Semantic matchmaking Local Closed-World Reasoning

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paper by Stephan Grimm & Pascal Hitzler

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Semantic matchmaking Local Closed-World Reasoning

  1. 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. 2. Web Ontology Language • • • • description logic first order predicate logic • (open world assumption) • • • negative knowledge absence of knowledge
  3. 3. Intro
  4. 4. Agenda
  5. 5. Description Logics e.g. Computer, OS e.g. hasComponent, runsOS e.g. Deep Blue, Windows 8
  6. 6. Description Logics e.g. hasComponent e.g. capacity
  7. 7. Description Logics Computer ⊓ MobileDevice ∃ hasComponent.DVDDrive Computer ⊓ ∀ runsOS.¬WindowsOS SHOIN D
  8. 8. Description Logics d 𝑎𝑖 𝑐𝑖 A p r s → n ⊥ ⊤ ¬ a1 an → ci → − cn C1 ⊓ C2 𝐶1 ⊔ 𝐶2 ∃ ∃ ∀ ≥ ≤ ∀ ≥ ≤
  9. 9. Description Logics
  10. 10. Description Logics ⊑ WindowsPC ⊑ Computer ⊓ ∃ runsOS.WindowsOS ≡ Laptop ⊔PocketPC ≡ Computer ⊓MobileDevice ⊑ hasGfx ⊑ hasComponent,
  11. 11. Description Logics Laptop(MyComputer) runsOS(MyComputer, WindowsXP)
  12. 12. Description Logics I ΔI
  13. 13. Description Logics SHOIN D
  14. 14. Description Logics I • • • • • ⊆ I I I I I I ⊆ ∈ I I I I M(KB) ∈ I
  15. 15. Description Logics • • • • • • • •
  16. 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. 17. Autoepistemic DL • • • K • • • • known to be
  18. 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. 19. Autoepistemic DL IW intersecting the extensions K I∈M IM KB ≠∅ KB
  20. 20. Circumscriptive DL • • • (M, F, V)
  21. 21. Circumscriptive DL • • • • • •
  22. 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. 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. 24. Circumscriptive DL • •J I • ΔJ ΔI • J I I • J • J⊆ I • ∈F ∈M ∈M J⊂ I
  25. 25. Circumscriptive DL • • • •
  26. 26. Modelling Resources in DL for Matchmaking problem • • • •
  27. 27. Resource Classes as DL Concepts • • • • •
  28. 28. Resource Classes as DL Concepts
  29. 29. Resource Classes as DL Concepts in OWA • • • •
  30. 30. Example Scenario
  31. 31. Example Scenario
  32. 32. Example Scenario
  33. 33. Example Ontology
  34. 34. Matching Resource Descriptions with DL Inferencing • • •
  35. 35. DL Inferences for Matching • • • •
  36. 36. Intersection Matching satisfiability of concept conjunction I∈M I ∩ I
  37. 37. Intersection Matching entailment of non-disjointness I∈M I ∩ I
  38. 38. Subsumption Matching Entailment of Concept Subsumption (Plugin) I∈M I ⊆ I
  39. 39. Subsumption Matching Entailment of Concept Subsumption (Subsumes) I∈M I ⊆ I
  40. 40. Exact Matching • ≡
  41. 41. Matching Inferences • fail ≺ intersect ≺ subsume − plugin ≺ exact
  42. 42. concept contraction and concept abduction • •
  43. 43. Matching Inferences • • •
  44. 44. Counterintuitive Matching Behavior due to OWA Intersection Matching and the Open-World Assumption • D = Laptop S = DesktopPC match(OPC,D, S) • ′ • ′
  45. 45. Counterintuitive Matching Behavior due to OWA Cases of Undesired Matching Behavior ∪ ∪
  46. 46. Demand D1 in OWA • • • • • • • •
  47. 47. Demand D2 in OWA • • • • • • • • •
  48. 48. Improved Matching with Local Closed-World Reasoning •
  49. 49. Forms of Local Closure for Matchmaking • • • • • •
  50. 50. Local Concept Closure • • •
  51. 51. Local Concept Closure • • ∃ •
  52. 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. 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. 54. Matching with Local Closure by Epistemic Operators • • • K DualScreenGfxCard K RAIDStorage
  55. 55. Autoepistemic for Closing Atomic Concepts ′
  56. 56. Autoepistemic for Closing Complex Concepts • ′ • • ′
  57. 57. Autoepistemic for Closing Complex Concepts ∗
  58. 58. Autoepistemic Role Closure (whole) ′ ′′
  59. 59. Autoepistemic Role Closure (partial) ′
  60. 60. Matching with Local Closure by Circumscription • • • • • • • ∅
  61. 61. Closing Atomic Concepts (Circumscriptive) • ∅ • • •
  62. 62. Closing Complex Concepts (Circumscriptive) • • • ≡∃ ∅ • • • ∃
  63. 63. Closing Complex Concepts (Circumscriptive) • ≡ ⊓∃ ⊓∀ ∃ • • ∪ ⊓ ∪
  64. 64. Closing Roles as a Whole with circumscription • • ∅ • •
  65. 65. Closing Roles Partially with circumscription •
  66. 66. Discussion • • • •
  67. 67. Discussion • •
  68. 68. Discussion • • • •
  69. 69. Thanks

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