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Ontology Contraction: beyond Propositional Paradise

Ontology Contraction: beyond Propositional Paradise. Bernardo Cuenca Grau , Computer Science Department, University of Oxford Evgeny Kharlamov, Dmitriy Zheleznyakov KRDB research centre , Free University of Bozen -Bolzano AMW 2012, Ouro Preto , Brazil. Ontologies: schema + data.

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Ontology Contraction: beyond Propositional Paradise

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  1. Ontology Contraction:beyond Propositional Paradise Bernardo Cuenca Grau,Computer Science Department, University of Oxford Evgeny Kharlamov, DmitriyZheleznyakovKRDB research centre, Free University of Bozen-Bolzano AMW 2012, OuroPreto, Brazil

  2. Ontologies: schema + data • Schema provide • standard vocabularies for data • classes (concepts) • properties (roles) • a way to structure data • means for machines to be able to understand data • Data is a collections of facts • Instantiations of classes • Instantiations of properties

  3. Usage of Ontologies • Ontology Based Data Access • provide unified query interface to heterogeneous data sources • e.g., Quest, OWLIM • Web Knowledge Bases • Wiki based Knowledge bases • e.g., Jago, DBpedia • Clinical sciencesontologies • provide standard vocabularies to communities • e.g., SNOMED CT,NCIt

  4. Evolution of Ontologies (1) • Ontology Based Data Access • the schema may change • Web Knowledge Bases • Wiki changes all the time, and so does Wiki-based knowledge bases • Clinical sciencesontologies • from 2002 to 2008 SNOMED went from 278k to 311kconcepts

  5. Evolution of Ontologies • At the high level ontologies are changed by • addition of information • usually referred as revision or update • deletion of information • usually referred as contraction • Evolution may affect both • schema level • data level

  6. Can Previous Works Help? • Evolution of knowledge is a classical problem in KR • intensively studied for propositional logic • there are different semantics for evolution • many complexity results • very few results beyond propositional case • Two main types of approaches to evolution • Model-Based Approach (MBA) • Formula-Based Approach (FBA) • Principal of minimal change • a knowledge base should change as little as possible Adam in the Garden of Eden

  7. MBA: Contraction Process • transform models • minimal change represents ? processing • models • evolvedmodels • evolvedontologyin L • ontologyin L • operator • newdata info to delete Contraction operator: takes models of the originalontology, transform them so they do not entail axioms to be deleted

  8. MBA: Propositional Case (1) • choose models of M2less distanced from M1 • distance is based on symmetric difference between models • I = {a, b} J = {b, c}  diff(I,J) = {a, c} • lots of operators to compute the distance between sets of models: • Winslett’s operator • Satoh’s operator • … models of new info dist original models M1 M2 M3 evolvedmodels [EG’92]

  9. MBA: Propositional Case (2) EXPnumber EXPnumber • Is M3axiomatizablein the propositional logic? • Yes! • The number of models is just exponentialin the size of the originalontology dist original models M1 M3 evolvedmodels Adam in the Garden of Eden

  10. FBA: Contraction Process • add/delete axioms • minimal change represents expand ? processing • evolvedclosurein L • evolvedontologyin L • ontologyin L • closurein L • operator • newdata info to delete Contraction operator: takes a subset of the ontology deductive closure which does not entail axioms to be deleted

  11. FBA: Propositional Case Adam and Eve in the Garden of Eden the closure • What subset to choose? • WIDTIO operator • Cross-product operator • … • Is evolved closure axiomatizablein the propositional logic? • Yes! • The size of closure is exponential in the size of the original ontology • ontology evolved closure:a subset not entailing new info [EG’92]

  12. Outline • Languages for ontologies • Ontology evolution under MBA • Ontology evolution under FBA • Evolution under semantic constraints • Conclusion & directions

  13. Languages for Ontologies • Languages that are natural for real-life ontologies • flexible to capture complex interaction • logic-based • propositional logic is not enough • fragments of FOL are needed • the situation becomes much more difficult The Fall of Adam and Eve The Expulsion from Paradise

  14. Languages for Ontologies • Languages that are natural for real-life ontologies • flexible to capture complex interaction • logic-based • propositional logic is not enough • fragments of FOL are needed • the situation becomes much more difficult • Ontology Web Language: OWL 2 – W3C standard • OWL 2 (based on SROIQ) • OWL 2 QL (based on DL-Lite) • OWL 2 EL (based on EL, EL++) • e.g. SNOMED these are not propositional tractable reasoning

  15. Description Logics DL-Lite & EL

  16. Outline • Languages for ontologies • Ontology evolution under MBA • Ontology evolution under FBA • Evolution under semantic constraints • Conclusion & directions

  17. MBA: Contraction Process • transform models • minimal change represents processing • models • evolvedmodels • evolvedontologyin L • ontologyin L • operator • newdata axioms to delete

  18. MBA: FOL Case • How to measure distance between models of a FOL theory? • There are two ways to generalize the propositional approach • propositional case: I = {a, b} J = {b, c}  diffp(I,J)= {a, c} • FOL case 1: I= {A(a), B(b)} J= {B(b), A(c)} diff1(I,J)= {A(a), A(c)} • FOL case 2: I = {A(a), B(b)} J = {B(b), A(c)}  diff2(I,J)= {A} • Each of the propositional operators can be generalized in two ways models of new info dist original models M1 M2 M3 evolvedmodels

  19. MBA: DL-Lite & EL Cases infinitenumber infinitenumber • Theorem: In general, M3 is notaxiomatizable in DL-Lite, nor in EL • the number of models is continuum • evolved models are “too many” & “too irregular”to capture them dist original models M1 M3 evolvedmodels The Flood

