The Implementation of the Conditions for the Existence of the Most Specific Generalizations w.r.t. General EL-TBoxes

Transcription

1 The Implementation of the Conditions fo the Existence of the Most Specific Genealizations w..t. Geneal EL-TBoxes Adian Nuadiansyah Technische Univesität Desden Supevised by: Anni-Yasmin Tuhan Febuay 12, 2016 Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

2 Oveview 1 Motivation behind the Implementation 2 Algoithm to Decide the Existence of the Most Specific Genealization 3 Implementation of the Algoithm 4 Evaluation of the Implementation in Cyclic Ontology 5 Conclusion and Futue Wok Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

3 Motivation behind the Implementation Most Specific Genealization Least common subsume (lcs) and Most Specific Concept (msc). The lcs yields a concept that captues all commonalities of pai of concepts (subsumption). The msc genealizes an individual into a single concept (instance checking). Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

4 Motivation behind the Implementation Most Specific Genealization Least common subsume (lcs) and Most Specific Concept (msc). The lcs yields a concept that captues all commonalities of pai of concepts (subsumption). The msc genealizes an individual into a single concept (instance checking). Suppot building and maintaining the knowledge base (KB) fom bottom up appoach. Pocessed, investigated, and added into KB new knowledge! Neithe the lcs no the msc need to exist in geneal EL-TBox. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

5 Motivation behind the Implementation Knowledge Base Family and its Canonical Model T family1 : {Wife Female Peson likes.husband; HappyPeson Peson likes.happypeson; Husband Male Peson likes.wife} A family1 : {likes(bob,caol); likes(bob,bob); Wife(caol); HappyPeson(bob)} Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

6 Motivation behind the Implementation Knowledge Base Family and its Canonical Model T family1 : {Wife Female Peson likes.husband; HappyPeson Peson likes.happypeson; Husband Male Peson likes.wife} A family1 : {likes(bob,caol); likes(bob,bob); Wife(caol); HappyPeson(bob)} {Husband, Male, HappyPeson, Peson} {Female, Peson, Wife} {Male, Husband, Peson} {Wife, Peson, Female} d Bob likes d Caol likes d Husband likes d Wife likes likes Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

7 Motivation behind the Implementation Knowledge Base Family and its Canonical Model T family1 : {Wife Female Peson likes.husband; HappyPeson Peson likes.happypeson; Husband Male Peson likes.wife} A family1 : {likes(bob,caol); likes(bob,bob); Wife(caol); HappyPeson(bob)} {Husband, Male, HappyPeson, Peson} {Female, Peson, Wife} {Male, Husband, Peson} {Wife, Peson, Female} d Bob likes d Caol likes d Husband likes d Wife likes likes lcs(male, Peson)=, but thee is no lcs fo Husband and HappyPeson Husband and HappyPeson ae cyclic concepts. msc(caol)=wife, but thee is no msc fo bob Wife(caol) and HappyPeson(bob). Wife and HappyPeson ae cyclic concepts. Diffeent esults fo the msc in a cyclic ontology! Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

8 Motivation behind the Implementation Knowledge Base Family and its Canonical Model T family1 : Wife Female Peson likes.husband; Husband Male Peson likes.wife HappyPeson Peson likes.happypeson; A family1 : likes(bob,caol); likes(bob,bob); Wife(Caol); HappyPeson(Bob) {Husband, Male, HappyPeson, Peson} {Female, Peson, Wife} {Male, Husband, Peson} {Wife, Peson, Female} d Bob likes d Caol likes d Husband likes d Wife likes likes How to compute and decide the existence of the most specific genealization w..t. geneal EL TBox? Fo the sake of simplicity, we only conside the notions elated to the least common subsume in futhe sections. Most specific concept can be defined analogously. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

9 Least Common Subsume A concept E is the least common subsume(lcs) of C and D w..t. T (lcs T (C, D)) iff: C T E and D T E Fo each concept F such that C T F and D T F, then E T F. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

10 Least Common Subsume A concept E is the least common subsume(lcs) of C and D w..t. T (lcs T (C, D)) iff: C T E and D T E Fo each concept F such that C T F and D T F, then E T F. We deal with a geneal EL TBox. The computed lcs can be captued in an infinite size. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

