Sears : BrandN ame (6.3.3) Mapping Identifiers (Model, PartNumber, MPN, EAN, SKU) Amazon uses several identifiers to describe a product: the Model (Model), the Model Product Number (MPN), the Part Number (PartNumber), the Stock Keeping Unit (SKU), the International Article Number (EAN), and for books, the International Standard Book Number (ISBN). Since this case study only examined products required for home improvement, ISBN numbers were not considered in our mappings. In contrast, Sears only utilizes two metadata tags that describe product identifiers: MfgPartNumber and SKU. Looking over the sample product data, we noticed that the SKU tags in Sears are empty 7. While the SKU concepts can be mapped together, the mapping is of little or no use since the following mapping cannot be verified with the product data: Amazon : SKU Sears : BrandN ame (6.3.4) Sears does not have any tags to describe the EAN number. Thus, only the MfgPartNumber in Sears could be mapped with Amazon s product identifiers. An interesting point to note is that the contents of Sear s MfgPartNumber are inconsistent; sometimes the model number is listed instead of the manufacturer s part number 8. Thus, we have also mapped MfgPartNumber to Amazon s Model. Amazon : Model Sears : MfgP artnumber (6.3.5) Amazon : P artnumber Sears : MfgP artnumber (6.3.6) Amazon : MP N Sears : MfgP artnumber (6.3.7) 7 Refer to Appendix D.2; the Sku and SkuList tags are empty. 8 For example, KNIPEX Comfort Grip Cable Shears listed in Amazon have a Model of and a MPN value of 95128, but in Sears, the MfgPartNumber is listed as , which is inconsistent with Amazon.

150 Chapter 6. Serviced At Home 137 Mapping Features, Product Titles, and Descriptions Another way to determine whether both vendors offer the same product is to compare their product titles. In Amazon, the Title tag contains the product title, whereas in Sears, the product titles are inconsistently described in the Title and DescriptionName identifiers. Amazon : T itle Sears : T itle (6.3.8) Amazon : T itle Sears : DescriptionN ame (6.3.9) Furthermore, product features are described as literals in Amazon under the Feature tag, whereas Sears also describes product features in literals in the ShortDescription, and LongDescription tags. Since there was no way of breaking down strings of literals to extract product feature information, only the following mappings could be developed to compare the literals found in these tags: Amazon : F eature Sears : ShortDescription (6.3.10) Amazon : F eature Sears : LongDescription (6.3.11) Mapping Product Details and Prices To map product details, Amazon utilizes the Offer tag that encompasses all of the tags described above. Sears also uses a ProductDetail tag that contains all of the product information tags. These two tags can be mapped together, but not verified since the contents are nested tags that further break down the description of a product (refer to Appendices D.1 and D.2). Amazon : Of f er Sears : P roductdetail (6.3.12) With product prices, Amazon uses the Price tag to describe prices, whereas Sears has two different tags for prices: RegularPrice and SalesPrice. These tags are mapped together as follows: Amazon : P rice Sears : RegularP rice (6.3.13)

151 Chapter 6. Serviced At Home 138 Amazon : P rice Sears : SaleP rice (6.3.14) Mapping Product Dimensions and Weight Amazon has the Height, Length, Width, and Weight to describe a product s dimensions and weight. In contrast, Sears does not have any tags to describe product dimensions, so there are no mappings between Amazon and Sears for these product concepts. Table 6.3: Direct mappings between relations found in the Amazon and Sears OWL ontologies. Amazon Relation amazon:publisher / amazon:brand amazon:publisher amazon:brand amazon:sku amazon:model amazon:partnumber amazon:mpn amazon:title amazon:title amazon:feature amazon:feature amazon:manufacturer amazon:height amazon:length amazon:width amazon:weight amazon:offer amazon:ean amazon:price Sears Relation sears:brandname sears:brandname sears:brandname sears:sku sears:mfgpartnumber sears:mfgpartnumber sears:mfgpartnumber sears:title sears:descriptionname sears:shortdescription sears:longdescription sears:brandname sears:productdetail sears:regularprice / sears:saleprice Preliminary Mappings Between HSO and GoodRelations Since the HSO ontology imports relations found in the gist ontology, it was possible to map the gist relations with those found in GoodRelations. Table 6.4 outlines the

152 Chapter 6. Serviced At Home 139 preliminary mappings between the two ontologies and the subsections that follow describe the rationale behind the mappings. Mapping Brand, Publisher, Manufacturer Tags The hasmanufacturer relation in GoodRelations can be mapped to the producedby relation found in gist since both describe the producer of a product. gr : hasm anuf acturer gist : producedby (6.3.15) Mapping Identifiers (Model, PartNumber, MPN, EAN, SKU) GoodRelations uses the model part number (hasmpn) and the International Article Number (hasean UCC-13) as product identifiers. The hasmpn relation is mapped to gist s ProductOffering relation, and the hasean UCC-13 relation is mapped to both the hasbeenallocated and ID relations in gist. Since gist does not have any specific relations to describe the various (international) identifiers, the hasbeenallocated relation can be used to indicate that a product has been allocated an identifier. Similarly, the hasstockkeepingunit relation in GoodRelations is mapped to the ID relation in gist. gr : hasmp N gist : P roductoffering gr : hasean UCC 13 gist : hasbeenallocated gr : hasean UCC 13 gist : ID gr : hasstockkeepingu nit gist : ID

153 Chapter 6. Serviced At Home 140 Mapping Features, Product Titles, and Descriptions GoodRelations has the name relation to describe the product, so it is also mapped to the name relation in gist to describe the product title. gr : name gist : name In GoodRelations, the description relation contains a textual description of the product, so it is mapped to the Offering relation found in gist. Similarly, the hasfeature relation in gist is mapped with description in GoodRelations. gr : description gist : Offering gr : description gist : hasf eature Mapping Product Details and Prices GoodRelations uses the hasmakeandmodel relation to indicate that a product instance has a definable make and model, while the ProductOffering relation in gist describes something that can be warehoused. While the concepts are similar in nature (they both describe a product), they are mapped as follows: gr : hasmakeandmodel gist : P roductoffering Likewise, the ProductOrService relation in GoodRelations describes all products and classes, which is equivalent to the ProductOffering relation in GIST. gr : P roductorservice gist : P roductoffering

154 Chapter 6. Serviced At Home 141 In GoodRelations, the Offering relation specifies a product or service that can be offered with commercial properties [36]. Similarly, in GIST, the Term relation is a description of the specifics of an offer, thus we consider the following equivalence: gr : Offering gist : T erm For currency values, the hascurrencyvalue relation in GoodRelations describes the amount of money for a price per unit, shipping charges, or payment charge [36]; and the currencyvalue relation in gist is the magnitude of a monetary value. gr : hascurrencyv alue gist : currencyv alue Mapping Product Dimensions and Weight In GoodRelations, the height, depth, and width relations are used to describe products, but since there are no relations in gist that describe product dimensions, we declared these relations as subclasses of the Magnitude 9 relation in gist. gr : height gist : Magnitude gr : depth gist : Magnitude gr : width gist : Magnitude The weight and Weight relations in GoodRelations and gist are also mapped together. gr : weight gist : W eight 9 The Magnitude relation indicates a scalar value which is either measured, estimated or set as a reference value [53].

155 Chapter 6. Serviced At Home 142 Table 6.4: Direct mappings between relations found in the GoodRelations and HomeServices/GIST OWL ontologies. GoodRelations gr:hasmakeandmodel gr:stockkeepingunit gr:productorservicemodel gr:hasmpn gr:name gr:description gr:hasmanufacturer gr:description gr:productorservice gr:height gr:depth gr:width gr:weight gr:offering gr:hasean UCC-13 gr:hasean UCC-13 gr:hascurrencyvalue HomeServices/GIST Relation gist:productoffering gist:id gist:productoffering gist:productoffering gist:name gist:hasfeature gist:producedby gist:offering gist:productoffering declare subclassof gist:magnitude declare subclassof gist:magnitude declare subclassof gist:magnitude gist:weight gist:term gist:hasbeenallocated gist:id gist:currencyvalue Transforming XML Product Data into RDF The XML product data was initially converted into the Terse RDF Triple Language (Turtle) (*.ttl) syntax with TopBraid Composer, an integrated development environment for building semantic applications provided by Hunch Manifest, Inc., but the converted data was unusable. The converted data contained many blank nodes that were inserted by the tool and the hierarchical structure of the datatype properties was not preserved. To remedy this, custom Extensible Stylesheet Language Transformations (XSLT) stylesheets were written to convert both vendors product data into the desired RDF format that preserved the structure found in the raw XML. Gleaning Resource Descriptions from Dialects of Languages (GRDDL) The Gleaning Resource Descriptions from Dialects of Languages (GRDDL) is used to obtain RDF data from XML documents and Extensible HyperText Markup Language

156 Chapter 6. Serviced At Home 143 (XHTML) web pages. Transformation algorithms are specified in XSL format in the <head> tag found in the document; GRDDL works by associating transformations using direct references found in the document to be transformed, or indirectly through profile and namespace documents [33]. Appendix D.4.1 briefly outlines the requirements for transforming XML/XHTML documents. Due to time constraints, we did not use GRDDL in this case study but developed custom XSLT stylesheets instead to directly transform the XML data into valid RDF documents. This was due to prior familiarity with developing XSLT stylesheets and the lack of time to learn how to develop transformations and mechanical rules in accordance to the GRDDL specifications of [11]. Furthermore, the XML output generated from the vendor APIs were simple in structure and were not XHTML documents that contained microformat data or embedded semantic markup; it was appropriate to apply a XSLT stylesheet to directly transform the data into the required format. However, we do note that it would be an area of future work to rewrite the XSLT stylesheets in accordance with the GRDDL mechanical rules to ensure greater reusability and to be done in accordance to the World Wide Web Consortium (W3C) standards. XSLT Stylesheets for Amazon and Sears Two XSLT stylesheets were created to convert the raw product data from each vendor into a validated RDF file 10. The xsltproc tool 11 that is included in the XSLT C library for the GNOME desktop environment was used to transform the XML into RDF. Each of the stylesheets matches a template to patterns found in the XML data. For example, in the code snippet below, a template is applied to the entire XML file and assigns the appropriate namespaces in the header of the RDF document. Then, the appropriate 10 All of the RDF triples generated in the transformation have been validated using the W3C s RDF Validation Service: 11 The Windows binaries of the xsltproc tool provided by Igor Zlatković were used to apply the stylesheets to the raw XML data. Instructions on how to apply the stylesheets to product data can be found in Appendix D.4.2.

157 Chapter 6. Serviced At Home 144 attributes and properties are added; the values found in the XML tags are extracted from the XML document using the xsl:value-of select statement. Code 6.1: Sample XSLT template to transform an XML document into a RDF document. <x s l : t e m p l a t e match= / > <x s l : e l e m e n t name= rdf:rdf x m l n s : x s l= h t t p : //www. w3. org /1999/ XSL/ Transform x m l n s : f o a f= h t t p : // xmlns. com/ f o a f /0.1/ x m l n s : r d f= h t t p : //www. w3. org /1999/02/22 rdf syntax ns# x m l n s : r d f s= h t t p : //www. w3. org /2000/01/ rdf schema# x m l n s : s e a r s= h t t p : //www. example. org / schemas / s e a r s# > <r d f : D e s c r i p t i o n> <x s l : a t t r i b u t e name= r d f : a b o u t ><x s l : v a l u e o f s e l e c t= / ProductDetail / SoftHardProductDetails / DescriptionName /></ x s l : a t t r i b u t e> <s e a r s : P r o d u c t D e t a i l> <s e a r s : S o f t H a r d P r o d u c t D e t a i l s> <sears:partnumber> <x s l : v a l u e o f s e l e c t= / ProductDetail / SoftHardProductDetails / PartNumber /> </ sears:partnumber> The stylesheets are organized and designed according to the original structure found in the XML documents. For example, in the Amazon product data, we have the following format: Code 6.2: Sample XML from Amazon product data. <ItemAttributes> <Binding>Tools &amp ; Home Improvement</ Binding> <Brand>Black &amp ; Decker</Brand> <CatalogNumberList> <CatalogNumberListElement> </ CatalogNumberListElement> <CatalogNumberListElement> LDX112C</ CatalogNumberListElement> </ CatalogNumberList> <EAN> </EAN>... </ ItemAttributes>

158 Chapter 6. Serviced At Home 145 This format is retained in the RDF version of the product data in the templates; for the above example, the vendor namespace (amazon or sears) is appended to the productspecific tags and the appropriate RDF attributes are added where needed. Code 6.3: RDF version of XML product data. <rdf:rdf x m l n s : r d f= h t t p : //www. w3. org /1999/02/22 rdf syntax ns# > <r d f : D e s c r i p t i o n r d f : a b o u t= B004443WVW > <amazon:itemattributes xmlns:amazon= h t t p : //www. example. org / schemas /amazon# rdf:parsetype= Resource > <amazon:binding>tools &amp ; Home Improvement</ amazon:binding> <amazon:brand>black &amp ; Decker</ amazon:brand> <amazon:catalognumberlist rdf:parsetype= Resource > <amazon:catalognumberlistelement> </ amazon:catalognumberlistelement> <amazon:catalognumberlistelement> LDX112C</ amazon:catalognumberlistelement> </ amazon:catalognumberlist> <amazon:ean> </amazon:ean>... </ amazon:itemattributes> </ r d f : D e s c r i p t i o n> </ rdf:rdf> After these stylesheets were applied to the XML product data, the RDF product data was imported 12 into the AllegroGraph RDF data store Mapping the Vendor Product Data In order to test the product mappings, the mappings discussed in Sections and were converted into RDF syntax and imported into AllegroGraph. As well, RDF subtheories were extracted 13 from the vendor OWL ontologies and imported into Allegro- Graph. To test the mappings, SPARQL queries based on the mapped relations specified 12 Detailed instructions on how to import the product data into AllegroGraph can be found in Appendix D The OWL ontologies were converted into RDF syntax. Since there were no semantics in the OWL ontologies, the conversion to RDF syntax did not affect the semantics of the ontologies.

