Semantic matchmaking Local Closed-World Reasoning
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Semantic matchmaking Local Closed-World Reasoning

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Cover on "Semantic Matchmaking of Resources with Local Closed-World Reasoning"

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 Semantic matchmaking Local Closed-World Reasoning Presentation Transcript

  • 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
  • Web Ontology Language • • • • description logic first order predicate logic • (open world assumption) • • • negative knowledge absence of knowledge
  • Intro
  • Agenda
  • Description Logics e.g. Computer, OS e.g. hasComponent, runsOS e.g. Deep Blue, Windows 8
  • Description Logics e.g. hasComponent e.g. capacity
  • Description Logics Computer ⊓ MobileDevice ∃ hasComponent.DVDDrive Computer ⊓ ∀ runsOS.¬WindowsOS SHOIN D
  • Description Logics d 𝑎𝑖 𝑐𝑖 A p r s → n ⊥ ⊤ ¬ a1 an → ci → − cn C1 ⊓ C2 𝐶1 ⊔ 𝐶2 ∃ ∃ ∀ ≥ ≤ ∀ ≥ ≤
  • Description Logics
  • Description Logics ⊑ WindowsPC ⊑ Computer ⊓ ∃ runsOS.WindowsOS ≡ Laptop ⊔PocketPC ≡ Computer ⊓MobileDevice ⊑ hasGfx ⊑ hasComponent,
  • Description Logics Laptop(MyComputer) runsOS(MyComputer, WindowsXP)
  • Description Logics I ΔI
  • Description Logics SHOIN D
  • Description Logics I • • • • • ⊆ I I I I I I ⊆ ∈ I I I I M(KB) ∈ I
  • Description Logics • • • • • • • •
  • Description Logics Reasoning tasks: • Knowledgebase satisfiability • Concept satisfiability I∈M C I KB ≠∅ • Instance checking I ∈ I I ∈M • Subsumption ⊑ I ⊆ I I∈M
  • Autoepistemic DL • • • K • • • • known to be
  • 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
  • Autoepistemic DL IW intersecting the extensions K I∈M IM KB ≠∅ KB
  • Circumscriptive DL • • • (M, F, V)
  • Circumscriptive DL • • • • • •
  • 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
  • Circumscriptive DL KB = { Laptop ⊑ Computer, Computer ⊑ Hardware, Application ⊓ ∃ runsUnder .LinuxOS(XOffice) } (M = {Hardware, Laptop, Application, LinuxOS}, F = {Computer}). • Laptop • Computer • Hardware • Application • LinuxOS • XOffice
  • Circumscriptive DL • •J I • ΔJ ΔI • J I I • J • J⊆ I • ∈F ∈M ∈M J⊂ I
  • Circumscriptive DL • • • •
  • Modelling Resources in DL for Matchmaking problem • • • •
  • Resource Classes as DL Concepts • • • • •
  • Resource Classes as DL Concepts
  • Resource Classes as DL Concepts in OWA • • • •
  • Example Scenario
  • Example Scenario
  • Example Scenario
  • Example Ontology
  • Matching Resource Descriptions with DL Inferencing • • •
  • DL Inferences for Matching • • • •
  • Intersection Matching satisfiability of concept conjunction I∈M I ∩ I
  • Intersection Matching entailment of non-disjointness I∈M I ∩ I
  • Subsumption Matching Entailment of Concept Subsumption (Plugin) I∈M I ⊆ I
  • Subsumption Matching Entailment of Concept Subsumption (Subsumes) I∈M I ⊆ I
  • Exact Matching • ≡
  • Matching Inferences • fail ≺ intersect ≺ subsume − plugin ≺ exact
  • concept contraction and concept abduction • •
  • Matching Inferences • • •
  • Counterintuitive Matching Behavior due to OWA Intersection Matching and the Open-World Assumption • D = Laptop S = DesktopPC match(OPC,D, S) • ′ • ′
  • Counterintuitive Matching Behavior due to OWA Cases of Undesired Matching Behavior ∪ ∪
  • Demand D1 in OWA • • • • • • • •
  • Demand D2 in OWA • • • • • • • • •
  • Improved Matching with Local Closed-World Reasoning •
  • Forms of Local Closure for Matchmaking • • • • • •
  • Local Concept Closure • • •
  • Local Concept Closure • • ∃ •
  • 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
  • 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 • • •
  • Matching with Local Closure by Epistemic Operators • • • K DualScreenGfxCard K RAIDStorage
  • Autoepistemic for Closing Atomic Concepts ′
  • Autoepistemic for Closing Complex Concepts • ′ • • ′
  • Autoepistemic for Closing Complex Concepts ∗
  • Autoepistemic Role Closure (whole) ′ ′′
  • Autoepistemic Role Closure (partial) ′
  • Matching with Local Closure by Circumscription • • • • • • • ∅
  • Closing Atomic Concepts (Circumscriptive) • ∅ • • •
  • Closing Complex Concepts (Circumscriptive) • • • ≡∃ ∅ • • • ∃
  • Closing Complex Concepts (Circumscriptive) • ≡ ⊓∃ ⊓∀ ∃ • • ∪ ⊓ ∪
  • Closing Roles as a Whole with circumscription • • ∅ • •
  • Closing Roles Partially with circumscription •
  • Discussion • • • •
  • Discussion • •
  • Discussion • • • •
  • Thanks