  20. MBA: Can We Do Anything? • Can we overcome the inexpressibility by allowing fewer models in the result? • E.g., take those models where there are less changes in roles I = {A(a), B(b), R(a,b)} J = {A(a), B(b)}K = {R(a,b)} [QD’09] A B R R a a b b • J or K is closer to I? It is K, since it does not differ from I on roles • Conjecture: In general, for OWL 2 EL + functionality + inverses,the result of evolution is not FOL expressible A B a b

  21. MBA: Can We Do Anything? Gehenna • Can we overcome the inexpressibility by allowing fewer models in the result? • E.g., take those models where there are less changes in roles I = {A(a), B(b), R(a,b)} J = {A(a), B(b)}K = {R(a,b)} [QD’09] A B R R a a b b • J or K is closer to I? It is K, since it does not differ from I on roles • Conjecture: In general, for OWL 2 EL + functionality + inverses,the result of evolution is not FOL expressible A B a b • need to distinguish even cycles of an arbitrary size • impossible in FOL(locality property of FOL)

  22. Outline • Languages for ontologies • Ontology evolution under MBA • Ontology evolution under FBA • Evolution under semantic constraints • Conclusion & directions

  23. FBA: Evolution Process • add/delete • minimal change represent expand processing • evolvedclosurein L • ontologyin L • closurein L • evolvedontologyin L • operator • newinfo axioms to delete Contraction operator: takes a maximal subset (w.r.t. set inclusion)of the ontology deductive closure which does not entail axioms to be deleted

  24. FBA: DL-Lite Case DL-Lite closure • What subset to choose? • WIDTIO operator • Cross-product operator • … • Theorem: DL-Lite is closed under FBA • closure is finite • ontology evolved closure:a subset not entailing new info [EG’92]

  25. FBA: EL Case Tower of Bable EL closure • What subset to choose? • WIDTIO operator • Cross-product operator • … Theorem: : In general, EL is not closed under FBA • too many (infinite number of) formulas to preserve • not always possible • ontology evolved closure:a subset not entailing new info [EG’92]

  26. Outline • Languages for ontologies • Ontology evolution under MBA • Ontology evolution under FBA • Evolution under semantic constraints • Conclusion & directions

  27. Our Proposal in a Nutshell [GJRKZ’12] • Our view of principle of minimal change • maximize preservation of ontology structure • maximize preservation of ontology entailments • Preservation language (LP) tells us which class of entailments should be maximized

  28. Evolution under Semantic Constraints SA FBA

  29. Contraction Process [GJRKZ’12] • add/delete • minimal change represent expand processing • sub-ontologyin L • evolvedclosurein LP • evolvedclosurein L • closurein LP • ontologyin L • closurein L • evolvedontologyin L • operator • newinfo axioms to delete Choosing relevant LP allows to • achieve expressibility(for any language) • reduce computational hardness

  30. Outline • Languages for ontologies • Ontology evolution under MBA • Ontology evolution under FBA • Evolution under semantic constraints • Conclusion & directions

  31. Conclusion & Directions Propositional case: FOL case: classical way Inexpressibility even in simple settings Expressibility & exponentiality Way to go! FOL case: evolution under SC Evolution under SC: FOL case: classical way … sometimes FOL inexpressibility Handling inexpressibility by tuning LP. Practical and logically sound.

  32. References • [HKR’08] Hartung, M.; Kirsten, T.; and Rahm, E. 2008. Analyzing the evolution of life science ontologies and mappings. In Proc. of DILS, 11–27. • [SM]Spackman K. SNOMED RT and SNOMEDCT. Promise of an international clinical terminology. MD Comput. 2000 Nov;17(6):29. • [SM-1] http://www.ihtsdo.org/snomed-ct/snomed-ct0/adoption-of-snomed-ct/ • [SM-2] http://www.ihtsdo.org/fileadmin/user_upload/doc/download/doc_UserGuide_Current-en-US_INT_20120131.pdf • [FMA] http://sig.biostr.washington.edu/projects/fm/AboutFM.html • [NCI] https://wiki.nci.nih.gov/display/EVS/NCI+Thesaurus+versus+NCI+Metathesaurus • [HS’05]Haase, P., Stojanovic, L.: Consistent evolution of OWL ontologies. In: ESWC. (2005) • [KPSCG’06] Kalyanpur, A., Parsia, B., Sirin, E., Grau, B.C.: Repairingunsatisfiableconcepts in OWL ontologies. In: ESWC. (2006) 170–184

  33. References • [JRCGHB’11] Jimenez-Ruiz, E., Cuenca Grau, B., Horrocks, I., Berlanga, R.: Supporting concurrent ontology development: Framework, algorithms and tool. DKE. 70:1 (2011) • [CKNZ’10] Calvanese D., Kharlamov E., Nutt W., Zheleznyakov D. 2010. Evolution of DL-Lite Knowledge Bases. In Proc. of ISWC, 112-128. • [CJKZ’12] Cuenca Grau B., Jiménez-Ruiz E., Kharlamov E., Zheleznyakov D. 2012. Ontology evolution under semantic constraints. In Proc. of KR. • [MSH’09] Motik B., Shearer R., Horrocks I. 2009. Hyper-tableau reasoning for description logics. Journal of AI Research 36: 165-228. • [KPHS’07] Kalyanpur A., Parsia B., Horridge M., Sirin E. 2007. Finding all justifications of OWL DL entailments. In Proc. of ISWC, 267-280.

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