Discordance Detection in Regional Ordinance: Ontology-based Validation

Transcription

1 Discordance Detection in Regional Ordinance: Ontology-based Validation Shingo HAGIWARA a and Satoshi TOJO a a School of Information and Science, Japan Advanced Institute of Science and Technology, 1 1 Asahidai, Nomi, Ishikawa ( ), Japan Abstract. In this paper, we propose a procedure of discordance detection in an actual legal code, that is the regional ordinance of Toyama Prefecture, Japan. In this study, we expand the notion of inconsistency to the discordance including antonyms based on an ontology, and precluded the conventional negative connective. We have implemented the system that converts XML logical formats to Prolog, and has inspected the whole code. Keywords. Conflict, Negation, Ontology, Order-sorted logic 1. Introduction In 2002 Toyama Prefecture in Japan changed the policy and the resident became able to submit various kinds of forms electrically, in accordance with the development of the Internet. At that time, many municipal offers were forced to rewrite the regional ordinance by hand. The legal codes are intrinsically destined to be modified and revised in longer years, to catch up with the requirement of our society. However, for each revision, the coherence of the code was always threatened, and in worse cases it may include discordance and inconsistency in itself. In many researches on legal reasoning, researchers often regard that the code is consistent though they may sometimes add incomplete knowledge to get beneficial consequences [11]. However, when a new legislation, jurists need to inspect whether the new law is coherent with the existing legislations stringently. In this revision procedure, jurists must assess how large area it affects. If (s)he finds a discordance with a new legislation, (s)he modifies it first, then (s)he needs to search for the affected area further from the newly revised law recursively. Thus, such a revision would be a tedious and painstaking work. Our motivation in this study is to identify the affected area automatically and to detect the discordance in a practical, large-scale code. The structure of this paper is as follows. First, we explain concepts of conflict and loop as the discordance, and then the algorithm for validation. Secondly, our implementation is introduced. Thirdly, we explain an experimental result with actual data. Finally, we summarize our contribution.

2 2. Discordance 2.1. Discordance The logical inconsistency becomes apparent only when both of A and A appear in a set of propositions. However, the inconsistency may not be seen from the superficial sentences of the legal code. To clarify such latent inconsitency, we need to supply some premises of the rules [12]. Below is an example, where AF is a function which retrieves the minimal set of assumptive facts. Example 2.1 For = {r u, r u},af ( ) = {r}. Then, AF ( ). In addition, there might be a loop of implications. For example, in a database { a, a b, b a} where is the logical truth, we cannot collect the evidences of b. However, the discrepancy or the discordance is not only the logical inconsistency. In the lexicon of legal code, such lexical items which includes negative prefixes as un-, dis-, in-, and so on cannot coexist with their original positive words. Also, there are antonyms that have conflictive meanings without prefixes, as liquid and solid, or vice and virtue. Furthermore, some situations are incompatible with each other, which we can easily know by our common sense. For example, submission with signature is incompatible with electric submission. In this paper, we call all those sources of conflict, including (i) inconsistent rules, (ii) loops of implication, and (iii) incomptible concepts discordance in the law Conflict Thus far, there have been many researches on expanding inconsitency [4,8,1,6,5,3]. Among them, we would like to rely on the notion of conflict [3] where the opposition of antonyms or negatively prefixed words are represented. Definition 2.1 Let be inconsistency, α, β be propositional variables. (α β). Then, α and β are in conflict. With this notion, we can avoid the arbitrary, rather subjective usage of the negative connective. In this study, we eliminate this symbol and only employ. However, if we were to define conflicts, we must enumerate all the possible combinations of predicates which appear in a legal code, where the number of pairs would be O(n 2 ). To avoid this problem, we employ order-sorted hierarchy of ontology Ontology An ontology consists of tree-structured hypernym-hyponym relations, together with extraneous knowledge base. In this study, we pay attention only to the sorted hierarchy. Nowadays we can find many such ontologies, implemented in OWL (Web Ontology Language) that is a kind of XML format, or in other languages of description logic [13]. In order to complement the common knowledge to a legal database, we consider such a word taxonomy, and employ order-sorted logic [10,2] to formalize it.