11 Least Common Subsume A concept E is the least common subsume(lcs) of C and D w..t. T (lcs T (C, D)) iff: C T E and D T E Fo each concept F such that C T F and D T F, then E T F. We deal with a geneal EL TBox. The computed lcs can be captued in an infinite size. Can we obtain a ole-depth bounded lcs with a depth k? Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

12 Least Common Subsume A concept E is the least common subsume(lcs) of C and D w..t. T (lcs T (C, D)) iff: C T E and D T E Fo each concept F such that C T F and D T F, then E T F. We deal with a geneal EL TBox. The computed lcs can be captued in an infinite size. Can we obtain a ole-depth bounded lcs with a depth k? The ole-depth (d(c)): the maximal nesting of -quantifies in C. Let k N and E, F ae the ole-depth bounded concepts with the ole-depth up to k, then E is the ole-depth bounded lcs (k-lcs T (C, D)) of C and D w..t. T. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

13 Least Common Subsume A concept E is the least common subsume(lcs) of C and D w..t. T (lcs T (C, D)) iff: C T E and D T E Fo each concept F such that C T F and D T F, then E T F. We deal with a geneal EL TBox. The computed lcs can be captued in an infinite size. Can we obtain a ole-depth bounded lcs with a depth k? The ole-depth (d(c)): the maximal nesting of -quantifies in C. Let k N and E, F ae the ole-depth bounded concepts with the ole-depth up to k, then E is the ole-depth bounded lcs (k-lcs T (C, D)) of C and D w..t. T. How to obtain this numbe k? How do we know that ou k-lcs is ou lcs, such that we can check whethe the lcs exists o not? Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

14 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

15 Desciption Logic EL and TBox EL concepts ae built by using the following stuctues: C,D ::= A C D.C Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

16 Desciption Logic EL and TBox EL concepts ae built by using the following stuctues: C,D ::= A C D.C An intepetation I = ( I, I ) consists of: I : a non-empty domain. I with A I I and I I I The mapping I can be extended to EL-concepts Name Syntax Semantic Top I Conjunction C D C I D I Existential Restiction.C {d I e I : (d,e) I and e C I } Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

17 Desciption Logic EL and TBox EL concepts ae built by using the following stuctues: C,D ::= A C D.C An intepetation I = ( I, I ) consists of: I : a non-empty domain. I with A I I and I I I The mapping I can be extended to EL-concepts Name Syntax Semantic Top I Conjunction C D C I D I Existential Restiction.C {d I e I : (d,e) I and e C I } A (geneal) EL TBox T is a finite set of Geneal Concept Inclusion (GCI) of the fom of C D. An intepetation I satisfies a GCI C D iff C I D I I is a model of T iff it satisfies all GCIs in T. C is subsumed by D w..t. T (denoted by C T D ) iff C I D I fo all models I of T. This easoning task is called subsumption. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

18 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

19 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T of C and D w..t. T ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

20 Canonical Model Canonical Model of Concept w..t. TBox It is denoted by I C,T. Recall this example: T family2 : Wife Female Peson likes.husband; Husband Male Peson likes.wife {Male, Peson I Husband,T family2 Husband} d Husband likes likes d Wife {Wife, Peson, Female} I d : an intepetation with d Id as an initial element such that all e Id ae eachable fom d. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

21 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T of C and D w..t. T ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

22 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models IC,T d and Ie D,T of C and D w..t. T ; 3. Compute the poduct IC,T f D,T of Id C,T and Ie D,T ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

23 Poduct Intepetation Poduct Intepetation is denoted by I 1 2 Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

24 Poduct Intepetation Poduct Intepetation is denoted by I 1 2 Example: I 1 {A} d A d C {C} Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

25 Poduct Intepetation Poduct Intepetation is denoted by I 1 2 Example: I 1 {A} I 2 {B} d A d B d C d C {C} {C} Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

26 Poduct Intepetation Poduct Intepetation is denoted by I 1 2 Example: I 1 {A} d A I 2 {B} d B I 1 2 {} d A,d B d C d C d A,d C d C,d C d B,d C {C} {C} {} {C} {} How to get the poduct of canonical models in the smalle size? Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

27 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models IC,T d and Ie D,T of C and D w..t. T ; 3. Compute the poduct IC,T f D,T of Id C,T and Ie D,T ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

28 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

29 Simulation Relation Subsumption can be chaacteized by a simulation elation. Let I 1 and I 2 be intepetations S I1 I2 is defined as a simulation fom I 1 to I 2. A simulation S max fom I 1 to I 2 is said to be maximal if fo all S fom I 1 to I 2, then it holds that S S max.