159 Chapter 6. Serviced At Home 146 in Tables 6.3 and 6.4 were written to retrieve and compare product information. These SPARQL queries are discussed in more detail in the next section. 6.4 Product Mappings in RDF and OWL The mappings outlined in Sections and use the owl:equivalentproperty relation in OWL to outline the equivalence between the concepts. We modified the mappings during this part of the project so that the HSO ontology maps into each vendor individually, as shown in Figure 6.2 below. HSO e.g., gist:producedby Amazon e.g., Amazon:Brand GoodRelations e.g., gr:hasbrand Sears e.g., Sears:BrandName Figure 6.2: Relationship between the mappings across the different ontologies Mappings Between HSO and Amazon This section outlines the mappings between the HomeServices Ontology and Amazon ontology in the Turtle format 14 using the owl:equivalentproperty relation. In OWL, the owl:equivalentproperty construct is used to state that two properties (relations) are equivalent. Thus, in the mappings below, the triples are listed in the subject-predicate-object format; for example, the gist:productoffering relation is equivalent to the amazon:publisher relation. 14 This format is also accepted by AllegroGraph in conjunction with the RDF sytanx and is easier to display in print.

160 Chapter 6. Serviced At Home 147 Mapping 6.4: Mapping between HSO and Amazon. g i s t : ProductOffering owl : equivalentproperty amazon : Publisher. g i s t : ProductOffering owl : equivalentproperty amazon : Brand. g i s t : ProductOffering owl : equivalentproperty amazon : hasmodel. g i s t : ProductOffering owl : equivalentproperty amazon :MPN. g i s t : name owl : e q u i valentproperty amazon : T i t l e. g i s t : hasfeature owl : e quivalentproperty amazon : Feature. g i s t : hasfeature owl : e quivalentproperty amazon : Feature. g i s t : producedby owl : e quivalentproperty amazon : Manufacturer. g i s t : Term owl : e q u i valentproperty amazon : O f f e r. g i s t : hasbeenallocated owl : equivalentproperty amazon :EAN. g i s t : ID owl : e q u i v a l entproperty amazon :EAN. g i s t : currencyvalue owl : equivalentproperty amazon : Price Mappings Between HSO and Sears This section outlines the mappings between the HomeServices Ontology and Sears ontology in Turtle form using the owl:equivalentproperty relation. Mapping 6.5: Mapping between HSO and Sears. g i s t : ProductOffering owl : equivalentproperty s e a r s : BrandName. g i s t : ProductOffering owl : equivalentproperty s e a r s : MfgPartNumber. g i s t : ProductOffering owl : equivalentproperty s e a r s : MfgPartNumber. g i s t : name owl : e q u i valentproperty s e a r s : T i t l e. g i s t : hasfeature owl : e quivalentproperty s e a r s : S h o r t D e s c r i p t i o n. g i s t : hasfeature owl : e quivalentproperty s e a r s : LongDescription. g i s t : producedby owl : e quivalentproperty s e a r s : BrandName. g i s t : Term owl : e q u i valentproperty s e a r s : ProductDetail. g i s t : currencyvalue owl : equivalentproperty s e a r s : RegularPrice. g i s t : currencyvalue owl : equivalentproperty s e a r s : S a l e P r i c e Mappings Between Amazon and Sears From the two previous sections, the following bidirectional mappings should be inferred by AllegroGraph s reasoner tool. These mappings have been included to indicate which concepts in both vendor ontologies should be mapped together. Mapping 6.6: Mapping between Amazon and Sears.

161 Chapter 6. Serviced At Home 148 amazon : P ublisher owl : e q uivalentproperty s e a r s : BrandName. amazon : Brand owl : e quivalentproperty s e a r s : BrandName. amazon :SKU owl : e q u i valentproperty s e a r s : Sku. amazon : Model owl : equivalentproperty s e a r s : MfgPartNumber. amazon : PartNumber owl : e quivalentproperty s e a r s : MfgPartNumber. amazon :MPN owl : e q u i valentproperty s e a r s : MfgPartNumber. amazon : T i t l e owl : equivalentproperty s e a r s : T i t l e. amazon : T i t l e owl : equivalentproperty s e a r s : DescriptionName. amazon : Feature owl : e q uivalentproperty s e a r s : S h o r t D e s c r i p t i o n. amazon : Feature owl : e q uivalentproperty s e a r s : LongDescription. amazon : Manufacturer owl : equivalentproperty s e a r s : BrandName. amazon : O f f e r owl : equivalentproperty s e a r s : ProductDetail. amazon : P rice owl : equivalentproperty s e a r s : RegularPrice. amazon : P rice owl : equivalentproperty s e a r s : S a l e P r i c e Mappings Between HSO and GoodRelations This section outlines the mappings between the HomeServices Ontology and GoodRelations ontology in Turtle form using the owl:equivalentproperty relation. Mapping 6.7: Mapping between HSO and GoodRelations. gr : hasmakeandmodel owl : equivalentproperty g i s t : ProductOffering. gr : StockKeepingUnit owl : equivalentproperty g i s t : ID. gr : ProductOrServiceModel owl : equivalentproperty g i s t : ProductOffering. gr : hasmpn owl : e q u ivalentproperty g i s t : ProductOffering. gr : hasname owl : e q u i valentproperty g i s t : name. gr : d e s c r i p t i o n owl : e quivalentproperty g i s t : hasfeature. gr : hasmanufacturer owl : equivalentproperty g i s t : producedby. gr : d e s c r i p t i o n owl : e quivalentproperty g i s t : O f f e r i n g. gr : ProductOrService owl : equivalentproperty g i s t : ProductOffering. gr : weight owl : e q u ivalentproperty g i s t : Weight. gr : O f f e r i n g owl : e quivalentproperty g i s t : Term. gr : hasean UCC 13 owl : e q uivalentproperty g i s t : hasbeenallocated. gr : hasean UCC 13 owl : e q uivalentproperty g i s t : ID. gr : hascurrencyvalue owl : equivalentproperty g i s t : currencyvalue.

162 Chapter 6. Serviced At Home Testing the Mappings via SPARQL Queries In order to utilize the tools provided by Hunch Manifest, Inc., the product data and mappings described in the previous section are expressed in a language that can be utilized with the AllegroGraph RDF data store. This section briefly outlines the queries that were written in SPARQL to test the mappings. Appendices D.5 and D.6 outline the settings used in AllegroGraph and the results returned from the SPARQL queries used to test the mappings, respectively. Our original intention of utilizing the HSO-Amazon and HSO-Sears mappings was to allow the inference of the bidirectional Amazon-Sears mappings from Section 6.4.3, but the reasoner tool in AllegroGraph could not make this inference. As a result of this limitation, only the direct 1:1 mappings between Amazon and Sears are tested via queries that compare and retrieve product information from both vendors. Thus, the following list summarizes the SPARQL queries that were run in AllegroGraph: Section describes a query to find the cheapest products offered by Sears and Amazon. Section describes a query that finds the cheapest products offered by Sears and Amazon based on a keyword. Section describes a query that finds the average price of products (specified by keyword) offered by Sears and Amazon. Section describes a query that finds the average price of all products offered by Sears and Amazon. Section describes a query that finds the average price of products offered by Sears and Amazon based on a keyword. Section describes a query that finds the combined product attributes of a product offered by both vendors. Section describes a federated query that combines the product data with information from DBPedia.

163 Chapter 6. Serviced At Home Cheapest Products The following query asks, Who offers the cheapest products and what is the price? The mapping between Amazon and Sears is indicated by matching the products with the sears:mfgpartnumber and amazon:mpn predicates; the query filters out the product with the lowest price and lists the manufacturer s part number and the price. Table D.1 in Appendix D.6 lists the results of this query. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT DISTINCT?mfgno? minprice WHERE {? s e a r s p r o d u c t sears : MfgPartNumber?mfgno.? s e a r s p r o d u c t sears : S a l e P r i c e? s e a r s p r i c e. BIND ( xsd : decimal (? s e a r s p r i c e ) AS? minprice ) OPTIONAL{? amazonproduct amazon :MPN? mfgno.?amazontemp amazon : ListPriceFormattedPrice? amazonprice.? amazonproduct amazon : L i s t P r i c e?amazontemp. BIND ( xsd : decimal ( substr (? amazonprice, 2 ) ) AS? o t h e r p r i c e ) FILTER(? o t h e r p r i c e <? minprice ) } FILTER (! bound (? o t h e r p r i c e ) ). } Code 6.8: SPARQL query to find the cheapest price of products Cheapest Products Based on Keyword The following query asks, Who offers the cheapest drill and what is the price? Since product features are described in literals in both vendors tags, we will need to utilize the FILTER regex switch in the SPARQL query. The mapping between Amazon and Sears is indicated by matching the products with the sears:mfgpartnumber and amazon:mpn predicates; the query uses the regular expression REGEX switch in

164 Chapter 6. Serviced At Home 151 SPARQL to filter out the cheapest products with the drill keyword in its product name, and lists the manufacturer s part number, price, and product name. Table D.2 in Appendix D.6 lists the results of this query. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT DISTINCT?mfgno? minprice? p r o d T i t l e WHERE {? s e a r s p r o d u c t sears : MfgPartNumber?mfgno.? s e a r s p r o d u c t sears : S a l e P r i c e? s e a r s p r i c e. BIND ( xsd : decimal (? s e a r s p r i c e ) AS? minprice )? s e a r s p r o d u c t sears : DescriptionName? p r o d T i t l e. OPTIONAL{? amazonproduct amazon :MPN? mfgno.?amazontemp amazon : ListPriceFormattedPrice? amazonprice.? amazonproduct amazon : L i s t P r i c e?amazontemp. BIND ( xsd : decimal ( substr (? amazonprice, 2 ) ) AS? o t h e r p r i c e ) FILTER(? o t h e r p r i c e <? minprice )? amazonproduct amazon : T i t l e? p r o d T i t l e. } FILTER (! bound (? o t h e r p r i c e ) ). FILTER regex (? prodtitle, d r i l l, i ). } Code 6.9: SPARQL query to find the cheapest price of products based on the drill keyword Average Price of Products Based on Keyword The following query returns the average price of products based on a keyword. In this case, it returns the average price for both companies, along with the product titles used. The mapping between Amazon and Sears is indicated by matching the products with the sears:descriptionname and amazon:title predicates, where the regular expression REGEX switch in SPARQL filters out products that contain the keyword drill ; the query then calculates the average price for the product per vendor, and lists the product

165 Chapter 6. Serviced At Home 152 titles for both vendors and their respective average prices. Table D.3 in Appendix D.6 lists the results of this query. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT? s e a r s T i t l e? amazontitle (AVG(? se arsval ) AS? searsavg ) ( AVG(? amazonval ) AS? amazonavg ) WHERE{? s e a r s p r o d u c t sears : DescriptionName? s e a r s T i t l e.? s e a r s p r o d u c t sears : S a l e P r i c e? s e a r s p r i c e. BIND ( xsd : decimal (? s e a r s p r i c e ) AS? searsval )? amazonproduct amazon : T i t l e? amazontitle.?amazontemp amazon : ListPriceFormattedPrice? amazonprice.? amazonproduct amazon : L i s t P r i c e?amazontemp. BIND ( xsd : decimal ( substr (? amazonprice, 2 ) ) AS?amazonVal ) FILTER regex (? s e a r s T i t l e, d r i l l, i ). FILTER regex (? amazontitle, d r i l l, i ). } GROUP BY? s e a r s T i t l e? amazontitle Code 6.10: SPARQL query to find the average price of products based on the drill keyword Average Price of Products for Both Vendors The following SPARQL query finds the average price of products, based on the model product number, for both vendors. The mapping between Amazon and Sears is indicated by matching the products with the sears:mfgpartnumber and amazon:mpn predicates; the manufacturer s part numbers and average prices for both vendors are listed in the results. It should be noted that the matches between sears:mfgpartnumber and amazon:mpn may not give desired results due to the fact that the sears:mfgpartnumber predicate may contain the incorrect manufacturer s part number, as previously discussed in Section Table D.4 in Appendix D.6 lists the results of this query.

166 Chapter 6. Serviced At Home 153 PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT?mfgno (AVG(? s e a rsval ) AS? searsavg ) (AVG(? amazonval ) AS? amazonavg ) WHERE{? s e a r s p r o d u c t sears : MfgPartNumber?mfgno.? s e a r s p r o d u c t sears : DescriptionName? s e a r s T i t l e.? s e a r s p r o d u c t sears : S a l e P r i c e? s e a r s p r i c e. BIND ( xsd : decimal (? s e a r s p r i c e ) AS? searsval )? amazonproduct amazon :MPN? mfgno.? amazonproduct amazon : T i t l e? amazontitle.?amazontemp amazon : ListPriceFormattedPrice? amazonprice.? amazonproduct amazon : L i s t P r i c e?amazontemp. BIND ( xsd : decimal ( substr (? amazonprice, 2 ) ) AS?amazonVal ) } GROUP BY?mfgno Code 6.11: SPARQL query to find the average price of products for both vendors Combination of Product Data with DBPedia Data The following SPARQL query combines the product data with information from DB- Pedia 15 to give a description of the product s brand company that produces that was founded more than 10 years ago. The mapping between Amazon and Sears is indicated by matching the products with the sears:brandname and amazon:brand predicates to ensure that both products have the same brand; this query is then combined with a federated query that queries the DBPedia SPARQL endpoint to find companies that match the brand name and to filter out these results based on the companies founding year. The combined results are then filtered according to whether the companies were founded in the past ten years. Table D.7 in Appendix D.6 lists the results of this 15 A LinkedData that extracts structured content from Wikipedia; DBpedia allows users to query relationships and properties associated with Wikipedia resources, including links to other related datasets.