3 Ordered sorts Here, we explain a part of order-sorted logic which we use in this paper. Ordered sorts S is constructed with a set of sorts S = {s 0,..., s n } and a set of sub-sort relations ( S S). An element of sub-sort relation (s i, s j ) is generally denoted by s i s j ; it is called a sub-sort declaration. Then, s i is called sub-sort of s j, and s j is called super-sort of s i. Furthermore, the sub-sort relations satisfy transitivity and reflexivity, is sub-sort of all sort, and is super-sort of all sort. In addition, for such a S, if (s, s ), then it can be denoted by S = s s s Conflict in Ordered Sorts Next, we consider a concept of conflict in order-sorted logic. First, we introduce (meet) operation that returns the infimum (the greatest lower bound) with regard to, taking two sorts [10]. Definition 2.2 exclusive relation Let s i, s j be sorts and be the minimum sort. Then, s i s j iff s i s j = Furthermore, a sort is regarded as a unary predicate [2] of FOL (first-ordered logic). Thus, the sort predicate is defined as follows. Definition 2.3 Sort predicate Let S = S, be ordered sorts, s be a sort and x be an individual variable. If s S hold, then a unary predicate s(x) exists. Then s(x) is denoted by P s (x). Therefore, the above exclusive relation is regarded as s i s j s i s j = x[p si (x) P sj (x) ]. As stated above, the exclusive relation can express the conflict on ordered sorts Application of Order-sorted Logic to Ontology Although a sort predicate in Definition. 2.3 is unary, a concept in an ontology may be used as a predicate with multiple arguments. Thus, we need to expand the sort predicate as follows. Definition 2.4 Sort Predicate for Ontology Let S = S, be ordered sorts, be a knowledgebase, P be a set of predicate of. If s S and s(x 0,..., x n ) P, then we call s(x 0,..., x n ) sort predicate for. A function which returns the sort predicate dependant on the knowledgebase is denoted by SP; Thus, SP (, s) = s(x 0,..., x n ). Since an ontology is described by XML, it can express some properties besides super-sub relations. Thus, we define a function, by which an ordered sorts are extracted from an ontology. Then we denote S O for ordered sorts of the ontology O 1 1 If the ontology is given in XML, such tags as class/subclass notation are converted to the subsumption of sorts.

4 Next, for the ordered sorts, we define a concept of conflict. Then, we revise the definition of the operator meet ( ) as follows, because the hierarchy of the ontology is not necessarily a lattice 2. Definition 2.5 Meet operator Let S = S, be ordered sorts. s i, s j S be sorts. For S, s i and s j, we assume Σ = {s s s i, s s j, s S} and Γ = {s s, s Σ, S s s }, then s i s j = Γ holds. Moreover, it is denoted by S = s i s j = Γ. As stated above, we define a function of extraction of conflict pairs of sorts from ordered sorts as follows. Definition 2.6 Function of Extraction of Conflict Relations Let S O = S, be ordered sorts, Arity be a function which returns th number of the arguments of the predicate, and be knowledgebase. For S O, S O = s i s j = { } and Arity(SP(, s i )) = Arity(SP(, s j )), then, for, we convert it into x 0,..., x n [SP(, s i ) SP(, s j ) O ]. O means that inconsistency on O. We denote such a function of conversion as Cnf. Hence, x 0,..., x n [SP(, s i ) SP(, s j ) O ] Cnf (, S O ), where x 0,..., x n are individual variables of sort predicates which are returned by a function of SP. Therefore, for a knowledgebase Σ, if Σ Cnf (Σ, S O ) O, then we can consider that Σ includes inconsistency on the ontology O Extraction of Supplement Knowledge from Ontology Thus far, we utilize an ontology to define a concept of conflict. However, the ontology is not limited to this, but also can be used to aid the knowledgebase of law interpretation. A sub-sort relation, denoted by s s, is equal to x[p s (x) P s (x)]. Therefore, information in an ontolory can be regarded as inclusion relations of lexicons which are not explicitly defined in the text of the law. Those inclusion relations are really helpful for validation. Then, for an ontology, we define a function of conversion of sub-sort relations into implication of FOL as follows. Definition 2.7 Function of Conversion of Sub-sort Declaration. Let be knowledgebase, S = S, be ordered sorts, Arity be a function which returns th number of the arguments of the predicate, and x 0,..., x n be individual variables of a predicate which is returned by SP. If S = s s s and Arity(SP(, s)) = Arity(SP(, s )) = n, then it can be regarded as x 0..., x n [SP(, s) SP(, s )]. Therefore, we denote such a function which returns a formula which is converted for all sort by Imp. Thus, in a case that formula was denoted by ϕ, ϕ Imp(, S). As observed above, we validate a knowledgebase into which AF ( ), Cnf (, S O ) and Imp(, S O ) are added. 2 A lattice is a partially ordered set (or poset) whose nonempty finitesubsets all habe a supremum (called join) and an infimum(called meet)