30 Simulation Relation Subsumption can be chaacteized by a simulation elation. Let I 1 and I 2 be intepetations S I1 I2 is defined as a simulation fom I 1 to I 2. A simulation S max fom I 1 to I 2 is said to be maximal if fo all S fom I 1 to I 2, then it holds that S S max. Example: I 1 {A} d 1 d 2 {A} I 2 ((I 1, d 1 ) is simulated ( ) by (I 2, d 2 )) {B} d 3 Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

31 Simulation Relation Subsumption can be chaacteized by a simulation elation. Let I 1 and I 2 be intepetations S I1 I2 is defined as a simulation fom I 1 to I 2. A simulation S max fom I 1 to I 2 is said to be maximal if fo all S fom I 1 to I 2, then it holds that S S max. Example: I 1 {A} d 1 d 2 {A} I 2 ((I 1, d 1 ) is simulated ( ) by (I 2, d 2 )) {B} d 3 d 4 {A,B} Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

32 Simulation Relation Subsumption can be chaacteized by a simulation elation. Let I 1 and I 2 be intepetations S I1 I2 is defined as a simulation fom I 1 to I 2. A simulation S max fom I 1 to I 2 is said to be maximal if fo all S fom I 1 to I 2, then it holds that S S max. Example: I 1 {A} d 1 d 2 {A} I 2 ((I 1, d 1 ) is simulated ( ) by (I 2, d 2 )) {B} d 3 d 4 {A,B} ((I 1, d 3 ) is simulated ( ) by (I 2, d 4 )) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

33 Simulation Relation Subsumption can be chaacteized by a simulation elation. Let I 1 and I 2 be intepetations S I1 I2 is defined as a simulation fom I 1 to I 2. A simulation S max fom I 1 to I 2 is said to be maximal if fo all S fom I 1 to I 2, then it holds that S S max. Example: I 1 {A} d 1 d 2 {A} I 2 ((I 1, d 1 ) is simulated ( ) by (I 2, d 2 )) {B} d 3 d 4 {A,B} ((I 1, d 3 ) is simulated ( ) by (I 2, d 4 )) (I 1,d) is equisimila to (I 2,e) (denoted by (I 1,d) (I 2,e)) if (I 1,d) (I 2,e) and (I 2,e) (I 1,d). Let [d] := {e I (I, d) (I, e)}. V as the set of -classes w..t. a simulation S Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

34 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

35 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; 5. Compute the equisimulation quotient I [f] (C,T D,T )/ of If C,T D,T I[f] (C,T D,T )/ := V; with Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

36 Equisimulation Quotient I / is an equisimulation quotient of I. It is computed to: Reduce the numbe of edundant ole-successo nodes Get the smalle numbe of oles to be tavesed duing computing the k-chaacteistic concept. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

37 Equisimulation Quotient I / is an equisimulation quotient of I. It is computed to: Reduce the numbe of edundant ole-successo nodes Get the smalle numbe of oles to be tavesed duing computing the k-chaacteistic concept. I d Caol K family {Female, Peson, Wife} 1 {Male, Husband, Peson} {Wife, Peson, Female} d Caol likes d Husband likes d Wife likes Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

38 Equisimulation Quotient I / is an equisimulation quotient of I. It is computed to: Reduce the numbe of edundant ole-successo nodes Get the smalle numbe of oles to be tavesed duing computing the k-chaacteistic concept. 1 2 I d Caol K family {Female, Peson, Wife} {Male, Husband, Peson} {Wife, Peson, Female} (I Kfamily,d Caol ) (I Kfamily, d Wife ) d Caol likes d Husband likes d Wife likes Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

