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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  • 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 ∃ ∃ ∀ ≥ ≤ ∀ ≥ ≤
  • 9. Description Logics
  • 10. Description Logics ⊑ WindowsPC ⊑ Computer ⊓ ∃ runsOS.WindowsOS ≡ Laptop ⊔PocketPC ≡ Computer ⊓MobileDevice ⊑ hasGfx ⊑ hasComponent,
  • 11. Description Logics Laptop(MyComputer) runsOS(MyComputer, WindowsXP)
  • 12. Description Logics I ΔI
  • 13. Description Logics SHOIN D
  • 14. Description Logics I • • • • • ⊆ I I I I I I ⊆ ∈ I I I I M(KB) ∈ I
  • 15. Description Logics • • • • • • • •
  • 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
  • 17. Autoepistemic DL • • • K • • • • known to be
  • 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
  • 20. Circumscriptive DL • • • (M, F, V)
  • 21. Circumscriptive DL • • • • • •
  • 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
  • 25. Circumscriptive DL • • • •
  • 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
  • 40. Exact Matching • ≡
  • 41. Matching Inferences • fail ≺ intersect ≺ subsume − plugin ≺ exact
  • 42. concept contraction and concept abduction • •
  • 43. Matching Inferences • • •
  • 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 • • • • • •
  • 50. Local Concept Closure • • •
  • 51. Local Concept Closure • • ∃ •
  • 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 ∗
  • 58. Autoepistemic Role Closure (whole) ′ ′′
  • 59. Autoepistemic Role Closure (partial) ′
  • 60. Matching with Local Closure by Circumscription • • • • • • • ∅
  • 61. Closing Atomic Concepts (Circumscriptive) • ∅ • • •
  • 62. Closing Complex Concepts (Circumscriptive) • • • ≡∃ ∅ • • • ∃
  • 63. Closing Complex Concepts (Circumscriptive) • ≡ ⊓∃ ⊓∀ ∃ • • ∪ ⊓ ∪
  • 64. Closing Roles as a Whole with circumscription • • ∅ • •
  • 65. Closing Roles Partially with circumscription •
  • 66. Discussion • • • •
  • 67. Discussion • •
  • 68. Discussion • • • •
  • 69. Thanks