5 Conflict of Rules Hence, we define conflict of rules. Then, we regard that a knowledgebase consists of a set of Horn clauses. When we detect the discordance, we employ the definition of argument [9,7] as follows. Definition 2.8 Argument Let ϕ be formula and Φ be a set of formulae. Φ, ϕ is an argument iff Φ ϕ, ψ[φ \ {ψ} ϕ] and Φ. With those definitions, we define the conflict of rules as follows. Definition 2.9 Conflict of Rules Let be knowledgebase of the text of the law, S O be ordered sorts made from an ontology, and ϕ and ψ be predicates. Also, we assume Γ = AF ( ) Cnf (, S O ) Imp(, S O ). Then, we consider an argument Arg 1 = Φ, ϕ, where Φ Γ. If (Φ AF ( )) Cnf (, S O ) Imp(, S O ) O, then, we consider that has conflict of rules on the ontology O. Particularly, in a case that (Φ AF ( )) Cnf (, S O ) Imp(, S O ) ψ, we consider that ϕ and ψ in conflict. A brief meaning of this definition is that a conflictive predicate must be not derived from facts which were used to derive another predicate which is in conflict. 3. Implementation In this section, we explain our implementation which consists of two programs. Its overview is Figure Programs One of the programs is a converter, written in Ruby, and the role is conversion of XML files into Prolog code. Another one is a validator, written in Prolog, and the role of which is validation of the code output by the converter Converter First, we explain how the converter converts XML to Prolog. Conversion of Rules We used two data files which are written in XML; one of them is the text of the law. This file includes rules which are expressed in FOL, as follows, where Japanese words are translated in Table. 1. <implies> <clause> <predicate value=" "/> <argument number="1"><var name="x"/></argument> <argument number="2"><var name="y"/></argument> <argument number="3"><var name="z"/></argument> </clause> <clause>

6 Rules of the law Ontology XML (FOL and OWL) Converter PSfrag replacements Knowledgebase of the law Ordered sorts Validation Code for Execution Prolog Validator Conflict Result Loop Result Text data Figure 1. Overview of Implementation Japanese English procedure of application officiallicense applicant intendance Table 1. Table of Mapping Japanese to English 1 <predicate value=" "/> <argument number="1"><var name="z"/></argument> </clause> <clause> <predicate value=" "/> <argument number="1"><var name="x"/></argument> </clause> <clause> <predicate value=" "/> <argument number="1"><var name="y"/></argument> </clause> </implies> When procedure of application, official license and intendance are expressed by application, licence, applicant and intendance as predicate names, respectively, the part of XML in the figure becomes x, y, z[application(x, y, z) licence(z) applicant(x) intendance(y)]. Actually, the XML is converted into a prolog code as

7 follows. 1:pv_sub(Root, (x,y,z)):- 2: usecheck(root,use_379,pv_sub(root, (x,y,z))), 3: pv(root, (z)), 4: pv(root, (x)), 5: pv(root, (y)), 6: pv(root,acceptable( : 8 : 1 )), 7: usedcheck(root,use_379,pv_sub(root, (x,y,z))). In the figure, n: means attached line numbers. From here, we simply explain some predicates which are used for validation. Both of pv and pv_sub execute their contents and record the execution logs. usecheck and usedcheck are used to detect a loop. acceptable is used to check whether a flag of a rule number is permitted or not. Extraction of Assumptive Facts We mentioned in Section 1 that we need to add premises of rules to the knowledgebase. Then, the converter extracts the premises, and converts them into Prolog code. The method is so simple. First, predicates which appear in head parts of the prolog code of rules are collected; this set is denoted by H. Second, in the similar way, predicates in body parts are collected; this set is denoted by B. Finally, B \ H is calculated, and the result is a set of assumptive facts. Ontology Next, we explain how to convert an ontology into Prolog code. As stated above, information of a concept of conflict and inclusion relations are extracted from an ontology. Then, basically those forms are the same one of rules except for rule number predicate acceptable. Therefore, the following XML data is converted into the following form in Prolog. <owl:class rdf:id=" "> <rdfs:subclassof> <owl:class rdf:id=" "/> </rdfs:subclassof> </owl:class> 1:pv_sub(Root, (Var_0)):- 2: usecheck(root,use_34,pv_sub(root, (Var_0))), 3: pv(root, (Var_0)), 4: usedcheck(root,use_34,pv_sub(root, (Var_0))). For the above data, the Prolog code expresses a FOL formula which is converted from a super-sub relation of OWL. In addition, relation data used to calculate a conflictive pair of predicates in execution of a validation program are extracted as follows. 1:relation(, ) Validator The execution of validation program is explained with in Figure. 2. In the figure, P n means predicates, P factn means a fact, means unification, and means the implication. Firstly, the validator performs P 0 (X). Then, the Prolog interpreter proves it, deducing some predicates; if it arrives at facts, it returns YES and terminates. In the process, the arguments of the predicates which were bound by constant individuals in the deduction are recorded. Therefore, the record is the argument of P 0 in Figure. 2. Secondly, the