167 Chapter 6. Serviced At Home 154 query. We note that this query is not entirely correct since the company/brand names are appended to a fixed URI and the query does not ensure that the returned entities are actually companies. It is suggested to use either the dbpedia-owl:organisation or dbpprop:companyname relations to verify that the returned entities in the federated query are actually companies listed in DBPedia. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> PREFIX dbpedia owl : <http : / / dbpedia. org / r e s o u r c e / c l a s s e s#> PREFIX dbpprop : <http : / / dbpedia. org / property/> SELECT? productbrand? foundingyear? s e a r s t i t l e? amazontitle? branddbpediauri WHERE {{ SELECT? productbrand? s e a r s t i t l e? amazontitle WHERE {? s e a r s p r o d u c t sears : BrandName? productbrand.? s e a r s p r o d u c t sears : DescriptionName? s e a r s t i t l e.? amazonproduct amazon : Brand? productbrand.? amazonproduct amazon : T i t l e? amazontitle. BIND(URI(CONCAT( http : / / dbpedia. org / r e s o u r c e /,? productbrand ) ) AS? branddbpediauri ). } } SERVICE <http : / / dbpedia. org / sparql > { SELECT DISTINCT? foundingyear WHERE {?branddbpediauri <http : / / dbpedia. org / property / foundation>? foundingyear. } FILTER (? foundingyear >1500 && (2013? foundingyear ) >= 10 ) } ORDER BY DESC(? foundingyear ) ASC(? productbrand ) LIMIT 1000 Code 6.12: Federated SPARQL query to combine the product with DBPedia data.

168 Chapter 6. Serviced At Home Average Price of Products for Both Vendors Based on Keyword The following SPARQL query finds the average price of products, based on the model product number and drill keyword, for both vendors. The mapping between Amazon and Sears is indicated by matching the products with the sears:mfgpartnumber and amazon:mpn predicates. It should be noted that the matches between sears:mfgpartnumber and amazon:mpn may not give desired results due to the fact that the sears:mfgpartnumber predicate may contain the incorrect manufacturer s part number, as previously discussed in Section The regular expression REGEX switch in SPARQL filters out products that contain the keyword drill, and the query then calculates the average price for the product per vendor, and lists the product titles for both vendors and their respective average prices. Table D.5 in Appendix D.6 lists the results of this query. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT?mfgno (AVG(? s e a rsval ) AS? searsavg ) (AVG(? amazonval ) AS? amazonavg ) WHERE{? s e a r s p r o d u c t sears : MfgPartNumber?mfgno.? s e a r s p r o d u c t sears : DescriptionName? s e a r s T i t l e.? s e a r s p r o d u c t sears : S a l e P r i c e? s e a r s p r i c e. BIND ( xsd : decimal (? s e a r s p r i c e ) AS? searsval )? amazonproduct amazon :MPN? mfgno.? amazonproduct amazon : T i t l e? amazontitle.?amazontemp amazon : ListPriceFormattedPrice? amazonprice.? amazonproduct amazon : L i s t P r i c e?amazontemp. BIND ( xsd : decimal ( substr (? amazonprice, 2 ) ) AS?amazonVal ) FILTER ( regex (? s e a r s T i t l e, d r i l l, i ) regex (? amazontitle, d r i l l, i ) ) } GROUP BY?mfgno Code 6.13: SPARQL query to find the average price of products for both vendors that are drills.

169 Chapter 6. Serviced At Home All Known Product Attributes for a Combined Product Model Query 6.14 finds all of the known product attributes for a product match for both vendors. The match is based on the model product number (sears:mfgpartnumber and amazon:mpn), and the features and descriptions for both vendors are listed alongside the model number in the results. The results are then ordered according to the model product number. Note that there are two description variables for Sears; this is due to the inconsistent metadata stored in the ShortDescription and LongDescription tags: both of these tags contain Sears product attributes. Table D.6 in Appendix D.6 lists the results of this query. PREFIX gist : <http : / / o n t o l o g i e s. s e m a n t i c a r t s. com/ gist#> PREFIX hso : <http : / /www. example. org / schemas /hso#> PREFIX rdf : <http : / /www. w3. o r g /1999/02/22 rdf syntax ns#> PREFIX rdfs : <http : / /www. w3. o r g /2000/01/ rdf schema#> PREFIX sears : <http : / /www. example. or g / schemas / sears#> PREFIX amazon : <http : / /www. example. org / schemas /amazon#> SELECT?mfgno? amazontitle? amazondescription? s e a r s T i t l e? s e a r s d e s c r i p t i o n? s e a r s d e s c r i p t i o n 2 WHERE{? s e a r s p r o d u c t sears : MfgPartNumber?mfgno.? s e a r s p r o d u c t sears : LongDescription? s e a r s d e s c r i p t i o n.? s e a r s p r o d u c t sears : S h o r t D e s c r i p t i o n? s e a r s d e s c r i p t i o n 2.? s e a r s p r o d u c t sears : DescriptionName? s e a r s T i t l e.? amazonproduct amazon :MPN? mfgno.? amazonproduct amazon : Feature? amazondescription.? amazonproduct amazon : T i t l e? amazontitle. } ORDER BY?mfgno Code 6.14: SPARQL query to find all product attributes for a combined product model. Each of the aforementioned queries produced successful results, as listed in Appendix D.6. With exception to the federated query, all of the queries returned the expected product matches and price values from our sample dataset. As noted earlier, the federated query requires further refinement to ensure that the returned entities are

170 Chapter 6. Serviced At Home 157 companies listed in DBPedia; since the query is still able to retrieve the company information from the DBPedia SPARQL endpoint, we still consider this mapping between product information and DBPedia to be successful. We note that our primary goal of this portion of the project was to test the mappings to make sure they were correct, and remind the reader that the focus of the project was to outline the methodology taken to develop these mappings as a proof of concept for Hunch Manifest, Inc. 6.6 Discussion The following section discusses the limitations of the applied methodologies in developing the vendor API ontologies and performing the data store queries Limitations of the Vendor Ontologies Due to the fact that the vendor API ontologies were developed based on the returned XML product data, they are limited in only providing a glimpse of how the product information is structured. Since no additional semantics or axioms were included in the OWL ontologies, these vendor ontologies are limited in what can be done with them in terms of reasoning. For example, it is still possible to reason with these OWL vendor ontologies to determine whether a class of products is part of another class, or to determine any subproperties of a given property Usage of RDF/XML to Test the Mappings Since Hunch Manifest, Inc. strongly preferred the testing of mappings to be done in AllegroGraph, the ontologies needed to be converted from OWL into RDF/XML in Protege. Since there were no additional axioms in the OWL ontologies, we were able to test the mappings without issues; otherwise, they could not have been expressed in RDF/XML due to the lack of expressivity when one traverses down the Semantic Web

171 Chapter 6. Serviced At Home 158 Stack from OWL to RDF (see Figure 6.3). It may become problematic in the future if axioms and/or more complex mappings are added to these vendor OWL ontologies and cannot be tested due to the expressive limitations of SPARQL and RDF/XML. Figure 6.3: The Semantic Web Stack of the hierarchy of languages found in the Semantic Web; image from [7] The Need for Adoption of Semantic Technologies in e- Commerce From this case study, we have seen how there is a lack of semantic technologies in e- commerce, particularly with vendors as large and well-known as Amazon and Sears. Since APIs provide a vendor with exposure to larger customer groups, the need for semantic technologies to be utilized in conjunction with the APIs has become prevalent, whether the semantic technologies adopted are with ontologies or the inclusion of Linked Data. With this case study, we have shown that there needs to be a greater push in e-commerce for more applications of semantic technologies to allow greater reuse of ontologies, deductive reasoning of rules in the product information data sets, and to

172 Chapter 6. Serviced At Home 159 provide (home improvement) industries with a greater niche of customers No One General Methodology for Ontology Mapping Furthermore, there does not appear to be one general methodology for developing ontology mappings. Since we were initially unsure of what kind of product information the vendor APIs utilized, we took longer than intended to determine what product concepts and properties could be mapped together between the two companies; as well, a more roundabout approach to developing the vendor OWL ontologies was taken due to changes in the project requirements and due to the lack of semantic technologies being used by the vendors. Despite these frustrations, the exploratory nature of this methodology has enabled us to realize that the adoption of semantic web technologies within e-commerce should become more prevalent. As well, there needs to be a greater push for mid-level ontologies that are slightly more specific than upper ontologies but are still general enough to allow vendor ontologies to map into them for greater reuse Existing Product Ontologies are Insufficient Throughout the course of this project, we have seen that existing product ontologies, including GoodRelations, were not sufficient enough to be used in the mapping process to describe products. Existing product ontologies include the Product Types Ontology Extension for GoodRelations and the Google Product Taxonomy. Both of these ontologies were insufficient to describe the actual features, not just the business aspects, of products and are described below. The Product Types Ontology is an extension of GoodRelations that provides a higher level of granularity to describe products. It provides product class definitions for every word found in the English Wikipedia pages [37]. The Product Types Ontology (PTO) uses the predefined GoodRelations properties for:

173 Chapter 6. Serviced At Home 160 gr:category gr:color gr:condition gr:depth gr:hasean UCC-13 gr:hasgtin-14 gr:hasmpn gr:hasmanufacturer gr:hasstockkeepingunit gr:height gr:isaccessoryorsparepartfor gr:isconsumablefor gr:issimilarto gr:weight gr:width The pitfall of this product ontology is that, while it may have classes of product categories, product features such as whether a product is battery-powered, solar-powered, or requires an AC adapter, are not adequately described. Similarly, the Google Product Taxonomy 16 is a tree of categories that aids users in classifying their products in the Google Merchant Centre 17. The Google Shopping site allows consumers to easily find product listings on Google, where the product taxonomy lists all of the possible values the Google product category attribute can take on in order for an item to be displayed on Google Shopping. Like the Product Types Ontology, this Google Product Taxonomy only describes the categories under which products follow, and does not describe any product features. 6.7 Insights From this case study, we have gathered additional insight on the ontology mapping process, along with the difficulties of developing semantics for vendor product specifications which lack the application of semantic formalisms within e-commerce. This project has outlined potential research and business areas that may be of interest within the ontology and e-commerce communities, as well as a starting point for vendors to adopt semantic

174 Chapter 6. Serviced At Home 161 technologies.

175 Chapter 7 Conclusion Throughout this thesis we have outlined four different relationships that demonstrate how ontologies can be decomposed into modules, combined together, provide meaning to other unstructured ontologies, and used to define constructs in new ontologies. In doing so, we sought to answer the larger question of how relationships between ontologies can be axiomatized in first-order logic. We began with the DOLCE ontology that captures the ontological categories underlying natural language and human common sense. We presented our approach to modularizing this ontology with the aid of translation definitions and theories found in COLORE, and presented the following modules: T dolce taxonomy, T dolce mereology, T dolce time mereology, T dolce present, T dolce temporary parthood, and T dolce constitution. We also introduced bipartite incidence structures that were used in the modularization process. Thus, we were able to verify the modules by showing that the models of the axioms are the intended models of the ontology. Next, we proceeded to determine additional relationships between the DOLCE and PSL ontologies based on similarities found between both ontologies notions of participation. We combined theories of time points and time intervals together from COLORE to create a new temporal theory that is used with the time interval version of T psl core to 162

176 Chapter 7. Conclusion 163 connect the DOLCE ontology with PSL. We were then able to show that theories from DOLCE can faithfully interpret theories found in PSL. We explored the notion of semantic augmentation with the CIMOSA framework and provided additional semantics to the framework constructs. We developed a first-order ontology for CIMOSA with the intention of linking the constructs with concepts and axioms found in PSL. In the process, however, we discovered that the technical jargon and ambiguous phrasing found in the CIMOSA documentation hindered our understanding of the intended semantics of the framework constructs; as well, the ambiguity and uncertainty surrounding the role of CIMOSA s dimensions in the specification of their behavioural rule sets also prevented us from axiomatizing some of the constructs in firstorder logic. We discussed the implications of these issues along with future areas of work pertaining to the looping rules found in CIMOSA. Finally, we developed and examined the applicability of mappings between two ontologies where rich sets of axioms were not provided. We first needed to understand which concepts were common between Amazon, Sears, and the HSO ontologies before attempting mapping them together. This case study outlined and demonstrated the ad-hoc methodology required to map these two ontologies together. We discussed the barriers to developing seamless mappings between these vendor ontologies and the insights gained from our attempts of axiomatizing, however trivial they may be, the concept equivalences between them. Revisiting our initial goal of examining and axiomatizing the relationships found between ontologies, we can say that our ventures into examining these relationships have been rewarding. Not only have we completed a partial verification of the DOLCE ontology, we have provided an example of how translation definitions can be used to modularize and verify a widely used upper ontology. As well, we have explicitly outlined the relationships between DOLCE and PSL, and between DOLCE and time ontologies found in COLORE. However, while we have managed to axiomatize these relationships

177 Chapter 7. Conclusion 164 found in the various ontologies, there are a few open issues in these case studies that need to be addressed in future work. 7.1 Open Issues While we have attempted to axiomatize four selected ontology relationships of ontology decomposition, ontology composition, semantic augmentation, and ontology mapping, we have just barely scratched the surface of axiomatizing these relationships. There are many other ontologies to consider when examining these relationships with COLORE theories, such as the BFO, SUMO, and OpenCyc upper ontologies. As we have mentioned earlier, we have partially modularized the DOLCE ontology. Since we only have the T dolce taxonomy, T dolce time mereology, T dolce present, T dolce mereology, T dolce temporary parthood, and T dolce constitution modules completed, the verification of the T dolce dependence, T dolce quality, and T dolce quales modules still needs to be completed. A potential issue that may arise with the verification of the T dolce dependence module is how it interacts with the T dolce temporary parthood and T dolce taxonomy modules since it combines axioms from both. Furthermore, the faithful interpretations between H dolce and H periods, and between H periods and H combined time have not been proven and need to be carried out. With respect to the proposed CIMOSA ontology, the current axiomatization has not been verified. In particular, the looping rules in Section are similar to the graphical formalisms found in the IDEF3 and the UML modelling languages. Since IDEF3 allows cyclic orderings in its formalisms, additional work will need to be done to determine how to represent these orderings axiomatically in CIMOSA; we may need to utilize the subactivity occurrence soo(s, a) and subactivity precedence soo precedes(s 1, s 2, a) relations from PSL, or other precedence relations found in other process ontologies, to accurately axiomatize these looping rules. Another open issue with the axiomatization of the CIMOSA constructs is that we are unsure what is the correct characterization of the

