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Rinke HoekstraJoostBreukerUniversity of Amsterdam Polishing Diamonds in OWL 2
OverviewBackgroundOntologies, frameworks and OWL 2Complex conceptsExchangeLimitations of OWL 2Design patternDiscussion
BackgroundESTRELLA Legal Knowledge Interchange Format (LKIF)LKIF Core Ontologyhttp://www.estrellaproject.org/lkif-coreNot everything in OWL 2 is an ontologybutNot everything that is an ontology fits OWL 2
Not everything in OWL is an ontologyOntologyContext independent, intrinsic propertiesDefinitionse.g. basic notions, subsumption hierarchiesFrameworkContext dependentDependencies, decompositione.g. part-of hierarchies, scripts, problem solving methods, scenarios, data-structures.
Not everything that is an ontology fits OWL… philosophical perspectivee.g. 4D ontologiesComplex, structured conceptsArtefactsBiological entities (e.g. organs)Exchange Physics: Heat Exchange, Balance/EquilibriumBiology: MetabolismEconomy/Law: Transactions, Hohfeldian Squares (rights/duties)
TransactionCharacteristicsReciprocityBalanceIdentityProblemDiamond-shape
OWL 2 DLDescription LogicsSubset of FOL, model theoryRestricted LanguageLimited ExpressivenessDecidability (sound & complete reasoning)Tree-shaped models
A ≡ p2some (B ⊓ p1some D) ⊓ p3some (C ⊓ p4some D)
Why not use rules?SupersetSWRL, not decidableSubsetOWL 2 RL / DLP / SROIQ Rules, decidable but inexpressiveHybridDL-Safe rules, decidable but closed worldDescription Graphs (Motik, 2005)Not standard, no scalable implementation
Polishing DiamondsPolishing DiamondsFine-tune the set of allowed modelsApproximate diamond-shaped modelsPatterns as TemplatesEmphasise a fixed structureKnowledge Patterns, Content Ontologies Design PatternsPatterns as RecipesEmphasise the design taskSteps in ontology design: justification, explanation
Initial Class DefinitionTransaction	≡ part some Transfer Transfer	≡ actor some Agent ⊓ recipient some Agent 				⊓ object some ObjectIdentify & EnforceFurther restrictionOnly ‘Transfer’ as parts, cardinality restriction on ‘part’?Specific ‘has_transfer’ relation?Qualified Cardinality Restrictions (OWL 2)Constrain Number of Role FillersTransaction 	≡ part some Transfer ⊓ part min 2 Transfer 			       ⊑   part exactly 2 TransferTransfer	≡ actor some Agent ⊓ recipient some Agent 				⊓ object some Object			       ⊑   actor exactly 1 Agent ⊓ recipient exactly 1 			            Agent ⊓ object exactly 1 ObjectIdentifyEquivalence axioms (no universal or max cardinality)EnforceSubclass axioms
Disambiguate Role FillersTransfer	≡ actor some Agent ⊓ recipient some Agent 				⊓ object some Object			       ⊑   actor exactly 1 Agent ⊓ recipient exactly 1 			            Agent ⊓ object exactly 1 ObjectProblemMore complex: distinct properties and rangesActor and recipient may still be the same individualSolutionAssert property disjointness
Completion graph
OWL 2 DL Role inclusion axiomsTraverse the treeBalanceobject−o part−o part o object ⊑ value_similarIdentitySimulateowl:sameAsactor−o part−o part o recipient ⊑ same_id_asrecipient−o part−o part o actor ⊑ same_id_as
Traverse the Tree (1)
Traverse the Tree (2)
Introduce AsymmetryProblem: actor and recipient are inferred to have the same identityDisambiguate branches of treeleft_part & right_partTautologicalIntroduce domain dependencee.g. “Sales Transaction”Domain independent transaction not representable
Sales TransactionGoods_Transfer     ⊑  Transfer 						≡ object some Good				⊑   recipientg some Agent ⊓ actorg some Agent recipientg 	       ⊑ recipient actorg 		       ⊑ actor actor−go part−o part orecipientm ⊑ same_id_asactor−mo part−o part orecipientg ⊑ same_id_asrecipient−go part−o part oactorm ⊑ same_id_asrecipient−mo part−o part oactorg ⊑ same_id_as
Polishing Diamonds In Owl2 Ekaw 2008 Acitrezza
DiscussionComplex conceptsApproximate diamond-shaped modelsFine-tune the set of valid modelsIdentify individuals in ABox, then Enforce additional restrictionsExtensive use of OWL 2 constructsQCR’s, role inclusionsCustom identity carrierowl:sameAs(x?,y?) same_id_as(x?,y?) Generalised toActions, roles, processes
Polishing Diamonds In Owl2 Ekaw 2008 Acitrezza