8 Argument of P 0(X) P 0(X) PSfrag replacements P 1(X) P 2(X, Y ) Argument of P 6(X) P 6(X) P 5(X) P 3(Y ) P 4(X) P fact0 (a) P fact1 (b) Assumptive Facts Conflict: x[p 0(x) P 6(x) O] Figure 2. Image of Validation validator calculates a predicate which is in conflict with P 0 on ordered sorts; in the case, the validator can get P 6 from x[p 0 (x) P 6 (x) O ]: in the fact, it is calculated with the code of relations. Thus, the validator execute P 6 ; however, the way of execution of P 6 is different from the case of P 0. In the execution of P 0, the interpreter can use all the knowledge, but in the case of execution of P 6, the interpreter uses only facts which exist in the record; viz, the interpreter confirms whether P 6 holds by the fact that P 0 holds. In the figure, since P 6 held, we can recognize that the knowledgebase has the discordance of conflict between P 0 and P Experiment In the experiment, firstly, we could not find a conflictive part. Then, we artificially removed some predicates from a rule to confirm our algorithm, and the programs output some conflictive parts. Therefore, we could confirm that the rules did not have some conflictive parts. However, several loops could be found as follows. pv_sub(root, (X)):- pv(root, (X)), pv(root, (Y)), pv(root, (Y,X)), pv(root,acceptable( : 4 : 1 )). pv_sub(root, (Var_0)):- pv(root, (Var_0)).

9 Symbol Japanese English α a person who has right of appointive power β educational boards of cities and towns γ a person who has right of permission of officialtrip Table 2. Table of Mapping Japanese to English 2 pv_sub(root, (Z)):- pv(root, (Z)), pv(root,acceptable( : 4 : 1 )). In the source code, there is a loop which is from α to β, from β to γ and from γ to α. The Japanese words are replaced for Table. 2. Therefore, in a case that x is a person who has right of appointive power, we cannot get an evidence for it. Namely, we regard that this part should be corrected. 5. Conclusion Our contribution of this study is summarized as follows. We have targeted the real problem of ordinance revision held in Toyama prefecture in 2002, instead of artificial toy problem. We employed Gabbay s conflict instead of the conventional negative connective. Thus, we could employ ordered sorted hierarchy in ontology to detect incompatible notions. We have implemented a discordance detection system based on the logical format of XML, where those XML files were converted into Prolog, and the verification program scans the code to detect discordance. Our future target target would be the handling of. We simply divided those rules including disjunctions to implement them in Horn clause. However, we need to consider the computational efficiency. Also the input format of our system is XML based on first order logic (FOL). Translating natural language sentences into FOL still remains a tough problem. References [1] B. H. Slater. Paraconsistent logic? Journal of Philosophical Logic, 25: , [2] C. Beierle, U. Hedtstuck, U. Pletat, P. H. Schmitt, and J. Siekmann. An order-sorted logic for knowledge representation systems. Artificial Intelligence, 55: , June [3] Dov M. Gabbay and A. Hunter. Negation and contradiction. In Dov Gabbay and Heinrich Wansing, editors, What is Negation?, pages Kluwer Publishers, [4] Dov M. Gabbay and H. Wansing. What is negation? Kluwer Academic Publishers, [5] G. Restall. Paraconsistent logics! Bulletin of the Section of Logic, 26:156 63, [6] G. Restall. Negation in relevant logics: How i stopped worrying and learned to love the routley star. In Dov Gabbay and Heinrich Wansing, editors, What is Negation?, pages Kluwer Academic Publishers, [7] H. Prakken. A logical framework for modelling legal argument. In ICAIL 93: Proceedings of the fourth international conference on Artificial intelligence and law, pages 1 9. ACM Press, [8] H. Wansing. Negation. In Lou Goble, editor, The Blackwell Guide to Philosophical Logic, pages Blackwell Philosophy Guides, 2001.

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