178 Chapter 7. Conclusion 165 intended models of the ontology. As discussed in Section 5.6, we are unsure of whether the proposed ontology s axioms accurately reflect the semantics that are embedded in [1], [39], and [40], so the axioms need to be further refined and verified using a theorem prover such as Prover Future Work Future work should include considerations for developing a general methodology to design and test the correctness of translation definitions for defined relations. In particular, attention should be paid with regards to how one can develop translation definitions between two ontologies that correctly translate the meaning of one concept from one ontology into terminology used in the other. In Chapter 3, the process of developing correct translation definitions between the DOLCE and PSL theories required trial and error to modify the translation definitions after iterations of theorem proving experiments failed to generate proofs. In addition, there needs to be a definitive distinction between the terminologies distinguishing ontology relationships. While we have not made any distinctions between the terminologies found in the literature, we list some of the terms here as an example: bridge axioms, ontology alignment, ontology articulation, ontology integration, ontology mapping, ontology merging, ontology reconciliation, ontology transformation, and ontology translation. By making clear and agreed-upon distinctions between the terminologies used to describe ontology relationships, it further assists the IAOA and OntoIOp groups with creating open standards within the ontology community and to capture the general consensus of the meaning of these terms. Other directions for future work would be to utilize the proposed CIMOSA ontology to aid the IAOA with their goal of providing semantics to already-developed standards. The proposed CIMOSA ontology can be used as an example within the IAOA of de-

179 Chapter 7. Conclusion 166 veloping a general methodology that could be adopted by others to provide semantics and additional meaning to standardized constructs found in other ISO documents. Additionally, another proposition would be to implement a methodology in place to utilize ontologies to remove the ambiguity found in standards documents which should be in place when the standards committee discusses and revises the various definitions of terms to include in the standard. Additionally, the development of a potential framework of negotiation that allows ontology designers to come up multiple axiomatizations that can be used and applied in different contexts. In the case of disagreement on how concepts are axiomatized, offering alternative axiomatizations provides users with a flexible ontology that suits their needs. A drawback of offering variations of axiomatizations, however, is that it may be too difficult to maintain the ontology if it contains many axioms. As well, it would be beneficial for the ontology community if a methodology for designing ontologies from scratch was developed for first-time ontology users. While both the Amazon and Sears API ontologies described in Chapter 6 were minimal and did not contain any rich semantics, it would be beneficial if there were some guidelines to aid the process of adding additional semantics from raw XML product data. In addition, the development of a general product ontology that describes actual product features, in contrast to the GoodRelations ontology and its lack of relations to describe product features and not just attributes from a business perspective, would be greatly beneficial for product vendors to describe product information in a structured manner. Since both product ontologies developed for this thesis lack rich sets of axioms that describe product information, it would also be of interest to analyze whether the GoodRelations ontology is sufficient to be used to map other less-structured/weak ontologies together. Furthermore, we have outlined our extensive use of the COLORE repository to store the modules of DOLCE throughout this thesis. It would be valuable if the repository can be used in conjunction with automated reasoners: additional repository functionality should be considered to facilitate the reuse of these COLORE theories, and the

180 Chapter 7. Conclusion 167 storage and organization of lemmas and theory subsets to help improve theorem prover performance. As we have seen in Chapters 3 and 4, the techniques of using lemmas and excluding unnecessary axioms may allow an increase in efficiency of the automated reasoner, but require manual modifications to the experiment input files; the amount of manual labour involved to modify these input files does not abode well when theories have many axioms and makes it difficult to find relationships between the numerous theories stored in COLORE. By developing automated tools to assist us with discovering and proving meta-theoretic relationships of theories stored in COLORE, such tools would greatly assist us with this task of axiomatizing and analyzing these relationships between ontologies. With this in mind, another area of future work would be to extend the functionality of COLORE to for applications in ontology engineering and design, ontology evaluation, and semantic integration.

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188 Bibliography 175 [62] J. van Benthem. The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse. Synthese Library. Springer, [63] Francois Vernadat. The CIMOSA Languages. Handbook on Architectures of Information Systems International Handbooks on Information Systems, P. Bernus et al., Springer-Verlag, Heidelberg, pages , [64] Evelyne Viegas, Boyan Onyshkevych, Victor Raskin, and Sergei Nirenburg. From Submit To Submitted Via Submission: On Lexical Rules In Large-Scale Lexicon Acquisition. In Proceedings of the 34th annual meeting on Association for Computational Linguistics, ACL 96, pages 32 39, Stroudsburg, PA, USA, Association for Computational Linguistics. [65] Gio Wiederhold. An Algebra for Ontology Composition. In Proceedings of 1994 Monterey Workshop on Formal Methods, pages 56 61, [66] Martin Zelm, François B. Vernadat, and Kurt Kosanke. The CIMOSA Business Modelling Process. Comput. Ind., 27(2): , October [67] Antoine Zimmermann, Markus Krötzsch, Jérôme Euzenat, and Pascal Hitzler. Formalizing Ontology Alignment and its Operations with Category Theory. In Proceedings of the 2006 conference on Formal Ontology in Information Systems: Proceedings of the Fourth International Conference (FOIS 2006), pages , Amsterdam, The Netherlands, The Netherlands, IOS Press.

189 Glossary API An Application Programming Interface is a specification of how software components should interact with each other. In the context of web development, an API is a set of Hypertext Transfer Protocol (HTTP) request messages, along with a definition of the structure of response messages, which is usually in an Extensible Markup Language (XML) or JavaScript Object Notation (JSON) format. 127, 128, , 134, 143, , 166 architectural specification Adopted from [3] and [48], a method of describing the modular structure found in software systems. It consists of list of unit declarations and unit terms that describe how modules are combined. 32, 176 automated theorem proving Automated theorem proving deals with the development of computer software that shows some statement, a conjecture, is a logical consequence of a set of statements, the axioms and hypotheses. ATP systems are capable of solving difficult problems under the aid of domain experts, and require problems to be written in a logical form in order to output proofs. Additional information can be found in [59]. 182 BFO The Basic Formal Ontology is a small, upper level ontology, developed by Barry Smith and Pierre Grenon, that consists of sub-ontologies at different levels of granularity. These sub-ontologies are divided into two categories: continuant (snapshot) ontologies, and occurrent (spanning) ontologies. 69, 70, 164 CASL The Common Algebraic Specification Language a general-purpose specification language based on first-order logic with induction, with support for partial functions and subsorting. It comprises of basic specifications (for the specification of single software modules), structured specifications (for the modular specification of modules), architectural specifications (for the prescription of the structure of implementations), and specification libraries (for storing specifications distributed over the Internet). Additional information can be found via uni-bremen.de/cofi/wiki/index.php/casl. 9, 23, 24, 33, 44 CIMOSA The Computer Integrated Manufacturing Open System Architecture modelling framework represents the business operations in the form of processes and allows the creation of executable enterprise models in computer integrated manufacturing (CIM) programs. It was developed in 1992 and has been standardized by 176

190 Glossary 177 the ISO since Its construct specification can be found in [39] and [40]. 4 7, 91 96, , , CLIF The Common Logic Interchange Format is one of the three standardized syntaxes found in the ISO 24707:2007 document for the Common Logic framework. Its syntax consists of quantified sentences, Boolean sentences, names for relations, functions, and individuals, and sequence names; as well, CLIF contains a vocabulary (a set of names and sequence names), and an interpretation of that vocabulary. For example, to say the following sentence, A cat is on a mat, we can write this in Common Logic as (exists ((x Cat) (y Mat)) (On x y)), which reads as there exists a cat x and a mat y, where x is on y. 8 10, 33, 68 COLORE The COmmon Logic Ontology Repository is an open repository of first-order ontologies that serves as a test bed for ontology evaluation and integration techniques, and that can support the design, evaluation, and application of ontologies in first-order logic. All ontologies are specified using Common Logic (ISO 24707), which is a standardized logical language for the specification of first-order ontologies and knowledge bases. 3, 6, 7, 10, 12, 15, 18, 33, 35, 38, 39, 43, 45, 49, 51, 55 57, 62, 68 72, 74, 77, 79, 80, 82, 84, 87, 88, 106, 107, 117, , 166, 167, 192 Common Logic Common Logic is a standardized logical language designed for the specification of first-order ontologies and knowledge bases, and its details can be found in the ISO 24707:2007 document [41]. It consists of three dialects: the Conceptual Graph Interchange Format (CGIF), the Common Logic Interchange Format (CLIF), and the Extended Common Logic Markup Language (XCL). 9, 10, 18, 25 completeness The derivation of all logically valid implications through reasoning. 10 conservative extension Adopted from [14], T 2 is a conservative extension of T 1 iff for any sentence σ L(T 1 ),. 11 T 2 = σ iff T 1 = σ conservativity triangle Adopted from [48], a graphical representation of relative consistency proofs, where the given theories T, T, and T and signature morphisms σ : T T, ι 1 : T T and ι 2 : T T, such that T is a conservativity triangle and is consistent. If ι 1 is conservative (definitional) and σ is a theory interpretation, then ι 2 is conservative and T is consistent. 32 Cyc A proprietary artificial intelligence project developed by Cycorp, Inc. that consists of an ontology and a knowledge base of everyday common sense knowledge that is used to perform human-like reasoning. Parts of the project are released as OpenCyc. 181

191 Glossary 178 definable equivalence Adopted from [29], two theories, T 1 and T 2, are definably equivalent iff T 1 is faithfully interpretable in T 2, and T 2 is faithfully interpretable in T DOLCE The Descriptive Ontology for Linguistic and Cognitive Engineering is the first module of the WonderWeb foundational ontologies library that aims at capturing the ontological categories underlying natural language and human common sense. 3, 5 9, 17, 20, 23 33, 35, 39, 43 45, 49, 51, 52, 55, 57, 59, 62 64, 68 73, 78, 82, 84, 85, 87, 88, , 181, 189 endurant In the philosophical sense, endurants are entities that exist in full in every instant that they exist [4]. 20, 24, 27 30, 51, 54, 56, 57, 68, 69, 181 extension Adopted from [14], let T 1 and T 2 be two first-order theories such that Σ(T 1 ) Σ(T 2 ). T 2 is an extension of T 1 iff for any sentence σ L(T 1 ),. 11 if T 1 = σ, then T 2 = σ faithful interpretation Adopted from [29], an interpretation π of a theory T 1 into a theory T 2 is a faithful interpretation, if and only if, for any sentence σl(t 1 ),. 14, 178 T 1 = σ T 2 = π(σ) first-order logic First-order logic is a formal language used in mathematics, philosophy, linguistics, and computer science that contains a set of symbols and a syntax. 1, 8 10, 18, 51, 70, 126 first-order theory Adopted from [14], a set of first-order sentences that are closed under logical entailment. 11 gist The gist ontology is minimalist upper ontology designed in OWL to have maximum coverage of typical business ontology concepts with the least amount of ambiguity. Additional information can be found via 126, 135, GoodRelations The GoodRelations ontology is a lightweight ontology for annotating offerings and other aspects of e-commerce on the Web. It is written in OWL-DL and provides a standard vocabulary for product, price, store, and company data that can be embedded into Web pages. Additional information can be found via http: // 135, , 148, 159

192 Glossary 179 graph database A database that uses graph structures with nodes, edges, and properties to represent and store data. 127 GRDDL The Gleaning Resource Descriptions from Dialects of Languages is a markup format that is a W3C Recommendation which enables users to obtain RDF triples out of XML documents, including XHTML. Additional information can be found via 142, 143 hierarchy Adopted from [29], a hierarchy, H = H,, is a partially ordered, finite set of theories H = T 1,..., T n, such that: 1. For all i and j, Σ(T i ) = Σ(T j ), 2. T i T j iff T j is an extension of T i, 3. T i < T j iff T j is a non-conservative extension of T i.. 10, 12 17, 37, 71 74, 77, 78, 80, 82, 88 HSO The Home Services Ontology is Hunch Manifest, Inc. s ontology designed to integrate data from home improvement service providers and vendors websites. 126, 127, 130, 138, 146, 163 IAOA The International Association of Ontology and its Applications is a non-profit organization that promotes the interdisciplinary research and international collaboration of the following fields: philosophical ontology, linguistics, logic, cognitive science, and computer science. The organization is interested in educating the community on what ontologies are and how they can be effectively utilized, supporting the development of collaborations between research and industry, and supporting the publication of journals and books. Additional information can be found via 91, 165 IDEF The Integration DEFinition family of modelling languages is used in the field of systems and software engineering, which include functional modelling, data simulation, object-oriented analysis/design, and knowledge acquisition. Additional information can be found via 120, 179 IDEF3 The Integrated DEFinition for Process Description Capture Method is a business process modelling method that is a scenario-driven process flow description capture method that represents: Process Flow Descriptions to capture the relationships between actions within the context of a specific scenario, and Object State Transition to capture the description of the allowable states and conditions. This method is part of the IDEF family of modelling languages in the field of systems and software engineering. Additional information can be found via http: // 122, 164

