Cover on "Semantic Matchmaking of Resources with Local Closed-World Reasoning" paper by Stephan Grimm & Pascal Hitzler

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
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description logic
first order predicate logic
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(open world assumption)
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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
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⊆
I
I
I
I
I
I
⊆
∈
I
I
I
I
M(KB)
∈
I

15. Description Logics
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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
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K
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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
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(M, F, V)

21. Circumscriptive DL
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22. Circumscriptive DL
KB = { Laptop ⊑ Computer, Computer ⊑ Hardware,
Application ⊓ ∃ runsUnder .LinuxOS(XOffice) }
(M = {Hardware, Laptop, Application, LinuxOS}, F = {Computer}).
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Laptop
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• 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}).
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Laptop
• Computer
• Hardware
• Application
• LinuxOS
• XOffice

24. Circumscriptive DL
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•J
I
• ΔJ ΔI
• J I
I
• J
• J⊆ I
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∈F
∈M
∈M
J⊂
I

25. Circumscriptive DL
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26. Modelling Resources in DL for
Matchmaking problem
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27. Resource Classes as DL
Concepts
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28. Resource Classes as DL
Concepts

29. Resource Classes as DL
Concepts in OWA
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30. Example Scenario

31. Example Scenario

32. Example Scenario

33. Example Ontology

34. Matching Resource Descriptions
with DL Inferencing
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35. DL Inferences for Matching
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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
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≡

41. Matching Inferences
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fail ≺ intersect ≺ subsume − plugin ≺ exact

42. concept contraction and
concept abduction
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43. Matching Inferences
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44. Counterintuitive Matching
Behavior due to OWA
Intersection Matching and the Open-World Assumption
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D = Laptop
S = DesktopPC
match(OPC,D, S)
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′

45. Counterintuitive Matching
Behavior due to OWA
Cases of Undesired Matching Behavior
∪
∪

46. Demand D1 in OWA
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47. Demand D2 in OWA
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48. Improved Matching with Local
Closed-World Reasoning
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49. Forms of Local Closure for
Matchmaking
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50. Local Concept Closure
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51. Local Concept Closure
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∃
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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
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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
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54. Matching with Local Closure
by Epistemic Operators
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K DualScreenGfxCard
K RAIDStorage

55. Autoepistemic for Closing
Atomic Concepts
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56. Autoepistemic for Closing
Complex Concepts
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57. Autoepistemic for Closing
Complex Concepts
∗

58. Autoepistemic Role Closure
(whole)
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59. Autoepistemic Role Closure
(partial)
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60. Matching with Local Closure
by Circumscription
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∅

61. Closing Atomic Concepts
(Circumscriptive)
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∅
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62. Closing Complex Concepts
(Circumscriptive)
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≡∃
∅
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∃

63. Closing Complex Concepts
(Circumscriptive)
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≡
⊓∃
⊓∀
∃
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∪
⊓
∪

64. Closing Roles as a Whole
with circumscription
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∅
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65. Closing Roles Partially with
circumscription
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66. Discussion
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67. Discussion
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68. Discussion
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69. Thanks