39 Equisimulation Quotient I / is an equisimulation quotient of I. It is computed to: Reduce the numbe of edundant ole-successo nodes Get the smalle numbe of oles to be tavesed duing computing the k-chaacteistic concept. I d Caol K family {Female, Peson, Wife} d Caol likes 1 {Male, Husband, Peson} d Husband likes likes {Wife, Peson, Female} d Wife 2 (I Kfamily,d Caol ) (I Kfamily, d Wife ) [d 1 ] := {d Husband } [d 2 ] := {d Caol, d Wife } Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

40 Equisimulation Quotient I / is an equisimulation quotient of I. It is computed to: Reduce the numbe of edundant ole-successo nodes Get the smalle numbe of oles to be tavesed duing computing the k-chaacteistic concept I d Caol K family {Female, Peson, Wife} d Caol likes {Male, Husband, Peson} d Husband likes likes {Wife, Peson, Female} d Wife (I Kfamily,d Caol ) (I Kfamily, d Wife ) [d 1 ] := {d Husband } [d 2 ] := {d Caol, d Wife } I [d 2 ] K family/ {Male, Husband, Peson} [d 1 ] likes likes {Wife, Peson, Female} [d 2 ] Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

41 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; 5. Compute the equisimulation quotient I [f] (C,T D,T )/ of If C,T D,T I[f] (C,T D,T )/ := V; with Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

42 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; 5. Compute the equisimulation quotient I [f] (C,T D,T )/ of If C,T D,T I[f] (C,T D,T )/ := V; with 6. Obtain the numbe k as a ole-depth fo ou lcs candidate by computing k = n 2 + m + 1, whee: n = I[f] C,T D,T / ; m = max({d(f ) F sub(t ) {C,D}}) 7. Compute the k-chaacteistic concept K by tavesing I [f] (C,T D,T )/ ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

43 k-chaacteistic Concept Role-Depth bounded concept K with the depth k can be obtained by tavesing a canonical model I. It is computed ecusively by means of k-chaacteistic concept X k (I,d) with d I. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

44 k-chaacteistic Concept Role-Depth bounded concept K with the depth k can be obtained by tavesing a canonical model I. It is computed ecusively by means of k-chaacteistic concept X k (I,d) with d I. Example: {A,B} I 1 {A} e d s f {B} Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

45 k-chaacteistic Concept Role-Depth bounded concept K with the depth k can be obtained by tavesing a canonical model I. It is computed ecusively by means of k-chaacteistic concept X k (I,d) with d I. Example: {A,B} I 1 {A} e d s f {B} k = 0; X 0 (I,e) := A k = 1; X 1 (I,e) := A.(A B) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

46 k-chaacteistic Concept Role-Depth bounded concept K with the depth k can be obtained by tavesing a canonical model I. It is computed ecusively by means of k-chaacteistic concept X k (I,d) with d I. Example: {A,B} I 1 {A} e d s f {B} k = 0; X 0 (I,e) := A k = 1; X 1 (I,e) := A.(A B) k = 2; X 2 (I,e) := A.(A B s.b ) k = 3; X 3 (I,e) := A.(A B s.(b.a)) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

47 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; 5. Compute the equisimulation quotient I [f] (C,T D,T )/ of If C,T D,T I[f] (C,T D,T )/ := V; with 6. Obtain the numbe k as a ole-depth fo ou lcs candidate by computing k = n 2 + m + 1, whee: n = I[f] C,T D,T / ; m = max({d(f ) F sub(t ) {C,D}}) 7. Compute the k-chaacteistic concept K by tavesing I [f] (C,T D,T )/ ; Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

48 Deciding the Existence of the Least Common Subsume 1. Given two concepts C, D and a TBox T as the inputs; 2. Compute the canonical models I d C,T and Ie D,T 3. Compute the poduct I f C,T D,T of Id C,T and Ie D,T ; of C and D w..t. T ; 4. Compute the maximal simulation S max1 fom I f C,T D,T to If C,T D,T and geneate the set V of -classes w..t. S max1 ; 5. Compute the equisimulation quotient I [f] (C,T D,T )/ of If C,T D,T I[f] (C,T D,T )/ := V; with 6. Obtain the numbe k as a ole-depth fo ou lcs candidate by computing k = n 2 + m + 1, whee: n = I[f] C,T D,T / ; m = max({d(f ) F sub(t ) {C,D}}) 7. Compute the k-chaacteistic concept K by tavesing I [f] (C,T D,T )/ ; 8. Compute the canonical model I K of K; 9. Check whethe (I [f] (C,T D,T )/, [f] ) is simulated by (Id K K,T,d K ). If it is simulated, then K is the lcs T (C, D). Othewise, C and D do not have lcs w..t. T. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

