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Semantic Matchmaking of Resources with Local
Closed-World Reasoning
Stephan Grimm
Pascal Hitzler
Khan “Sadh” N. Mostafa
Web Ontology Language
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•
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• description logic
• first order predicate logic• (open world assumption)
• negative knowledge absence of knowledge
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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
→ ⊥ ⊤ ￢ C1 ⊓ C2 𝐶1 ⊔ 𝐶2 ∃ ∀ ≥ ≤
a1 an ∃ ∀ ≥ ≤
→ ci cn
→ −
A p r s
d𝑎𝑖𝑐𝑖n
Description Logics
Description Logics
⊑WindowsPC ⊑ Computer ⊓ ∃ runsOS.WindowsOS
≡
Laptop ⊔PocketPC ≡ Computer ⊓MobileDevice
⊑hasGfx ⊑ hasComponent,
Description Logics
Laptop(MyComputer)
runsOS(MyComputer, WindowsXP)
Description Logics
ΔII
Description Logics
SHOIN D
Description Logics
I• I ⊆ I
• I I
• I ⊆ I
• I ∈ I
• I I ∈ I
M(KB)
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
Autoepistemic DL
••
• 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
′
Autoepistemic DL
IW
intersecting the extensions
K KB
KBI ∈M IM ≠∅
Circumscriptive DL
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(M, F, V)
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
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
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• J I• ΔJ ΔI
• J I
• J I ∈ F
• J⊆ I ∈ M
• ∈ M J⊂ I
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
Resource Classes as DL Concepts in OWA•
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Example Scenario
Example Scenario
Example Scenario
Example Ontology
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
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
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≡
Matching Inferences
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fail ≺ intersect ≺ subsume − plugin ≺ exact
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
∪ ∪
Demand D1 in OWA
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Demand D2 in OWA
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Improved Matching with Local Closed-World Reasoning•
Forms of Local Closure for Matchmaking•
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Local Concept Closure
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Local Concept Closure
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• ∃
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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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• 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
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Matching with Local Closure by Epistemic Operators•
• K DualScreenGfxCard
• K RAIDStorage
Autoepistemic for Closing Atomic Concepts
′
Autoepistemic for Closing Complex Concepts• ′
•′
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Autoepistemic for Closing Complex Concepts
∗
Autoepistemic Role Closure (whole)
′ ′′
Autoepistemic Role Closure (partial)
′
Matching with Local Closure by Circumscription•
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•∅
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Closing Atomic Concepts (Circumscriptive)• ∅
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Closing Complex Concepts (Circumscriptive)•
• ≡ ∃
• ∅•
∃
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Closing Complex Concepts (Circumscriptive)• ≡ ⊓ ∃ ∃
⊓ ∀•
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⊓ ∪∪
Closing Roles as a Whole with circumscription• ∅
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Closing Roles Partially with circumscription•
Discussion
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Discussion
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Discussion
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Thanks