193 Glossary 180 intended structure Adopted from [23], an intended structure is a set of structures that characterizes the semantics of an ontology s terminology. They are specified with respect to models of well-understood mathematical theories, such as partial ordering, geometries, and algebra. 17 interpretation Adopted from [29], an interpretation π of a theory T 1 with the signature Σ(T 1 ) into a theory T 2 with the signature Σ(T 2 ) is a function on the set of nonlogical symbols of Σ(T 1 ) and formulae in L(T 1 ), such that π assigns to a formula π of L(T 2 ), in which at most the variable v 1 occurs free, such that T 2 = ( v 1 )π 2. π assigns to each n-place relation symbol P a formula π P of L(T 2 ), in which at most the variable v 1,..., v n occur free. 3. For any sentence σ L(T 1 ), T 1 = σ T 2 = π(σ) ISO The International Organization for Standardization is an international standardsetting body composed of various national standards organizations. The organization mainly produces international standard documents, technical reports, technical specifications, publicly available specifications, technical corrigenda, and guides. Additional information can be found via 92, 166 language Adopted from [14], the set of first-order formulae that only use the non-logical symbols in the signature Σ(T ). 11 Mace4 A program that searches for finite models of first-order formulas and can be used in conjunction with Prover9 to find a proof and counter-example. 16 non-conservative extension Adopted from [14], T 2 is a non-conservative extension of T 1 iff T 2 is an extension of T 1 and there exists a sentence σ Σ(T 1 ) where. 11 T 1 = σ and T 2 = σ NSERC The Natural Sciences and Engineering Research Council of Canada is a government agency that provides grants for research in the natural sciences and in engineering by supporting university students in their advanced studies, and encouraging Canadian companies to participate and invest in postsecondary research projects. Additional information about NSERC can be accessed via their home page: 125

194 Glossary 181 OntoIOp The Ontology Integration and Interoperability is a working item proposed in ISO TC37/SC3 that is intended to support the specification of a formal language for enabling distributed knowledge representation in ontologies; as well, the intent is to achieve interoperability across ontologies, services and devices. Additional information can be accessed via their home page: 91, 165 OpenCyc The OpenCyc ontology is the open-source version of the Cyc ontology, which includes the entire Cyc ontology containing hundreds of thousands of terms, along with millions of taxonomic assertions relating the terms to each other. This version of Cyc does not contain the complex rules available in Cyc. Additional information about OntoIOp can be found via 69, 70, 164, 177 OWL The Web Ontology Language is a World Wide Web Consortium (W3C) knowledge representation language used for authoring ontologies that is characterized by formal semantics and RDF/XML-based serializations. There are three variants of OWL, each of which have different levels of expressiveness: OWL-Lite, OWL-DL, and OWL Full. Additional information about OWL can be found via 8, 70, , 131, 145, 146, , 178 participation In the context of DOLCE, the authors of [51] indicate that there are endurants involved in an occurrence, so the notion of participation is not considered parthood. In DOLCE, participation is time-indexed in order to account for the varieties of participation in time, such as temporary participation and constant participation. 29, 181 perdurant In the philosophical sense, perdurants are entities that exist over successive temporal parts of phases [4]. 20, 27, 28, 30, 51, 54, 68, 69 Prover9 An automated theorem prover for first-order and equational logic. It is the successor of the Otter theorem prover. 9, 16, 33, 49, 56, 57, 165 PSL Adapted from [12], the Process Specification Language is a neutral, interchange language that integrates multiple process-related applications throughout the manufacturing life cycle. 3 6, 15, 18, 19, 69 72, 78 82, 85, 87, 88, 91, 97, , 110, 111, 113, 114, 116, 122, , 185, 187 RDF The Resource Description Framework is family of World Wide Web Consortium (W3C) specifications that are similar to conceptual modelling approaches, such as entity-relationship diagrams and class diagrams, that is based upon the notion of making statements about resources in the form of subject-predicate-object expressions known as triples. The subject denotes the resource, and the predicate denotes the traits/aspects of the resource and expresses a relationship between the subject and object. 8, 127, 128, 142, 143, 145, 146, 149, 157, 158, 181, 183, 211 reducibility A theory, T, is reducible to a set of theories T 1,..., T n iff:

195 Glossary T faithfully interprets each theory T i, and T 1... T n faithfully interprets T relative consistency proof Adopted from [15], within the Interactive Mathematical Proof System (IMPS), there is a set of theories deemed foundational and are regarded or known to be consistent. Since all proofs begin with a foundational theory and any theory developed from another is a conservative extension of the original theory, all theories developed are consistent relative to the original foundational theory, thus all proofs generated are guaranteed to be consistent. 32 representation theorem In mathematics, a representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to a concrete structure. 17 semantic augmentation In the context of the work done in this thesis, semantic augmentation means that constructs that have not been defined will be linked with concepts from already-defined theories and axioms found in ontologies in order to benefit from the reasoning capabilities of semantic technologies that utilize computerinterpretable ontology formats. Mapping rules were created with these first-order theories to define the CIMOSA terminologies using the PSL axioms. 4, 89 semantic heterogeneity Semantic heterogeneity occurs when software applications and databases used by the data providers ascribe disparate meanings to the same terms or use distinct terms to convey the same meaning. 3, 127 signature Adopted from [14], it is the non-logical lexicon, of a first-order theory T is denoted by Σ(T ). It is the set of all constant symbols, function symbols, and relation symbols that are used in T. 11 soundness The derivation of true statements through reasoning. 10 SPARQL The SPARQL Protocol and RDF Query Language is a query language for databases, able to retrieve and manipulate data stored in Resource Description Framework format. 128, 130, 145, 146, , 155, 157, 158, 214 strong ontology A strong ontology is characterized by the ability to characterize complex semantics/meaning in a set of axioms [55, 31]. 5 SUMO Adapted from [12], the Suggested Upper Merged Ontology is a neutral, interchange language that integrates multiple process-related applications throughout the manufacturing life cycle. 69, 70, 164 TPTP The Thousands of Problems for Theorem Provers is a library of test problems for automated theorem proving (ATP) systems, and consists of: a comprehensive library of the ATP test problems, a comprehensive list of references and information

196 Glossary 183 for each problem, arbitrary size instances of generic problems, a utility to convert the problems to existing ATP systems formats, general guidelines outlining the requirements for ATP system evaluation, and standards for input and output for ATP systems. 32 translation definition Adopted from [29]. Let T 0 be a theory with the signature Σ(T 0 ) and T 1 be a theory with the signature Σ(T 1 ), such that Σ(T 0 ) Σ(T 1 ) =. If there is an interpretation of T 0 in T 1, then there exists a set of sentences that axiomatizes the mapping, called a translation definition, in the language of L 0 L 1 of the form: ( x)p i ( x) Φ x where p i ( x) is a relation symbol in L 0 and (Φ x) is a formula in L 1 whose only free variables are x. 6, 10, 15, 16, 165 Turtle The Terse RDF Triple Language is a format for expressing data in the RDF data model that uses triples, each of which consists of a subject, a predicate, and an object. Turtle groups three URIs to make a triple, and provides ways to abbreviate information by factoring out common portions of URIs. For example, to express that Mark Twain was the author of Huckleberry Finn, the triple would be written as: person:mark Twain relation:author books:huckleberry Finn. Additional information can be found via 142, 146 UML The Unified Modelling Language is a general-purpose modelling language in the field of software engineering that is standardized in ISO/IEC 19501:2005. The Unified Modelling Language includes a set of graphic notation techniques to create visual models of object-oriented software-intensive systems. Additional information about UML can be found via 122, 164 unit declaration Adopted from [3], indicates the component modules required with specifications of each of them. 176 unit term Adopted from [3], descriptions of how modules are to be combined within an architectural specification. 176 weak ontology A weak ontology is characterized by the lack of the expressible or characterizable semantics and the ability to express very simple meaning; these include a collection of terms found in thesauri and dictionaries, as well as taxonomies and database schemas [55, 31]. 5 XML The Extensible Markup Language is a markup language defines rules for encoding documents in a format that is both human-readable and machine-readable. It was designed with the intent to emphasize simplicity, generality, and usability over the Internet [8]. It is a textual data format that used to represent arbitrary data

197 Glossary 184 structures as well as documents. Additional information about the specifications of XML can be found in [8]. 127, 128, 131, 132, 134, 135, , 157, 158, 166, 181, 211

198 Appendix A Additional Background Information A.1 The PSL Ontology This section contains additional information about the PSL ontology. A.1.1 Axioms of T psl core The following are the axioms of T psl core : ( x (activity(x) activity occurrence(x) timepoint(x) object(x))). (A.1.1) ( t 1 t 2 (before(t 1, t 2 ) timepoint(t 1 ) timepoint(t 2 ))). ( t 1 t 2 (timepoint(t 1 ) timepoint(t 2 ) t 1 = t 2 before(t 1, t 2 ) before(t 2, t 1 ))). (A.1.2) (A.1.3) ( t 1 before(t 1, t 1 )). (A.1.4) ( t 1 t 2 t 3 (before(t 1, t 2 ) before(t 2, t 3 ) before(t 1, t 3 ))). (A.1.5) ( t (timepoint(t) t! = inf before( inf, t))). (A.1.6) ( t (timepoint(t) t! = inf + before(t, inf + ))). (A.1.7) 185

199 Appendix A. Additional Background Information 186 ( t (timepoint(t) t inf ( u (before( inf, u) before(u, t))))). ( t (timepoint(t) t inf + ( u (before(t, u) before(u, inf + ))))). ( x ((activity(x) (activity occurrence(x) object(x) timepoint(x))) (activity occurrence(x) (object(x) timepoint(x))) (object(x) timepoint(x)))). (A.1.8) (A.1.9) (A.1.10) ( a occ (occurrence of(occ, a) activity(a) activity occurrence(occ))). (A.1.11) ( occ (activity occurrence(occ) ( a(activity(a) occurrence of(occ, a))))). (A.1.12) ( occ a1 a2 (occurrence of(occ, a1) occurrence of(occ, a2) a1 = a2)). ( a x (occurrence of(x, a) object(x) timepoint(beginof(x)) timepoint(endof(x)))). (A.1.13) (A.1.14) ( x (activity occurrence(x) object(x) bef oreeq(beginof(x), endof(x)))). (A.1.15) ( x occ t (participates in(x, occ, t) object(x) activity occurrence(occ) timepoint(t))). (A.1.16) ( x occ t (participates in(x, occ, t) at(x, t) is occurring at(occ, t))). ( t 1 t 2 (beforeeq(t 1, t 2 ) timepoint(t 1 ) timepoint(t 2 ) (before(t 1, t 2 ) t 1 = t 2 ))). (A.1.17) (A.1.18) ( t 1 t 2 t 3 (betweeneq(t 1, t 2, t 3 ) beforeeq(t 1, t 2 ) beforeeq(t 2, t 3 ))). (A.1.19) ( x t ( at(x, t) object(x) betweeneq(beginof(x), t, endof(x)))) (A.1.20) ( occ t (is occurring at(occ, t) betweeneq(beginof(occ), t, endof(occ)))). (A.1.21)

200 Appendix A. Additional Background Information 187 T actocc T complex T atomic T disc state T subactivity T duration T occtree T psl core Figure A.1: The core theories of the PSL Ontology, adapted from [22]. Solid lines indicate conservative extension, while dashed lines indicate an extension that is not conservative. A.1.2 Core Theories of the PSL Ontology Figure A.1 outlines the core theories of the PSL ontology. A.2 PSL Lexicon Table A.1 outlines the lexicon used in the core theories of the PSL ontology.

201 Appendix A. Additional Background Information 188 Table A.1: Lexicon used in the core theories of the PSL ontology. Theory Predicate Description T psl core activity(a) a is an activity activity occurrence(o) o is an activity occurrence object(x) x is an object occurrence of(o, a) o is an occurrence of a beginof(o) the beginning timepoint of o endof(o) the ending timepoint of o before(t 1, t 2 ) timepoint t 1 precedes timepoint t 2 on the timeline T subactivity subactivity(a 1, a 2 ) a 1 is a subactivity of a 2 primitive(a) a is a minimal element of the subactivity ordering T atomic atomic(a) a is either primitive or a concurrent activity conc(a 1, a 2 ) the activity that the concurrent composition of a 1 and a 2 T occtree legal(s) s is an element of a legal occurrence initial(s) s is the root of an occurrence tree earlier(s 1, s 2 ) s 1 precedes s 2 in an occurrence tree T discstate holds(f, s) the fluent f is true immediately after the activity occurrence s prior(f, s) the fluent f is true immediately before the activity occurrence s T complex min precedes(s 1, s 2, a) The atomic subactivity occurrence s 1 precedes the atomic subactivity s 2 in an activity tree for a root(s, a) the atomic subactivity occurrence s is the root of an activity tree for a T actocc subactivity occurrence(o 1, o 2 ) o 1 is a subactivity occurrence of o 2 root occ(o) the initial atomic subactivity occurrence of o leaf occ(s, o) s is the final atomic subactivity occurrence of o T duration timeduration(d) d is a time duration duration(t 1, t 2 ) the time duration whose value is the distance from timepoint t 1 to timepoint t 2 lesser(d1, d2) the linear ordering relation over time durations

202 Appendix B Additional DOLCE Information B.1 DOLCE Axioms from WonderWeb The following DOLCE axioms are from the original WonderWeb document [51]. Parthood Argument Restrictions P (x, y) (AB(x) P D(x)) (AB(y) P D(y)) (Ad1) P (x, y) (P D(x) P D(y)) (Ad2) P (x, y) (AB(x) AB(y)) (Ad3) (P (x, y) SB(R, φ) X(φ)) (φ(x) φ(y)) (Ad4) Ground Axioms (AB(x) P D(x)) P (x, x) (Ad5) (P (x, y) P (y, x)) x = y (Ad6) (P (x, y) P (y, z)) P (x, z) (Ad7) ((AB(x) P D(x)) P (x, y)) z (P (z, x) O(z, y)) (Ad8) ( x φ(x) ( x (φ(x) AB(x)) x (φ(x) P D(x)))) y (y = σxφ(x)) (Ad9) 189

