1. Interoperation of Information Sources via Articulation of Ontologies Prasenjit Mitra, Gio Wiederhold Stanford University Supported by AFOSR- New World Vistas Program

2. Prasenjit Mitra2 Outline zIntroduction zPreliminaries zArticulation Generation Toolkit zOntology Algebra zConclusion

3. Prasenjit Mitra3 Interoperation of Information Sources zCompose information zMultiple independent, heterogeneous sources zReliability, scalability zSemantic heterogeneity - same term different semantics - different term same semantics

4. Prasenjit Mitra4 Preliminaries: Ontology zOntology - hierarchy of terms and specification of their properties. zModeled as a directed labeled graph + set of rules. zOnt = ( V, E, R) V - set of nodes(concepts) E - set of edges(properties) R - set of rules involving V,E

5. Prasenjit Mitra5 Example Car H123 Instance List_Price VID PMitra Name Unit $ 40kCA Address Amount Vehicle LuxuryCa r PMitra Buyer Instance SubClass Instance VIN H123 OwnerRetail_ Price CA NameAddr $35k SubClass Buyer Owner Attribute Equ

6. Prasenjit Mitra6 Articulation Rules zArticulation rules - logic-based rules that relate concepts in two ontologies: -Binary Relationships (O1.Car SubClassOf O2.Vehicle) (O1.Buyer Equ O2.Owner) (O2.LuxuryCar SubClassOf O1.Car)

7. Prasenjit Mitra7 Articulation Rules (contd.) zHorn Clauses - (O1.Car O1.Instance X), (X O1.Price Y), (Y > $30000) => (O2.LuxuryCar Instance X) - (V O2.Retail_Price P), (C O1.List_Price L), (L Unit U), (L Amount A), (V Equ C) => (P Equ concat(U,A))

8. Prasenjit Mitra8 Contributions zArticulation Generation Toolkit - produce translation rules semi-automatically - a library of reusable heuristic methods - a GUI to display ontologies and interact with the expert zOntology Algebra - query rewriting and planning

9. Prasenjit Mitra9 Articulation Generator Driver Ont1Ont2 Phrase Relator Thesaurus Structural Matcher Semantic Network Human Expert Context-based Word Relator OntA

10. Prasenjit Mitra10 Articulation Generation Methods zNon-iterative Methods - Lexical Matcher - Thesaurus-based Matcher - Corpus-based Matcher - Instance-based Matcher zIterative Methods - Structural Matcher - Inference-based Matcher

11. Prasenjit Mitra11 Lexical Methods zPreprocessing rules. -Expert-generated seed rules. e.g., (O1.List_Price Equ O2.Retail_Price) -Context-based preprocessing directives. e.g., (O1.UK_Govt Equ O2.US_Govt) -Stop-word Removal & Stemming -Word match (full or partial) -Phrase match e.g., (O1.Ministry_Of_Defence Equ O2.Defense_Ministry) 0.6

12. Prasenjit Mitra12 Thesaurus-based methods zConsult a dictionary/thesaurus to find synonyms, related words zGenerate a similarity measure or relatedness measure - words that have similar words in their definitions are similar zGet more semantically meaningful relationships from WordNet (syn, hyper)

13. Prasenjit Mitra13 Candidate Match Repository Term linkages automatically extracted from 1912 Webster’s dictionary * * free, other sources. being processed. Based on processing headwords ý definitions Notice presence of 2 domains: chemistry, transport

14. Prasenjit Mitra14 Corpus-based zCollect a set of text documents preferably from same domain - search using keywords in google zBuild a context vector (1000-character neighbourhood) for each word zCompute word-pair similarity based on the cosine of the vectors zUse word-pair similarity to find similarity among labels of nodes/edges

15. Prasenjit Mitra15 Structural Methods zUses results of lexical match zIf x% of parent nodes match & y% of children nodes match zSpecial relations (AttributeOf) match

16. Prasenjit Mitra16 Tools to create articulations Graph matcher for Articulation- creating Expert Vehicle ontology Transport ontology Suggestions for articulations

17. Prasenjit Mitra17 continue from initial point Also suggest similar terms for further articulation: by spelling similarity, by graph position by term match repository Expert response: 1. Okay 2. False 3. Irrelevant to this articulation All results are recorded Okay ’s are converted into articulation rules

