The document discusses bridging the gap between PR-OWL and OWL semantics. It introduces probabilistic ontologies which include types of entities, properties, relationships, processes/events, statistical regularities, and uncertainty. It describes how the mapping between PR-OWL and OWL is currently incomplete and proposes solutions to better represent binary and n-ary relations between concepts.

1. PR-OWL 2.0 - Bridging the gap
to OWL semantics
Rommel Carvalho, Kathryn Laskey, and Paulo Costa
Center of Excellence in C4I, George Mason University, USA
Sixth International Workshop on Uncertainty Reasoning
for the Semantic Web (URSW 2010)
11/07/2010
Sunday, December 19, 2010

2. Agenda
2
Sunday, December 19, 2010

3. Agenda
Introduction
2
Sunday, December 19, 2010

4. Agenda
Introduction
PR-OWL 2.0
What’s missing?
Mapping binary relations
Mapping n-ary relations
The bridge joining OWL and PR-OWL
2
Sunday, December 19, 2010

5. Agenda
Introduction
PR-OWL 2.0
What’s missing?
Mapping binary relations
Mapping n-ary relations
The bridge joining OWL and PR-OWL
Conclusion
2
Sunday, December 19, 2010

6. Introduction
Introduction - PR-OWL 2.0 - Conclusion 3
Sunday, December 19, 2010

7. Ontology
An ontology is an explicit, formal knowledge representation that
expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain;
Properties of those entities;
Relationships among entities;
Processes and events that happen with those entities;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 4
Sunday, December 19, 2010

8. Ontology
An ontology is an explicit, formal knowledge representation that
expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities;
Relationships among entities;
Processes and events that happen with those entities;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 4
Sunday, December 19, 2010

9. Ontology
An ontology is an explicit, formal knowledge representation that
expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities;
Processes and events that happen with those entities;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 4
Sunday, December 19, 2010

10. Ontology
An ontology is an explicit, formal knowledge representation that
expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
Processes and events that happen with those entities;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 4
Sunday, December 19, 2010

11. Ontology
An ontology is an explicit, formal knowledge representation that
expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
analyzing if requirements
Processes and events that happen with those entities; are met,
choosing better proposal, ...
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 4
Sunday, December 19, 2010

12. Probabilistic Ontology
A probabilistic ontology is an explicit, formal knowledge representation
that expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
analyzing if requirements
Processes and events that happen with those entities; are met,
choosing better proposal, ...
Statistical regularities that characterize the domain;
Inconclusive, ambiguous, incomplete, unreliable, and dissonant knowledge related to entities
of the domain;
Uncertainty about all the above forms of knowledge;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 5
Sunday, December 19, 2010

13. Probabilistic Ontology
A probabilistic ontology is an explicit, formal knowledge representation
that expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
analyzing if requirements
Processes and events that happen with those entities; are met,
choosing better proposal, ...
Statistical regularities that characterize the domain;
Inconclusive, ambiguous, incomplete, unreliable, and dissonant knowledge related to entities
of the domain;
Uncertainty about all the above forms of knowledge;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 5
Sunday, December 19, 2010

14. Probabilistic Ontology
A probabilistic ontology is an explicit, formal knowledge representation
that expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
analyzing if requirements
Processes and events that happen with those entities; are met,
choosing better proposal, ...
Statistical regularities that characterize the domain;
Inconclusive, ambiguous, incomplete, unreliable, and dissonant knowledge related to entities
of the domain;
Uncertainty about all the above forms of knowledge;
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 5
Sunday, December 19, 2010

15. Probabilistic Ontology
A probabilistic ontology is an explicit, formal knowledge representation
that expresses knowledge about a domain of application. This includes:
Types of entities that exist in the domain; Person, Procurement, Enterprise, ...
Properties of those entities; firstName, lastName, ...
Relationships among entities; motherOf, ownerOf, isFrontOf ...
analyzing if requirements
Processes and events that happen with those entities; are met,
choosing better proposal, ...
Statistical regularities that characterize the domain;
Inconclusive, ambiguous, incomplete, unreliable, and dissonant knowledge related to entities
of the domain; P(isFrontOf|
valueOfProcurement = >1M,
Uncertainty about all the above forms of knowledge; annualIncome = <10k) = 90%
where the term entity refers to any concept (real or fictitious, concrete or abstract) that
can be described and reasoned about within the domain of application. [3]
Introduction - PR-OWL 2.0 - Conclusion 5
Sunday, December 19, 2010