203 Appendix B. Additional DOLCE Information 190 Temporary Parthood Argument Restrictions P (x, y, t) (ED(x) ED(y) T (t)) P (x, y, t) (P ED(x) P ED(y)) P (x, y, t) (NP ED(x) NP ED(y)) (Ad10) (Ad11) (Ad12) Ground Axioms (P (x, y, t) P (y, z, t)) P (x, z, t) (Ad13) (ED(x) ED(y) P RE(x, t) P RE(y, t) P (x, y, t)) z (P (z, x, t) O(z, y, t)) (Ad14) ( x φ(x) x (φ(x) ED(x))) y (y = σ te xφ(x)) (Ad15) Links With Other Primitives (ED(x) P RE(x, t)) P (x, x, t) (Ad16) P (x, y, t) (P RE(x, t) P RE(y, t)) (Ad17) P (x, y, t) t (P (t, t) P (x, y, t )) (Ad18) (P ED(x) P (x, y, t)) x S < y, t > (Ad19) Constitution Argument Restrictions K(x, y, t) ((ED(x) P D(x)) (ED(y) P D(y)) T (t)) K(x, y, t) (P ED(x) P ED(y)) K(x, y, t) (NP ED(x) NP ED(y)) K(x, y, t) (P D(x) P D(y)) (Ad20) (Ad21) (Ad22) (Ad23) Ground Axioms K(x, y, t) K(y, x, t) (K(x, y, t) K(y, z, t)) K(x, z, t) (Ad24) (Ad25) Links With Other Primitives K(x, y, t) (P RE(x, t) P RE(y, t)) K(x, y, t) t (P (t, t) K(x, y, t )) (K(x, y, t) P ED(x)) x S < y, t > (K(x, y, t) P (y, y, t)) x (P (x, x, t) K(x, y, t)) (Ad26) (Ad27) (Ad28) (Ad29)

204 Appendix B. Additional DOLCE Information 191 Links Between Categories GK(NAP O, M) GK(AP O, NAP O) GK(SC, SAG) (Ad30) (Ad31) (Ad32) General Properties Participation K(x, x, t) SK(φ, ψ) SD(φ, ψ) GK(φ, ψ) GD(φ, ψ) (SK(φ, ψ) SK(ψ, ρ) DJ(φ, ρ)) SK(φ, ρ) (GK(φ, ψ) GK(ψ, ρ) DJ(φ, ρ)) GK(φ, ρ) Argument Restrictions P C(x, y, t) (ED(x) P D(y) T (t)) (Td1) (Td2) (Td3) (Td4) (Td5) (Ad33) Existential Axioms (P D(x) P RE(x, t)) y (P C(y, x, t)) (Ad34) ED(x) y t (P C(x, y, t)) (Ad35) Links With Other Primitives P C(x, y, t) (P RE(x, t) P RE(y, t)) P C(x, y, t) t (P (t, t) P C(x, y, t )) (Ad36) (Ad37) Ground Properties P C(x, x, t) (Td6) P C(x, y, t) P C(y, x, t) (Td7) Being Present Argument Restrictions (ED(x) P D(x) Q(x)) t (P RE(x, t)) ((P ED(x) P Q(x)) P RE(x, t)) s (P RE(s, x, t)) (Td15) (Td16)

205 Appendix B. Additional DOLCE Information 192 Ground Axioms (P RE(x, t) P (t, t)) P RE(x, t ) (Td17) P RE(s, x, t) P RE(x, t) (Td18) B.2 Additional DOLCE Axioms B.2.1 Axiomatization of T dolce present Figure B.1 lists all of the axioms found in T dolce present ; as well, the axioms can be found in COLORE 1. ( x) (ED(x) P D(x)) ( t) P RE(x, t) (B.2.1) ( x, t, t 1 ) P RE(x, t) P (t 1, t) P RE(x, t 1 ) (B.2.2) ( x, t) P RE(x, t) T (t) (B.2.3) ( x, t, t 1, t 2 ) P RE(x, t 1 ) P RE(x, t 2 ) SUM(t, t 1, t 2 ) P RE(x, t) (B.2.4) Figure B.1: Axioms of T dolce present. 1 present/dolce_present_star.clif

206 Appendix C Additional CIMOSA Information C.1 Axiomatizations of PSL Constructs Used in the CIMOSA Ontology The following axiomatizations of PSL constructs are from complex.clif in the PSL hierarchy in COLORE. Root Activity in Occurrence Trees ( cl comment Root o c c u r r e n c e s in the a c t i v i t y t r e e correspond to atomic s u b a c t i v i t y o c c u r r e n c e s o f the a c t i v i t y. ) ( f o r a l l ( a s ) ( i f ( root s a ) ( e x i s t s ( a1 ) ( and ( s u b a c t i v i t y a1 a ) ( atocc s a1 ) ) ) ) ) Leaf Nodes in Occurrence Trees ( cl comment An occurrence i s the l e a f o f an a c t i v i t y t r e e i f and only i f t h e r e e x i s t s an e a r l i e r atomic s u b a c t i v i t y occurrence but t h e r e does not e x i s t a l a t e r atomic s u b a c t i v i t y occurrence. ) 193

207 Appendix C. Additional CIMOSA Information 194 ( f o r a l l ( s a ) ( i f f ( l e a f s a ) ( and ( or ( root s a ) ( min precedes s1 s a ) ) ( not ( e x i s t s ( s2 ) ( min precedes s s2 a ) ) ) ) ) ) Precedence in Occurrence Trees ( cl comment A c t i v i t y t r e e s are s u b t r e e s o f the occurrence t r e e. ) ( f o r a l l ( s1 s2 a ) ( i f ( min precedes s1 s2 a ) ( precedes s1 s2 ) ) ) C.2 Common Logic Version of the CIMOSA Ontology ( cl t e x t cimosa ( cl comment Sources : ISO 19439:2006, ISO 19440:2007, Vernadat1998. ) ( cl comment Comment : The f o l l o w i n g ontology i s c r e a t e d to d e s c r i b e the behavioural r u l e s e t found in CIMOSA. ) ( cl comment Import the PSL Core ontology s i n c e the CIMOSA ontology uses PSL c o n s t r u c t s. ) ( cl imports psl core ) ( cl comment Import the complex subtheory o f the PSL ontology s i n c e the CIMOSA ontology uses PSL c o n s t r u c t s. ) ( cl imports complex ) ( c l comment ===== Mappings ===== ) ( cl comment Map between CIMOSA and PSL c o n s t r u c t s. ) ( cl comment A b u s i n e s s p r o c e s s in CIMOSA i s an a c t i v i t y in PSL. ) ( f o r a l l ( x ) ( i f ( b u s i n e s s p r o c e s s x ) ( a c t i v i t y x ) ) )

208 Appendix C. Additional CIMOSA Information 195 ( cl comment An e n t e r p r i s e a c t i v i t y in CIMOSA i s an a c t i v i t y in PSL. ) ( f o r a l l ( x ) ( i f ( e n t e r p r i s e a c t i v i t y x ) ( a c t i v i t y x ) ) ) ( cl comment An e n t e r p r i s e f u n c t i o n in CIMOSA i s an a c t i v i t y in PSL. ) ( f o r a l l ( x ) ( i f ( e n t e r p r i s e f u n c t i o n x ) ( a c t i v i t y x ) ) ) ( cl comment An e n t e r p r i s e o b j e c t in CIMOSA i s an o b j e c t in PSL. ) ( f o r a l l ( x ) ( i f ( e n t e r p r i s e o b j e c t x ) ( o b j e c t x ) ) ) ( cl comment An event in CIMOSA i s an a c t i v i t y in PSL. ) ( f o r a l l ( x ) ( i f ( event x ) ( a c t i v i t y x ) ) ) ( cl comment An occurrence in CIMOSA i s an a c t i v i t y occurrence in PSL. ) ( f o r a l l ( x ) ( i f ( occurrence x ) ( a c t i v i t y o c c u r r e n c e x ) ) ) ( cl comment All e n t e r p r i s e f u n c t i o n s are b u s i n e s s p r o c e s s e s or e n t e r p r i s e a c t i v i t i e s. ) ( f o r a l l ( x ) ( i f ( e n t e r p r i s e f u n c t i o n x ) ( or ( b u s i n e s s p r o c e s s x ) ( e n t e r p r i s e a c t i v i t y x ) ) ) ) ( cl comment ===== Behavioural Rule Set ===== ) ( cl comment Ending Status (ES) Values ) ( cl comment e n d s t a t 1 i s a constant / value ) ( f o r a l l ( o x ) ( i f ( o c c u r r e n c e o f o ( e n t e r p r i s e f u n c t i o n x ) ) ( holds e n d s t a t 1 o ) ) ) ( cl comment Process T r i g g e r i n g Rules ) ( c l comment WHEN (START WITH event i AND event j ) DO EF1 ) ( f o r a l l ( o1 o2 x f ) ( i f ( and ( o c c u r r e n c e o f o1 ( domain process x ) ) ( root o2 o1 ) ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n f ) ) )

209 Appendix C. Additional CIMOSA Information 196 ( e x i s t s ( o3 o4 i j ) ( and ( precedes o3 o2 ) ( precedes o4 o2 ) ( o c c u r r e n c e o f o3 ( a c t i v i t y i ) ) ( o c c u r r e n c e o f o4 ( a c t i v i t y j ) ) ) ) ) ) ( c l comment WHEN (START) DO EF1 ) ( cl comment OR f o r a l l b u s i n e s s p r o c e s s e s, t h e r e e x i s t a parent p r o c e s s i m p l i c i t that o precedes o1 because o f root ) ( f o r a l l ( o1 x ) ( i f ( o c c u r r e n c e o f o1 ( b u s i n e s s p r o c e s s x ) ) ( e x i s t s ( o y ) ( and ( root o o1 ) ( o c c u r r e n c e o f o ( b u s i n e s s p r o c e s s y ) ) ( precedes o o1 ) ) ) ) ) ( cl comment Forced S e q u e n t i a l Rules ) ( c l comment WHEN (ES(EFx) = ANY) DO EFy ) ( cl comment Note : ANY i s a r e s e r v e d key word. ) ( f o r a l l ( o1 x ) ( i f ( and ( holds ANY o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 y ) ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o2 ) ) ) ) ) ( cl comment Conditional S e q u e n t i a l Rules ) ( cl comment WHEN (ES(EF1) = e n d s t a t 1 ) DO EF2 ) ( cl comment I f the e n t e r p r i s e f u n c t i o n x has an ending s t a t u s value o f e n d s t a t 1, and o1 i s an occurrence o f x, then t h e r e e x i s t s an o2 which i s an occurrence o f e n t e r p r i s e f u n c t i o n y that occurs a f t e r o1. ) ( cl comment e n d s t a t 1, e n d s t a t 2, e t c. are v a l ues. ) ( f o r a l l ( o1 x ) ( i f ( and ( holds e n d s t a t 1 o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 y ) ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o2 ) ) ) ) )

210 Appendix C. Additional CIMOSA Information 197 ( cl comment WHEN (ES(EF1) = e n d s t a t 2 ) DO EF3 ) ( f o r a l l ( o2 x ) ( i f ( and ( holds e n d s t a t 2 o2 ) ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o3 y ) ( and ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o2 o3 ) ) ) ) ) ( cl comment WHEN (ES(EF1) = e n d s t a t 3 ) DO EF4 ) ( f o r a l l ( o3 x ) ( i f ( and ( holds e n d s t a t 3 o3 ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o4 y ) ( and ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o3 o4 ) ) ) ) ) ( cl comment Spawning Rules ) ( c l comment Asynchronous Spawning ) ( cl comment WHEN (ES(EF1) = value ) DO EF2 & EF3 & EF4 ) ( cl comment value i s a s p e c i f i c ending s t a t u s. We do not know in which order EF2, EF3, and EF4 occurs. ) ( f o r a l l ( o1 x ) ( i f ( and ( holds value o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 o3 o4 t y z ) ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n t ) ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n z ) ) ( precedes o1 o2 ) ( precedes o1 o3 ) ( precedes o1 o4 ) ) ) ) ) ( c l comment Synchronous Spawning ) ( cl comment WHEN (ES(EF1) = value ) DO SYNC (EF2 & EF3 & EF4) ) ( cl comment Note : EF2, EF3 and EF4 s t a r t at the same time point. ) ( f o r a l l ( o1 x ) ( i f ( and ( holds value o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 o3 o4 t y z )

211 Appendix C. Additional CIMOSA Information 198 ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n t ) ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n z ) ) ( precedes o1 o2 ) ( precedes o1 o3 ) ( precedes o1 o4 ) (= ( b e g i n o f o2 ) ( b e g i n o f o3 ) ) (= ( b e g i n o f o2 ) ( b e g i n o f o4 ) ) ) ) ) ) ( c l comment Rendez vous Rules ) ( cl comment WHEN (ES(EF2) = v a l u e 2 AND ES(EF3) = v a l u e 3 AND ES(EF4) = v a l u e 4 ) DO EF5 ) ( f o r a l l ( o2 o3 o4 x y z ) ( i f ( and ( holds v a l u e 2 o2 ) ( holds v a l u e 3 o3 ) ( holds v a l u e 4 o4 ) ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n x ) ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n z ) ) ) ( e x i s t s ( o5 t ) ( and ( o c c u r r e n c e o f o5 ( e n t e r p r i s e f u n c t i o n t ) ) ( precedes o2 o5 ) ( precedes o3 o5 ) ( precedes o4 o5 ) ) ) ) ) ( cl comment Loop Rules ) ( cl comment WHEN (ES(EF1) = l o o p v a l u e ) DO EF1 ) ( f o r a l l ( o1 x ) ( i f ( and ( holds l o o p v a l u e o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ) ( cl comment Process Completion Rules ) ( cl comment WHEN (ES(EF1) = e n d s t a t x AND ES(EF2) = e n d s t a t y ) DO FINISH ) ( cl comment use l e a f node to r e p r e s e n t the end o f a p r o c e s s / occurrence t r e e )