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Polishing Diamonds In Owl2 Ekaw 2008 Acitrezza

  • 1. Rinke HoekstraJoostBreukerUniversity of Amsterdam Polishing Diamonds in OWL 2
  • 2. OverviewBackgroundOntologies, frameworks and OWL 2Complex conceptsExchangeLimitations of OWL 2Design patternDiscussion
  • 3. BackgroundESTRELLA Legal Knowledge Interchange Format (LKIF)LKIF Core Ontologyhttp://www.estrellaproject.org/lkif-coreNot everything in OWL 2 is an ontologybutNot everything that is an ontology fits OWL 2
  • 4. Not everything in OWL is an ontologyOntologyContext independent, intrinsic propertiesDefinitionse.g. basic notions, subsumption hierarchiesFrameworkContext dependentDependencies, decompositione.g. part-of hierarchies, scripts, problem solving methods, scenarios, data-structures.
  • 5. Not everything that is an ontology fits OWL… philosophical perspectivee.g. 4D ontologiesComplex, structured conceptsArtefactsBiological entities (e.g. organs)Exchange Physics: Heat Exchange, Balance/EquilibriumBiology: MetabolismEconomy/Law: Transactions, Hohfeldian Squares (rights/duties)
  • 7. OWL 2 DLDescription LogicsSubset of FOL, model theoryRestricted LanguageLimited ExpressivenessDecidability (sound & complete reasoning)Tree-shaped models
  • 8. A ≡ p2some (B ⊓ p1some D) ⊓ p3some (C ⊓ p4some D)
  • 9. Why not use rules?SupersetSWRL, not decidableSubsetOWL 2 RL / DLP / SROIQ Rules, decidable but inexpressiveHybridDL-Safe rules, decidable but closed worldDescription Graphs (Motik, 2005)Not standard, no scalable implementation
  • 10. Polishing DiamondsPolishing DiamondsFine-tune the set of allowed modelsApproximate diamond-shaped modelsPatterns as TemplatesEmphasise a fixed structureKnowledge Patterns, Content Ontologies Design PatternsPatterns as RecipesEmphasise the design taskSteps in ontology design: justification, explanation
  • 11. Initial Class DefinitionTransaction ≡ part some Transfer Transfer ≡ actor some Agent ⊓ recipient some Agent ⊓ object some ObjectIdentify & EnforceFurther restrictionOnly ‘Transfer’ as parts, cardinality restriction on ‘part’?Specific ‘has_transfer’ relation?Qualified Cardinality Restrictions (OWL 2)Constrain Number of Role FillersTransaction ≡ part some Transfer ⊓ part min 2 Transfer ⊑ part exactly 2 TransferTransfer ≡ actor some Agent ⊓ recipient some Agent ⊓ object some Object ⊑ actor exactly 1 Agent ⊓ recipient exactly 1 Agent ⊓ object exactly 1 ObjectIdentifyEquivalence axioms (no universal or max cardinality)EnforceSubclass axioms
  • 12. Disambiguate Role FillersTransfer ≡ actor some Agent ⊓ recipient some Agent ⊓ object some Object ⊑ actor exactly 1 Agent ⊓ recipient exactly 1 Agent ⊓ object exactly 1 ObjectProblemMore complex: distinct properties and rangesActor and recipient may still be the same individualSolutionAssert property disjointness
  • 14. OWL 2 DL Role inclusion axiomsTraverse the treeBalanceobject−o part−o part o object ⊑ value_similarIdentitySimulateowl:sameAsactor−o part−o part o recipient ⊑ same_id_asrecipient−o part−o part o actor ⊑ same_id_as
  • 17. Introduce AsymmetryProblem: actor and recipient are inferred to have the same identityDisambiguate branches of treeleft_part & right_partTautologicalIntroduce domain dependencee.g. “Sales Transaction”Domain independent transaction not representable
  • 18. Sales TransactionGoods_Transfer ⊑ Transfer ≡ object some Good ⊑ recipientg some Agent ⊓ actorg some Agent recipientg ⊑ recipient actorg ⊑ actor actor−go part−o part orecipientm ⊑ same_id_asactor−mo part−o part orecipientg ⊑ same_id_asrecipient−go part−o part oactorm ⊑ same_id_asrecipient−mo part−o part oactorg ⊑ same_id_as
  • 20. DiscussionComplex conceptsApproximate diamond-shaped modelsFine-tune the set of valid modelsIdentify individuals in ABox, then Enforce additional restrictionsExtensive use of OWL 2 constructsQCR’s, role inclusionsCustom identity carrierowl:sameAs(x?,y?) same_id_as(x?,y?) Generalised toActions, roles, processes

Editor's Notes

  1. A ⊑ psome BA(a)C(x?) A(x?) ∧B(y?) ∧p(x?,y?)