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