Ontology Evolution Under Semantic Constraints

Ontology EvolutionUnder Semantic Constraints Bernardo Cuenca Grau, Ernesto Jiménez-RuizComputer Science Department, University of Oxford Evgeny Kharlamov, DmitriyZheleznyakovKRDB research centre, Free University of Bozen-Bolzano KR 2012, Rome

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

Domain Ontologies • Goal: to provide standard vocabularies to communities • Clinical sciencesontologies: • SNOMED CT: Systematized Nomenclature of Medicine - Clinical Terms • > 311k concepts • NCIt: National CancerInstitute thesaurus • ~ 89k concepts, 200m cross links between them [NCI] • FMA: Foundational Model of Anatomy • 75k classes, 168k relations, 120k terms, 3.1m relat. inst.

Evolution of Domain Ontologies • Evolution of SNOMED: • 5 geographically distributed teams making modifications • every 2 weeks the main team integrates changes, resolves conflicts • from 2002 to 2008 SNOMED went from 278k to 311k concepts [SM-1] • Evolution of NCIt: • 20 full time editors for NCI • Developers of NCI do over 900 monthly changes [HKR’08] • Evolution of FMA: • FMA “is an evolving computer-based knowledge source ...” [FMA]

Evolution of Domain 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 • A natural requirement: principle of minimal change; changes should minimally affect ontology • structure • semantics

Languages for Domain Ontologies • Evolution of ontologies 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 paradise” • 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

Basic DLs EL & FL0

Outline • Existing approaches to evolution • Syntactic approach • Deductive approach • Our approach: evolution under constraints • Conclusion & directions

SA: Evolution Process • add/delete • minimal change(syntactic) processing • ontologyin L • evolvedontologyin L • operator • newinfo either axioms to add or axioms to delete E.g., contraction operator: takes a maximal subset (w.r.t. set inclusion) of the original ontology which does not entail axioms to be deleted

Syntactic Approach to Evolution • In the ontology: • “Oenophiles are gourmets” • “Oenophiles are not koalas” • To delete: “Oenophiles are gourmets” • To this end it is enough to delete [HS’05] [KPSCG’06] [JRGHB’11] and • In the resulted ontology: • “Oenophiles are not gourmets” • “Oenophiles are not koalas” is lost OK Not desirable

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

What Is Known? • DA have been studied for propositional logic • WIDTIO • Cross-product • … • What about ontologies? • Practical extensions of SA to preserve certain inference • [JRGHB’11] implemented in ContentCVS • “Manchester” grammar [GPS’12]: extension of [JRGHB’11]with combination of sub-concepts of the ontology axiom  A ⊑ B | A ⊑ ¬ B | A ⊑ ∃ R.B | A ⊑ ∀ R.B

Syntactic Approach to Evolution • In the resulted ontology: • “Oenophiles are not gourmets” • “Oenophiles are not koalas” is lost • ContentCVS & “Manchester” grammar allow to restore the missing disjointness OK Not desirable

Our Proposal in a Nutshell • Generalization of SA and DA under a common framework • 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 • ContentCVS & “Manchester grammar” are instantiations for particular “finite” LP

Syntactic-Deductive Approach SA DA

Evolution Process • add/delete • minimal change represent expand processing • sub-ontologyin L • sub-ontologyin LO • evolvedclosurein LP • evolvedclosurein L • ontologyin LI • closurein LP • ontologyin L • closurein L • evolvedontologyin L • evolvedontologyin LO • operator • newinfo either axioms to add or axioms to delete

Evolution under Semantic Constraints processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (C+,C-) • C+: axioms that should be present in the result • C−: axioms that should be absent in the result • General evolution encompasses both • contraction via C− • revision via C+

Example: Contraction processing • sub-ontologyin LI • Task: delete an axiom A1 ⊑ A2 from an LI-ontology K • LO-ontology K’is a contraction of an LI-ontology Kw.r.t. A1 ⊑ A2 if: • K’⊭ A1 ⊑ A2 • K⊨ K’ • Contraction may not be optimal • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (∅,C-) LI: input lang. LO: output lang. LP: preservation lang.

Example: Contraction processing • sub-ontologyin LI • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (∅,C-) • newdta LI: input lang. LO: output lang. LP: preservation lang. • Task: delete an axiom A1 ⊑ A2 from and LI-ontology K • AcontractionK’ of K isoptimalw.r.t. LP if it maximally preserves: • structure of KK’ ∩ K⊄ K’’∩ Kfor every contr. K’’ • LP-entailments of Knot true: if K’⊨α then K’’⊨α for every contr. K’’

Example: Contraction Delete: Gourmet ⊑ French Contraction Optimal ✔ ✘ ✔ Contraction Optimal ✔

Evolution with Finite LP processing • sub-ontologyin LO • Ontology language Lover a finite signatureΣisfinite if there are finitely many non-equivalent L-formulas over Σ • Examples of LP: • ContentCVS &”Manchester” grammars finite • OWL 2 QL (DL-Lite) finite • OWL 2 EL (EL, EL++, FL0) infinite • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (C+,C–)

Evolution with Finite LP processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (C+,C–) always exists finite LP Theorem: If the preservation language LP is finite, then • an optimal evolution always exists (provided an evolution exists) • both O and LP-closure of O are finite  we can simply write the result

Evolution with Infinite LP processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (C+,C–) finite representationmay not exist infinite LP • What if LP is infinite? • We have a problem! • Optimal evolution may not exist!

Evolution with Infinite LP processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (C+,C–) FL0 EL FL0 EL EL FL0 Theorem: • If FL0 setting optimal evolution does not exist in general • If EL setting optimal evolution does not exist in general • complex interaction of cycles and recursions

Infinite LP: Exponential Case processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (∅,C-) acyclic EL acyclic EL chain EL cyclic • ChainEL consists of inclusion assertions • A1⊑ ∃R1…Rn.A2or • ∃R1…Rn.A1 ⊑ A2 • It is a simple infinite language to study expressibility • An acyclic ontology has acyclic canonical model • SNOMED and NCItare acyclic • opt. contraction always exists • EXP time computation

Infinite LP: Polynomial Case processing • sub-ontologyin LO • ontologyin LI • closurein LP • operator • evolvedontologyin LO • evolvedclosurein LP • semanticconstraints • (∅,C-) non-rec EL non-rec EL chain EL non-recursive • An ontology is non-recursiveif concepts of the form ∃R.C donot appear at the left-hand side of axioms • Simplest non-recursive EL sub-language • opt. contraction always exists • PTimecomputation

Summary ruled out by LP

Conclusion & Directions • We introduced SDA: • a novel framework for ontology evolution • SDA generalizes: • syntactic approaches and • deductive approaches • it provides flexible means to navigate between SA and DA We studied 4 settings for SDA: • Directions: • extend the current results to richer LP: chain EL  ? • evolution beyond EL

Thank you!

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-1] http://www.ihtsdo.org/snomed-ct/snomed-ct0/adoption-of-snomed-ct/ • [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 • [JRCGHB’11] Jimenez-Ruiz, E., Cuenca Grau, B., Horrocks, I., Berlanga, R.: Supporting concurrent ontology development: Framework, algorithms and tool. DKE. 70:1 (2011) • [GPS’12]: Rafael S. Gonçalves, BijanParsia, Ulrike Sattler. 2012. Concept-based semantic difference in expressive description logics. In Proc. of DL

Ontology Evolution Under Semantic Constraints