18. Prasenjit Mitra18 An Ontology Algebra Operations can be composed Operations can be rearranged Alternate arrangements can be evaluated Optimization is enabled The record of past operations can be kept and reused when sources change

19. Prasenjit Mitra19 Binary Operators A knowledge-based algebra for ontologies The Articulation Function (ArtGen), given two ontologies, supplies articulation rules between them. Intersection create a subset ontology keep sharable entries Union create a joint ontology merge entries Difference create a distinct ontology remove shared entries

20. Prasenjit Mitra20 Intersection: Definition zO1 = (V1, E1, R1) O2 = (V2, E2, R2) zOI = ( O1 Int ArtGen O2) = (VI, EI, RI) zArules = ArtGen( O1, O2 ) zVI = Nodes( Arules ) zEI = Edges( Arules ) + Edges(E1, VI.V1) + Edges( E2, VI.V2) zRI = Arules + Rules( R1, VI.V1) + Rules( R2, VI.V2)

21. Prasenjit Mitra21 Intersection: Example z ARules = { (O1.Car SubClass O2.LuxuryCar), (O1.MSRP Equ O2.Price)} z NI = ( O1.Car, O1.MSRP, O2.LuxuryCar, O2.Price ) z EI = Edges(ARules) + {(O1.Car Attribute O1.MSRP), (O2.LuxuryCar Attribute Price)} InexpCar Car LuxuryCar MSRPPrice LuxuryTax SubClass Equ O1 O2 OI

22. Prasenjit Mitra22 Intersection: Properties zCommutative? OI 12 =(O1 Int ArtGen O2) = (O2 Int ArtGen O1)=OI 21 VI 12 = VI 21, EI 12 = EI 21, RI 12 =RI 21 ARules 12 = ARules 21 ArtGen(O1, O2) = ArtGen(O2, O1) zInt ArtGen is commutative iff ArtGen is commutative

23. Prasenjit Mitra23 Semantically Commutative Example: zArtGen(O1,O2) : ( O1.Car SubClassOf O2.Vehicle) zArtGen(O2,O1) : ( O2.Vehicle SuperClassOf O1.Car) zDefn: ArtGen is Semantically Commutative iff ArtGen(O1,O2) ArtGen(O2,O1) Operands to intersection can be rearranged if ArtGen is semantically commutative

24. Prasenjit Mitra24 Associativity Example zExample: zArtRules(O1, O3) : (O1.Car SubClassOf O3.Vehicle) zArtRules(O2, O3) : (O2.Truck SubClassOf O3.Vehicle) zArtRules(O1, O2) : null zIntersection is not associative!

25. Prasenjit Mitra25 Associativity z(O1.O2).O3 = O1.(O2.O3) iff ArtGen is consistent and transitively connective zconsistent - given two nodes it generates the same relationship irrespective of relationships between other nodes

26. Prasenjit Mitra26 Associativity (contd.) zArtGen relates A and B: (A Rel B) = (A R1 B) or (B R2 A) zTransitively connective: If ArtGen generates (A Rel B), (B Rel C) then it also generates (A Rel C’)  where A  O1, B  O2, C,C’  O3

27. Prasenjit Mitra27 Transitive Connectivity A B C E D O1 O2 O3

28. Prasenjit Mitra28 Exploiting the result. Processing & query evaluation is best performed within Source Domains & by their engines Result has links to source Avoid n 2 problem of interpreter mapping [Swartout HPKB year 1]

29. Prasenjit Mitra29 Using the Articulation Rules zQ(X) :- (LuxuryCar Instance X), (X Owner Y), (Y Addr `CA’) zTranslated using Articulation Rules Q(X) :- (Car Instance X),(X List_Price Y) (Y Unit ‘$’),(Y Amount A), (A > 30000), (X Buyer Z), (Z Address ‘CA’)

30. Prasenjit Mitra30 Related Work zTsimmis zGarlic zInfomaster zInformation Manifold zClio zLSD

31. Prasenjit Mitra31 Conclusion zIntroduced an Ontology Interoperation System. zInteroperation based on articulations that bridge the semantic gap. zGraph-oriented data model, logical rules zFounded on Ontology Algebra Thanks to Stefan Decker, Alex Carobus, Jan Jannink, Sergey Melnik, Shrish Agarwal