212 Appendix C. Additional CIMOSA Information 199 ( cl comment i f EF( f ) i s l e a f node, then i t must mean EF1 and EF2 reached t h e i r s p e c i f i c end s t a t e s o3 and o4, r e s p e c t i v e l y...? ) ( f o r a l l ( s a o1 o2 f ) ( i f ( and ( l e a f o c c o2 o1 ) ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n f ) ) ) ( e x i s t s ( o3 o4 g i j ) ( and ( precedes o3 o2 ) ( precedes o4 o2 ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n f ) ) ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n g ) ) ( holds e n d s t a t x o3 ) ( holds e n d s t a t x o4 ) ) ) ) ) ( c l comment Run Time Choice Rules ) ( cl comment WHEN (ES(EF1) = e n d s t a t 1 ) DO S = (EF2 XOR EF3 XOR EF4) ) ( cl comment use d i s j u n c t i v e c l a u s e s to model XOR ) ( cl comment XOR i s d e f i n e d as (p xor q = (p ˆ not q ) v ( not p ˆ q ) ) ) ( cl comment f o r s i m p l i c i t y s sake, we assume t h e r e i s an a l t e r n a t i v e between TWO d i f f e r e n t e n t e r p r i s e f u n c t i o n s ) ( f o r a l l ( o1 x ) ( i f ( and ( holds e n d s t a t 1 o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 o3 y ) ( or ( and ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o2 ) ) ( not ( and ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o3 ) ) ) ) ( and ( and ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o3 ) )

213 Appendix C. Additional CIMOSA Information 200 ( not ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n y ) ) ( precedes o1 o2 ) ) ) ) ) ) ) ) ( cl comment Unordered Set Rules ) ( cl comment WHEN (ES(EF1) = e n d s t a t 1 ) DO S = {EF2, EF3, EF4} ) ( cl comment s e t o f execution i s unknown AND a l l EF need to be repeated at l e a s t once ) ( f o r a l l ( o1 x ) ( i f ( and ( holds value o1 ) ( o c c u r r e n c e o f o1 ( e n t e r p r i s e f u n c t i o n x ) ) ) ( e x i s t s ( o2 o3 o4 t y z ) ( and ( o c c u r r e n c e o f o2 ( e n t e r p r i s e f u n c t i o n t ) ) ( o c c u r r e n c e o f o3 ( e n t e r p r i s e f u n c t i o n y ) ) ( o c c u r r e n c e o f o4 ( e n t e r p r i s e f u n c t i o n z ) ) ( precedes o1 o2 ) ( precedes o1 o3 ) ( precedes o1 o4 ) ) ) ) ) )

214 Appendix D Additional HomeServices Information D.1 Sample Item XML Result from Amazon <Item> <ASIN>B0002TXNX0</ASIN> <DetailPageURL> h t t p : //www. amazon. com/black Decker 9099KC 7 2 Volt Cordless /dp /B0002TXNX0%3FSubscriptionId%3DAKIAJHNOF4OERYF3SWSQ%26tag%3 Dserv07 20%26linkCode%3Dxm2%26camp%3D2025%26 c r e a t i v e%3 D165953%26creativeASIN%3DB0002TXNX0</DetailPageURL> <ItemAttributes> <Binding>Tools &amp ; Home Improvement</ Binding> <Brand>Black &amp ; Decker</Brand> <CatalogNumberList> <CatalogNumberListElement>9099KC</ CatalogNumberListElement > <CatalogNumberListElement>315273</ CatalogNumberListElement > </ CatalogNumberList> <EAN> </EAN> <EANList><EANListElement> </ EANListElement></ EANList> <Feature>Balanced mid handle design i n c r e a s e s the o v e r a l l comfort o f the d r i l l and the user s c o n t r o l when using the d r i l l </Feature> 201

215 Appendix D. Additional HomeServices Information 202 <Feature>Fan cooled motor c o n t r i b u t e s to a l o n g e r l i f e o f the d r i l l </Feature> <Feature>Keyless chuck f o r quick and easy b i t changes </ Feature> <Feature >2 speeds switch with forward / r e v e r s e Low f o r c o n t r o l when s c r e w d r i v i n g ; high f o r d r i l l i n g </Feature> <Feature>I n c l u d e s : 7.2 Volt d r i l l with i n t e g r a l battery and k e y l e s s chuck and charger </Feature> <ItemDimensions> <Height Units= hundredths i n c h e s >300</Height> <Length Units= hundredths i n c h e s >910</Length> <Weight U n i t s= pounds >3</Weight> <Width Units= hundredths i n c h e s >890</Width> </ItemDimensions> <Label>Black &amp ; Decker </Label> <L i s t P r i c e > <Amount>4028</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$40.28</ FormattedPrice> </L i s t P r i c e > <Manufacturer>Black &amp ; Decker </Manufacturer> <Model >9099KC</Model> <MPN>9099KC</MPN> <PackageDimensions> <Height Units= hundredths i n c h e s >300</Height> <Length Units= hundredths i n c h e s >910</Length> <Weight U n i t s= hundredths pounds >305</Weight> <Width Units= hundredths i n c h e s >890</Width> </PackageDimensions> <PackageQuantity >1</PackageQuantity> <PartNumber >9099KC</PartNumber> <ProductGroup>Home Improvement</ProductGroup> <ProductTypeName>TOOLS</ProductTypeName> <Publisher >Black &amp ; Decker</Publisher > <SKU>EMY </SKU> <Studio >Black &amp ; Decker </Studio> <Title >Black &amp ; Decker 9099KC 7.2 Volt Cordless D r i l l with Keyless Chuck</Title > <UPC> </UPC> <UPCList><UPCListElement > </ UPCListElement></ UPCList> <Warranty>2 y e a r Warranty</Warranty> </ItemAttributes >

216 Appendix D. Additional HomeServices Information 203 <OfferSummary> <LowestNewPrice> <Amount>2270</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$22.70</ FormattedPrice> </LowestNewPrice> <LowestUsedPrice> <Amount>1969</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$19.69</ FormattedPrice> </LowestUsedPrice> <TotalNew>21</TotalNew> <TotalUsed >9</TotalUsed> <T o t a l C o l l e c t i b l e >0</T o t a l C o l l e c t i b l e > <TotalRefurbished >0</TotalRefurbished > </OfferSummary> <Offers > <TotalOffers >2</TotalOffers > <TotalOfferPages >1</TotalOfferPages > <MoreOffersUrl > h t t p : //www. amazon. com/gp/ o f f e r l i s t i n g /B0002TXNX0%3 FSubscriptionId%3DAKIAJHNOF4OERYF3SWSQ%26tag%3Dserv07 20%26linkCode%3Dxm2%26camp%3D2025%26 c r e a t i v e%3d386001%26 creativeasin%3db0002txnx0</moreoffersurl> <Offer > <O f f e r A t t r i b u t e s ><Condition>New</Condition ></ O f f e r A t t r i b u t e s > <O f f e r L i s t i n g > <O f f e r L i s t i n g I d > 4JTBFiR1gdxwdpzRIuosYP68Tw6jz0ds%2 F65G6plTWXSSGFyOFdNdBHZi CVWMC5qLFwwKHjpHl9g9idyEQCPz9CSGY60Xg7RS1%2 BwYCCotii6fZrRL ql98ug%3d%3d</o f f e r L i s t i n g I d > <Price > <Amount>2270</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$22.70</ FormattedPrice> </Price > <AmountSaved> <Amount>1758</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$17.58</ FormattedPrice> </AmountSaved> <PercentageSaved >44</PercentageSaved>

217 Appendix D. Additional HomeServices Information 204 <A v a i l a b i l i t y >Usually s h i p s in 24 hours </A v a i l a b i l i t y > <A v a i l a b i l i t y A t t r i b u t e s > <AvailabilityType >now</availabilitytype > <MinimumHours>0</MinimumHours> <MaximumHours>0</MaximumHours> </ A v a i l a b i l i t y A t t r i b u t e s > <I s E l i g i b l e F o r S u p e r S a v e r S h i p p i n g > 1</ I s E l i g i b l e F o r S u p e r S a v e r S h i p p i n g > </O f f e r L i s t i n g > </Offer > <Offer > <O f f e r A t t r i b u t e s > <Condition >Used</Condition > </O f f e r A t t r i b u t e s > <O f f e r L i s t i n g > <O f f e r L i s t i n g I d > S51qO27ut2KczOkvKuUcnj0RVg2GlhO1jQGkhnfy6UX0EvRdCtWV% 2 Bf85SftDPZZj%2FO1AP47fxSGHXoN67%2FKnVrc2AeN9CKoW9grfJ9z 6hTtrLIevhuVh95Xb4P5BdeWOl7xbRWe0Nry%2BD3qtkJeMecZf0Yy5 Xnrx</O f f e r L i s t i n g I d > <Price > <Amount>1969</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$19.69</ FormattedPrice> </Price > <AmountSaved><Amount>2059</Amount> <CurrencyCode>USD</CurrencyCode> <FormattedPrice >$20.59</ FormattedPrice ></AmountSaved> <PercentageSaved >51</PercentageSaved> <A v a i l a b i l i t y >Usually s h i p s in 1 2 b u s i n e s s days</ A v a i l a b i l i t y > <A v a i l a b i l i t y A t t r i b u t e s > <AvailabilityType >now</availabilitytype > <MinimumHours>24</MinimumHours> <MaximumHours>48</MaximumHours> </ A v a i l a b i l i t y A t t r i b u t e s > <I s E l i g i b l e F o r S u p e r S a v e r S h i p p i n g > 0</ I s E l i g i b l e F o r S u p e r S a v e r S h i p p i n g > </O f f e r L i s t i n g > </Offer > </Offers > </Item>

218 Appendix D. Additional HomeServices Information 205 D.2 Sample Item XML Result from Sears <?xml version= 1. 0 encoding= UTF 8?> <ProductDetail> <SoftHardProductDetails> <PartNumber>SPM </PartNumber> <MfgPartNumber><! [CDATA[ e 6 3 q f s l k y 1 ] ]></MfgPartNumber> <VendorId>MKT</ VendorId> <MapIndicator /> <MapPriceDescription /> <MapPriceValidDate /> <SaveStory><! [CDATA[< div c l a s s ="youpay bl"><span c l a s s =" p r i c i n g " itemprop=" p r i c e "> $ </ span></div>] ]></ SaveStory> <BrandName><! [CDATA[ Black & Decker ] ]></BrandName> <DescriptionName><! [CDATA[ Black & Decker LDX120C 20 Volt MAX Lithium Ion D r i l l / Driver ] ]></ DescriptionName> <KsnValue/> <MainImageUrl><! [CDATA[ h t t p : // c. shld. net / rpx / i / s / pi /mp2/27946/ ahr0cdovl2ltzy5yzxzlcnnlzguuy29tl2ltywdlcy9jlz UxaVVHaTYyNFpMLmpwZw==?s r c=http%3a%2f%2fimg. r e v e r s e d e. com%2 Fimages%2FI%2F51iUGi624ZL. j p g&d=c65 d296925e933c276cd92e12f02159f3701da04 ] ]></MainImageUrl> <StoreId>10153</ StoreId> <CatalogId>12605</ CatalogId> <SellerCount>0</ SellerCount> <InStock>1</ InStock> <WebStatus>1</ WebStatus> <LangId/> <P ro du ct V ar ia nt><! [CDATA[NONVARIATION ] ]></ Pr od uc tv a ri an t> <S t o r e p i c k u p e l i g i b l e>0</ S t o r e p i c k u p e l i g i b l e> <SRESEligible>0</ SRESEligible> <StsType/><RelatedUrl /> <F r e e S h i p p i n g E l i g i b l e>f a l s e</ F r e e S h i p p i n g E l i g i b l e> <S p e c i a l O f f e r >f a l s e</ S p e c i a l O f f e r> <ZeroFinance /> <SkuDiff /><FitmentRequired /><Swatches /> <Rating /> <NumReview>0</NumReview> <CatEntryId> </ CatEntryId> <ViewOnly> f a l s e</viewonly> <ClickToTalk><! [CDATA[ f a l s e ] ]></ ClickToTalk>

219 Appendix D. Additional HomeServices Information 206 <MailInRebate>0</ MailInRebate> <OnlineOnlyPrice>0</ OnlineOnlyPrice> <S a l e P r i c e>128.27</ S a l e P r i c e> <RegularPrice>128.27</ RegularPrice> <AutomotiveDivision>f a l s e</ AutomotiveDivision> <OptionTab>f a l s e</optiontab> <IsFrequencyModel /><MappedPriceIndicator /><MaintenanceAgreement / > <ProductProtectionPlan /><I n s t a l l a t i o n K i t /> <Connection /><Accessory /><SmartPlan/><GiftWrap/><HaulAway/> <ProductVariants /> <S h o r t D e s c r i p t i o n><! [CDATA[<ul><l i >Lithium Ion Technology: Lighter, more compact, no memory, l o n g e r l i f e </ l i ><l i >20V Max Lithium Ion B a t t e r y : Holds charge l o n g e r between use and has l o n g e r c y c l e l i f e </ l i ><l i >11 P o s i t i o n Clutch: Provides p r e c i s e c o n t r o l f o r d r i l l i n g i n t o wood, metal, p l a s t i c, and a l l s c r e w d r i v i n g tasks </ l i ><l i >Compact and L i g h t w e i g h t : Less f a t i g u e and a l l o w s u s e r s to d r i l l / screw in c o n f i n e d spaces </ l i ><l i >Variable Speed: Allows c o u n t e r s i n k i n g without damaging material </ l i ></ul>] ]></ S h o r t D e s c r i p t i o n> <LongDescription><! [CDATA[ The Black &amp ; Decker LBXR20 20 Volt MAX Extended Run Time Lithium Battery i s compatible with the 20 Volt MAX l i n e o f power and gardening t o o l s. These b a t t e r i e s have been formulated f o r l o n g e r runtime and improved performance. This battery i s compatible with c o r d l e s s t o o l models BDC120VA100, BDCDMT120, BDCDMT120 2, BDCDMT120F, BDCDMT120IA, BDCF20, BDH2000SL, LD3K220, LCC220, LCS120, LCS120B, LD120VA, LDX120C, LDX120PK, LDX120SB, LDX220SB, LDX220SBFC, LGC120, GLC120B, LHT210, LHT2220, LHT2220B, LLP120, LLP120B, LPHT120, LPHT120B, LPP120, LPP120B, LST220, LSW120, LSW20, LSW20B, SSL20SB, SSL20SB 2. ] ]></ LongDescription> <GroupDescription /> <SkuList> <Sku> <CatEntryId> </ CatEntryId> </Sku> </ SkuList> <ArrivalMethods> <ArrivalMethod>Ship</ ArrivalMethod> </ ArrivalMethods> <P r e S e l l I n d>no</ P r e S e l l I n d> <FollowItFlag>true</ FollowItFlag> <LMPStoreDetails> <Time><TimeX/><TimeY/><TimeZ/></Time>