49 Implementation of the Algoithm Desktop-based application Executed in console command-line. It is implemented in Java pogamming language. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

50 Implementation of the Algoithm Desktop-based application Executed in console command-line. It is implemented in Java pogamming language. input: ontology file, two EL concepts o single individual in OWL fomat Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

51 Implementation of the Algoithm Desktop-based application Executed in console command-line. It is implemented in Java pogamming language. input: ontology file, two EL concepts o single individual in OWL fomat Pocess: OWL API (OWL 2.0) + ELASTIQ libay (computing canonical model) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

52 Implementation of the Algoithm Desktop-based application Executed in console command-line. It is implemented in Java pogamming language. input: ontology file, two EL concepts o single individual in OWL fomat Pocess: OWL API (OWL 2.0) + ELASTIQ libay (computing canonical model) output: If the lcs/the msc exists, the etuned concept is epesented of the fom of Mancheste OWL syntax Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

53 Implementation of the Algoithm Desktop-based application Executed in console command-line. It is implemented in Java pogamming language. input: ontology file, two EL concepts o single individual in OWL fomat Pocess: OWL API (OWL 2.0) + ELASTIQ libay (computing canonical model) output: If the lcs/the msc exists, the etuned concept is epesented of the fom of Mancheste OWL syntax Notes: The bigge the numbe of ole depth k needed, the bigge the size of computed concepts. The pesentation of the output of the fom of complex concept is quite edundant Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

54 Evaluation: Puposes and Test Ontologies Puposes: To decide the existence of the most specific genealization in cyclic ontologies. To measue the time of computation and analyze the size of computed lcs and msc concepts. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

55 Evaluation: Puposes and Test Ontologies Puposes: To decide the existence of the most specific genealization in cyclic ontologies. To measue the time of computation and analyze the size of computed lcs and msc concepts. Test Ontologies Cyclic EL ontologies that ae applied in the eal and pactical aea of knowledge base. Using 10 vesions of GeneOntology. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

56 Evaluation: in Cyclic Ontologies 1. Least Common Subsume Test the cyclicity in all test ontologies nnotations1, nnotations2, and nnotations8 have cyclic concepts. Thee ae 5 cyclic concepts fom nnotations1 and nnotations2, espectively. Fo nnotations8, thee ae only 2 cyclic concepts. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

57 Evaluation: in Cyclic Ontologies 1. Least Common Subsume Test the cyclicity in all test ontologies nnotations1, nnotations2, and nnotations8 have cyclic concepts. Thee ae 5 cyclic concepts fom nnotations1 and nnotations2, espectively. Fo nnotations8, thee ae only 2 cyclic concepts. Compute the existence of the LCS of each pai of cyclic concepts w..t. thei ontologies. 2 out of 10 pais of cyclic concepts in both of nnotations1 nnotations2 do not have the lcs. One pai of cyclic concepts in nnotations8 does not have lcs. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

58 Evaluation: in Cyclic Ontologies 1. Least Common Subsume Test the cyclicity in all test ontologies nnotations1, nnotations2, and nnotations8 have cyclic concepts. Thee ae 5 cyclic concepts fom nnotations1 and nnotations2, espectively. Fo nnotations8, thee ae only 2 cyclic concepts. Compute the existence of the LCS of each pai of cyclic concepts w..t. thei ontologies. 2 out of 10 pais of cyclic concepts in both of nnotations1 nnotations2 do not have the lcs. One pai of cyclic concepts in nnotations8 does not have lcs. Concept Name 1 Concept Name 2 Ontology k (ole depth) Result PomBase SPBC c PomBase SPCC18B5.03 nnotations1 148 Yes, the lcs exists PomBase SPCC4B3.15 PomBase SPBC2F12.13 nnotations1 260 Yes, the lcs exists PomBase SPBC c PomBase SPBC2F12.13 nnotations No, the lcs does not exist PomBase SPCC18B5.03 PomBase SPCC4B3.15 nnotations No, the lcs does not exist PomBase SPBC c PomBase SPCC4B3.15 nnotations2 293 Yes, the lcs exists UniPotKB D9PTP5 UniPotKB Q9GYJ9 nnotations8 260 No, the lcs does not exist Table: Evaluation fo the Existence of the LCS (1) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

