Semantic matchmaking Local Closed-World Reasoning
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Cover on "Semantic Matchmaking of Resources with Local Closed-World Reasoning" paper by Stephan Grimm & Pascal Hitzler
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Semantic matchmaking Local Closed-World Reasoning
- 1. Khan “Sadh” N. Mostafa Semantic Matchmaking of Resources with Local Closed-World Reasoning Stephan Grimm Pascal Hitzler stephan.grimm@fzi.de hitzler@aifb.uni-karlsruhe.de
- 2. Web Ontology Language • • • • description logic first order predicate logic • (open world assumption) • • • negative knowledge absence of knowledge
- 3. Intro
- 4. Agenda
- 5. Description Logics e.g. Computer, OS e.g. hasComponent, runsOS e.g. Deep Blue, Windows 8
- 6. Description Logics e.g. hasComponent e.g. capacity
- 7. Description Logics Computer ⊓ MobileDevice ∃ hasComponent.DVDDrive Computer ⊓ ∀ runsOS.￢WindowsOS SHOIN D
- 8. Description Logics d 𝑎𝑖 𝑐𝑖 A p r s → n ⊥ ⊤ ￢ a1 an → ci → − cn C1 ⊓ C2 𝐶1 ⊔ 𝐶2 ∃ ∃ ∀ ≥ ≤ ∀ ≥ ≤
- 10. Description Logics ⊑ WindowsPC ⊑ Computer ⊓ ∃ runsOS.WindowsOS ≡ Laptop ⊔PocketPC ≡ Computer ⊓MobileDevice ⊑ hasGfx ⊑ hasComponent,
- 16. Description Logics Reasoning tasks: • Knowledgebase satisfiability • Concept satisfiability I∈M C I KB ≠∅ • Instance checking I ∈ I I ∈M • Subsumption ⊑ I ⊆ I I∈M
- 18. Autoepistemic DL KB = {Application(XOffice), runsUnder(XOffice,RedHat)} D = Application ⊓ ∃ runsUnder .￢WindowsOS RedHat XOffice WindowsOS D D = Application ⊓ ∃ K runsUnder .￢K WindowsOS RedHat ′ WindowsOS RedHat XOffice
- 19. Autoepistemic DL IW intersecting the extensions K I∈M IM KB ≠∅ KB
- 22. Circumscriptive DL KB = { Laptop ⊑ Computer, Computer ⊑ Hardware, Application ⊓ ∃ runsUnder .LinuxOS(XOffice) } (M = {Hardware, Laptop, Application, LinuxOS}, F = {Computer}). • Laptop • • Computer • Hardware • Computer ∈F • Application • XOffice (∈F Hardware
- 23. Circumscriptive DL KB = { Laptop ⊑ Computer, Computer ⊑ Hardware, Application ⊓ ∃ runsUnder .LinuxOS(XOffice) } (M = {Hardware, Laptop, Application, LinuxOS}, F = {Computer}). • Laptop • Computer • Hardware • Application • LinuxOS • XOffice
- 24. Circumscriptive DL • •J I • ΔJ ΔI • J I I • J • J⊆ I • ∈F ∈M ∈M J⊂ I
- 26. Modelling Resources in DL for Matchmaking problem • • • •
- 27. Resource Classes as DL Concepts • • • • •
- 28. Resource Classes as DL Concepts
- 29. Resource Classes as DL Concepts in OWA • • • •
- 30. Example Scenario
- 31. Example Scenario
- 32. Example Scenario
- 33. Example Ontology
- 34. Matching Resource Descriptions with DL Inferencing • • •
- 35. DL Inferences for Matching • • • •
- 36. Intersection Matching satisfiability of concept conjunction I∈M I ∩ I
- 37. Intersection Matching entailment of non-disjointness I∈M I ∩ I
- 38. Subsumption Matching Entailment of Concept Subsumption (Plugin) I∈M I ⊆ I
- 39. Subsumption Matching Entailment of Concept Subsumption (Subsumes) I∈M I ⊆ I
- 41. Matching Inferences • fail ≺ intersect ≺ subsume − plugin ≺ exact
- 42. concept contraction and concept abduction • •
- 44. Counterintuitive Matching Behavior due to OWA Intersection Matching and the Open-World Assumption • D = Laptop S = DesktopPC match(OPC,D, S) • ′ • ′
- 45. Counterintuitive Matching Behavior due to OWA Cases of Undesired Matching Behavior ∪ ∪
- 46. Demand D1 in OWA • • • • • • • •
- 47. Demand D2 in OWA • • • • • • • • •
- 48. Improved Matching with Local Closed-World Reasoning •
- 49. Forms of Local Closure for Matchmaking • • • • • •
- 52. Local Role Closure If a role r is locally closed, only such pairs of objects should occur in the extension of r for which there is evidence to be in there • • • • supports
- 53. If a role r is locally closed, only such pairs of objects should occur in the extension of r for which there is evidence to be in there • • •
- 54. Matching with Local Closure by Epistemic Operators • • • K DualScreenGfxCard K RAIDStorage
- 55. Autoepistemic for Closing Atomic Concepts ′
- 56. Autoepistemic for Closing Complex Concepts • ′ • • ′
- 57. Autoepistemic for Closing Complex Concepts ∗
- 60. Matching with Local Closure by Circumscription • • • • • • • ∅
- 64. Closing Roles as a Whole with circumscription • • ∅ • •
- 65. Closing Roles Partially with circumscription •
- 67. Discussion • •
- 69. Thanks