220 Appendix D. Additional HomeServices Information 207 <OrderCutOffTime/> <TomorrowHolidayFlag/><TodayHolidayFlag /><LDFlag/> <StandardTimeZone/><PrepTime/><StoreUnitNumber/> <OnHandQuantity/><SPU/><Mailable /> <SRES/><WeekDayOpenTime/><WeekDayCloseTime/><SatOpenTime/> <SatCloseTime /><SunOpenTime/><SunCloseTime/> <LMPstock/><GetItNow/><RespFfm/><LeadTime/> <StoreZipCode /> </ LMPStoreDetails><PickUpOption>0</ PickUpOption> <D i s t r i b u t i o n C e n t e r>vd</ D i s t r i b u t i o n C e n t e r> <CheckOutEnable>t r u e</ CheckOutEnable> <IsKMartSPU> f a l s e</iskmartspu> <Variant>NONVARIATION</ Variant> <RegAvlMainFlag> f a l s e</ RegAvlMainFlag> <ExpressCheckOutEligible>Y</ ExpressCheckOutEligible> <MobileExpressCheckOutEligible>Y</ MobileExpressCheckOutEligible> <SoldBy><! [CDATA[ OnlineWholeSale ] ]></ SoldBy> <OtherFBMMerchants/><OtherCPCMerchants/> </ SoftHardProductDetails> <StatusData> <ResponseCode>0</ ResponseCode> <RespMessage>The a c t i o n i s s u c c e s s f u l</respmessage> </ StatusData> <ApiTracking>S e r v e r : PROD SERVER Tracking ID: { } API C l i e n t S e s s i o n Key: n u l l Time : Tue Apr : 0 1 : 2 6 CDT 2013 UID : From Cache : Y </ ApiTracking> </ ProductDetail> D.3 API Queries for Product Information Retrieval The queries performed against the Amazon API include parameters that are not listed in the left sidebar of the tool. The queries need to copied into the Unsigned URL text box as shown in Figure D.1. The respective API queries/commands for both the Amazon Web Service and curl tools are listed under each product subsection and the XML output can be found in the appendices.

221 Appendix D. Additional HomeServices Information 208 Figure D.1: Amazon API queries need to be copied into the Unsigned URL text box. Black & Decker LDX112C 12-Volt MAX Lithium-Ion Drill/- Driver This drill is offered by both companies on the following web pages: Amazon: h t t p : // w e b s e r v i c e s. amazon. com/ onca /xml? S e r v i c e= AWSECommerceService&Operation=ItemLookup&S u b s c r i p t i o n I d= AKIAJHNOF4OERYF3SWSQ&AssociateTag=serv07 20&Version = &ItemId=B004443WVW&IdType=ASIN&C o n d i t i o n=new& ResponseGroup=Images, ItemAttributes, Offers, A c c e s s o r i e s, AlternateVersions, BrowseNodes, EditorialReview, OfferFull, OfferSummary, Reviews, SalesRank, S i m i l a r i t i e s, Tracks, VariationImages, VariationMatrix, VariationSummary, V a r i a t i o n s Sears: p p c u r l h t t p : // api. developer. s e a r s. com/v1/ p r o d u c t d e t a i l s? apikey=0ea bb5217b3973bd2c315be39&s t o r e=sears& showspec=y e s&textonly=y e s&partnumber = P Tajima Tool Corp - Rapid Pull TPI blade This blade is offered by both companies on the following web pages:

222 Appendix D. Additional HomeServices Information 209 Amazon: h t t p : // w e b s e r v i c e s. amazon. com/ onca /xml? S e r v i c e= AWSECommerceService&Operation=ItemLookup&S u b s c r i p t i o n I d= AKIAJHNOF4OERYF3SWSQ&AssociateTag=serv07 20&Version = &ItemId=B0008IVWVU&IdType=ASIN&C o n d i t i o n=new& ResponseGroup=Images, ItemAttributes, Offers, A c c e s s o r i e s, AlternateVersions, BrowseNodes, EditorialReview, OfferFull, OfferSummary, Reviews, SalesRank, S i m i l a r i t i e s, Tracks, VariationImages, VariationMatrix, VariationSummary, V a r i a t i o n s Sears: p p c u r l h t t p : // api. developer. s e a r s. com/v1/ p r o d u c t d e t a i l s? apikey=0ea bb5217b3973bd2c315be39&s t o r e=sears& showspec=y e s&textonly=y e s&partnumber = P Craftsman 16 oz. Rubber Mallet This mallet is offered by both companies on the following web pages: Amazon: h t t p : // w e b s e r v i c e s. amazon. com/ onca /xml? S e r v i c e= AWSECommerceService&Operation=ItemLookup&S u b s c r i p t i o n I d= AKIAJHNOF4OERYF3SWSQ&AssociateTag=serv07 20&Version = &ItemId=B001O8QSTY&IdType=ASIN&C o n d i t i o n=new& ResponseGroup=Images, ItemAttributes, Offers, A c c e s s o r i e s, AlternateVersions, BrowseNodes, EditorialReview, OfferFull, OfferSummary, Reviews, SalesRank, S i m i l a r i t i e s, Tracks, VariationImages, VariationMatrix, VariationSummary, V a r i a t i o n s Sears: c u r l h t t p : // api. developer. s e a r s. com/v1/ p r o d u c t d e t a i l s? apikey=0ea bb5217b3973bd2c315be39&s t o r e=sears& showspec=y e s&textonly=y e s&partnumber = P

223 Appendix D. Additional HomeServices Information 210 Delta Faucet U4993-SS Universal Showering Components Shower Arm and Flange, Stainless This faucet flange is offered by both companies on the following web pages: Amazon: h t t p : // w e b s e r v i c e s. amazon. com/ onca /xml? S e r v i c e= AWSECommerceService&Operation=ItemLookup&S u b s c r i p t i o n I d= AKIAJHNOF4OERYF3SWSQ&AssociateTag=serv07 20&Version = &ItemId=B006WKZVM4&IdType=ASIN&C o n d i t i o n=new& ResponseGroup=Images, ItemAttributes, Offers, A c c e s s o r i e s, AlternateVersions, BrowseNodes, EditorialReview, OfferFull, OfferSummary, Reviews, SalesRank, S i m i l a r i t i e s, Tracks, VariationImages, VariationMatrix, VariationSummary, V a r i a t i o n s Sears: c u r l h t t p : // api. developer. s e a r s. com/v1/ p r o d u c t d e t a i l s? apikey=0ea bb5217b3973bd2c315be39&s t o r e=sears& showspec=y e s&textonly=y e s&partnumber = P KNIPEX Comfort Grip Cable Shears This faucet flange is offered by both companies on the following web pages: Amazon: h t t p : // w e b s e r v i c e s. amazon. com/ onca /xml? S e r v i c e= AWSECommerceService&Operation=ItemLookup&S u b s c r i p t i o n I d= AKIAJHNOF4OERYF3SWSQ&AssociateTag=serv07 20&Version = &ItemId=B000I1L6QI&IdType=ASIN&C o n d i t i o n=new& ResponseGroup=Images, ItemAttributes, Offers, A c c e s s o r i e s, AlternateVersions, BrowseNodes, EditorialReview, OfferFull, OfferSummary, Reviews, SalesRank, S i m i l a r i t i e s, Tracks, VariationImages, VariationMatrix, VariationSummary, V a r i a t i o n s Sears: p p

224 Appendix D. Additional HomeServices Information 211 c u r l h t t p : // api. developer. s e a r s. com/v1/ p r o d u c t d e t a i l s? apikey=0ea bb5217b3973bd2c315be39&s t o r e=sears& showspec=y e s&textonly=y e s&partnumber = P D.4 Transforming Raw Vendor Product Data This section discusses how to transform the raw product data into RDF/XML format. D.4.1 Using GRDDL to Transform XHTML/XML into RDF The simplest method for transforming XHMTL documents into RDF is embed a reference of transformations using the <link> element found in the head of the document (see below from an example from [33]). Within XHTML pages, microformats are used to embed semantic markup for a specific domain in human-readable documents [33]. <!DOCTYPE html PUBLIC //W3C//DTD XHTML 1. 1//EN http : / /www. w3. org /TR/ xhtml11 /DTD/ xhtml11. dtd > <html xmlns= http : / /www. w3. org /1999/ xhtml xml : lang= en lang= en > <head profile= http : / /www. w3. org /2003/ g/data view > <t i t l e>robin s Schedule</ t i t l e> <link rel= t r a n s f o r mation href= http : / /www. w3. org /2002/12/ c a l / glean hcal /> </head> <body>... Similarly, to apply GRDDL to a XML document, one needs to add the grddl namespace declaration and a grddl:transformation attribute that contains an internationalized resource identifier (IRI) to the root element of the document. The example below is taken from [11]; the XML document is linked to two GRDDL transformations, and

225 Appendix D. Additional HomeServices Information 212 <html xmlns= http : / /www. w3. org /1999/ xhtml xmlns : grddl = http : / / www. w3. org /2003/ g/data view# grddl : transformation= g l e a n t i t l e. x s l http : / /www. w3. org /2001/sw/ grddl wg/ td / getauthor. x s l > <head> <t i t l e>are You Experienced?</ t i t l e> [... ] </html> D.4.2 Using xsltproc In order to transform the XML into RDF, we utilize the xsltproc tool that is included in the XSLT C library for the GNOME desktop environment. We utilize the Windows binaries of this tool that are included in the libxml XML processor. To use xsltproc, we copy over the binary files into one folder (e.g., C:\libxslt\bin\). For simplicity s sake, it is best to keep the stylesheet and raw XML files in the same folder as the binary files. In Microsoft Windows Command Prompt, we enter the following commands to convert the raw XML file into the RDF by applying the XSLT spreadsheet to the processor: x s l t p r o c. exe x m l 2 r d f 3 s e a r s. x s l s h e a r s s e a r s. xml > s h e a r s s e a r s. r d f x s l t p r o c. exe x m l 2 r d f 3 s e a r s. x s l shears amazon. xml > shears amazon. r d f The first argument is the xsltproc program, the second is file name of the stylesheet to be applied, then the raw XML file and the file name of the resultant RDF file. The resultant RDF files are found in the same folder as the raw XML and XSLT files. D.5 Using AllegroGraph to Test Product Mappings This section outlines how to load and test the ontology mappings in AllegroGraph.

226 Appendix D. Additional HomeServices Information 213 D.5.1 Importing the Data into AllegroGraph For this project, we use the AllegoGraph RDFStore provided by Hunch Manifest, Inc. to test the preliminary mappings that are listed in Sections and All of the product data is imported into the STLBack data store on the AllegroGraph server. Note that we had to manually enter in the required namespaces into AllegroGraph (the URIs are subject to change): amazon: gist: hso: sears: D.5.2 Using AllegroGraph s Materializer and Reasoner Since AllegroGraph stores the product information in triple form, the preliminary mappings were rewritten in SPARQL and are discussed in the subsequent section. Before we can carry out the SPARQL queries in AllegroGraph, the following steps must be followed: 1. Load in triples and owl:equivalentproperty mappings into the STLBack data store by uploading the following files: RDF triples: bd drill amazon.rdf bd drill sears.rdf flange amazon.rdf flange sears.rdf mallet amazon.rdf mallet sears.rdf sawblade amazon.rdf sawblade sears.rdf shears amazon.rdf shears sears.rdf RDF/OWL Mappings in Turtle form: mappings.nt 2. Define the required namespaces (such as amazon, hso, sears) in the Namespaces tab. 3. In the repository Overview screen, materialize the triples by clicking on Materialize Entailed Triples and select all rules offered, as shown in Figure D Enable Reasoning while running the queries, as shown in Figure D.3.

227 Appendix D. Additional HomeServices Information 214 Figure D.2: Selecting rules for AllegroGraph s materializer. Figure D.3: Enabling reasoning in the SPARQL query. D.6 Results from SPARQL Queries for HSO Mappings The following section outlines the results from the SPARQL queries used to test the ontology mappings. These results are summarized as follows: Table D.1 lists the cheapest products offered by Sears and Amazon. Table D.2 lists the cheapest products offered by Sears and Amazon based on a keyword. Table D.3 lists the average price of products (specified by keyword) offered by Sears and Amazon. Table D.4 lists the average price of all products offered by Sears and Amazon. Table D.5 lists the average price of products offered by Sears and Amazon based on a keyword. Table D.6 lists the combined product attributes of a product offered by both vendors. Table D.7 lists product data from the vendors, combined with information from DBPedia.