59 Evaluation: in Cyclic Ontologies Concept Name 1 Concept Name 2 Ontology Size of the LCS Time of Computation PomBase SPBC c PomBase SPCC18B5.03 nnotations ,882 s PomBase SPCC4B3.15 PomBase SPBC2F12.13 nnotations ,525 s PomBase SPBC c PomBase SPBC2F12.13 nnotations1 52,963 s PomBase SPCC18B5.03 PomBase SPCC4B3.15 nnotations2 686,037 s PomBase SPBC c PomBase SPCC4B3.15 nnotations ,936 s UniPotKB D9PTP5 UniPotKB Q9GYJ9 nnotations8 27,18 s Table: Evaluation fo the Existence of the LCS (2) Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

60 Evaluation: in Cyclic Ontologies Concept Name 1 Concept Name 2 Ontology Size of the LCS Time of Computation PomBase SPBC c PomBase SPCC18B5.03 nnotations ,882 s PomBase SPCC4B3.15 PomBase SPBC2F12.13 nnotations ,525 s PomBase SPBC c PomBase SPBC2F12.13 nnotations1 52,963 s PomBase SPCC18B5.03 PomBase SPCC4B3.15 nnotations2 686,037 s PomBase SPBC c PomBase SPCC4B3.15 nnotations ,936 s UniPotKB D9PTP5 UniPotKB Q9GYJ9 nnotations8 27,18 s Table: Evaluation fo the Existence of the LCS (2) 2. Most Specific Concept Thee is no cyclic individual in all test ontologies. MSC always exist in this evaluation. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

61 Conclusion and Futue Wok Conclusions Implementing the algoithm to decide the existence of the lcs and the msc by means of canonical model and simulation elation. Involving the computation of building the poduct of canonical model in the smalle size. Canonical model with an initial element. Equisimulation quotient of poduct of canonical model. Deciding the existence of the lcs and the msc w..t. some samples of GeneOntology vesion (Cyclic ontology). 3 out of 10 samples of GeneOntology vesion ae cyclic ontologies; Some pais of cyclic concepts w..t. those cyclic ontologies do not have lcs. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

62 Conclusion and Futue Wok Conclusions Implementing the algoithm to decide the existence of the lcs and the msc by means of canonical model and simulation elation. Involving the computation of building the poduct of canonical model in the smalle size. Canonical model with an initial element. Equisimulation quotient of poduct of canonical model. Deciding the existence of the lcs and the msc w..t. some samples of GeneOntology vesion (Cyclic ontology). 3 out of 10 samples of GeneOntology vesion ae cyclic ontologies; Some pais of cyclic concepts w..t. those cyclic ontologies do not have lcs. Futue Woks Optimizing the simulation algoithm. Simplifying the size of etuned concept. Extended to the othe small DL language: FL 0 Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

63 The LCS of FL 0 Input Concepts w..t. Geneal TBox Ideas: Using a decision pocedue simila to EL s case. Not using canonical model anymoe. Instead, least functional model J C,T of FL 0 concept C w..t. Geneal FL 0 TBox. Both of them have simila stuctue in tems of to label the domain elements and the ole-edges. But, fo the case of least functional model, each ole name only connects one element to its single successo element. Due to diffeent types of and semantics. C T D J D,T J C,T Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

64 The LCS of FL 0 Input Concepts w..t. Geneal TBox Reseach Questions: How to chaacteize subsumption w..t. Geneal FL 0 TBox by means of simulation elation? How to pove that the canonical model of k-chaacteistic concept is also a model of TBox? How to pove that thee exists a k s.t. the canonical model of k-chaacteistic concept w..t. T simulates the poduct of the canonical models of input concepts? Can we also use the same fomula, which is k = n 2 + m + 1? Most pobably, it will be diffeent, but the idea will be quite simila to EL s case using asynchonous and synchonous elements. Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27

65 Thank You Adian Nuadiansyah EMCL Wokshop 2016 Febuay 12, / 27