16. PR-OWL
*reproduced with permission from [3] - extended version
Introduction - PR-OWL 2.0 - Conclusion 6
Sunday, December 19, 2010

17. Mapping problem
Introduction - PR-OWL 2.0 - Conclusion 7
Sunday, December 19, 2010

18. Mapping problem
Introduction - PR-OWL 2.0 - Conclusion 7
Sunday, December 19, 2010

19. Mapping problem
Introduction - PR-OWL 2.0 - Conclusion 7
Sunday, December 19, 2010

20. Mapping problem
?
1. Mapping - winner
2.Types - value
Introduction - PR-OWL 2.0 - Conclusion 7
Sunday, December 19, 2010

21. PR-OWL 2.0
Introduction - PR-OWL 2.0 - Conclusion 8
Sunday, December 19, 2010

22. Mapping is incomplete
OWL
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

23. Mapping is incomplete
OWL
winnerOf
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

24. Mapping is incomplete
OWL
winnerOf
Procurement
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

25. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

26. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

27. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

28. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

29. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf_RV_procurement
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

30. Mapping is incomplete
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf_RV_procurement
_MFrag.procurement
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 9
Sunday, December 19, 2010

31. Simple solution
OWL
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

32. Simple solution
OWL
winnerOf
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

33. Simple solution
OWL
winnerOf
Procurement
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

34. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

35. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

36. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

37. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

38. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf_RV_procurement
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

39. Simple solution
OWL
winnerOf
Procurement Enterprise
winnerOf
PR-OWL winnerOf_RV
winnerOf_RV_procurement
_MFrag.procurement
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 10
Sunday, December 19, 2010

40. What about n-ary relations?
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

41. What about n-ary relations?
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

42. What about n-ary relations?
OWL
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

43. What about n-ary relations?
OWL
Procurement
hasContract
Price Contract Enterprise
hasPrice hasEnterprise
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

44. What about n-ary relations?
OWL
Procurement contract1
hasContract hasPrice hasEnterprise
hasPrice hasEnterprise
Price Contract Enterprise $10,000.00 $500,000.00 enterprise1 enterprise2
hasPrice hasEnterprise
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

45. What about n-ary relations?
X X
OWL
Procurement contract1
hasContract hasPrice hasEnterprise
hasPrice hasEnterprise
Price Contract Enterprise $10,000.00 $500,000.00 enterprise1 enterprise2
hasPrice hasEnterprise
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

46. What about n-ary relations?
X X
OWL
Procurement contract1
hasContract hasPrice hasEnterprise
hasPrice hasEnterprise
Price Contract Enterprise $10,000.00 $500,000.00 enterprise1 enterprise2
hasPrice hasEnterprise
contractOf
Contract _:id1
originOf enterpriseOf priceOf
Procurement Enterprise Price
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

47. What about n-ary relations?
X X
OWL
Procurement contract1
hasContract hasPrice hasEnterprise
hasPrice hasEnterprise
Price Contract Enterprise $10,000.00 $500,000.00 enterprise1 enterprise2
hasPrice hasEnterprise
contract1
contractOf
Contract _:id1 contractOf contractOf
originOf enterpriseOf priceOf _:3-aryInst1 _:3-aryInst2
enterpriseOf priceOf enterpriseOf
priceOf
Procurement Enterprise Price
enterprise1 $10,000.00 $500,000.00 enterprise2
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 11
Sunday, December 19, 2010

48. Solution for n-ary mapping
OWL
contractOf
Contract _:id1
originOf enterpriseOf priceOf
Procurement Enterprise Price
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 12
Sunday, December 19, 2010

49. Solution for n-ary mapping
OWL enterpriseOf priceOf
contractOf
Contract _:id1 range domain domain range
Enterprise _:id1 Price
originOf enterpriseOf priceOf
domain
Contract contractOf
Procurement Enterprise Price range
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 12
Sunday, December 19, 2010

50. Solution for n-ary mapping
OWL enterpriseOf priceOf
contractOf
Contract _:id1 range domain domain range
Enterprise _:id1 Price
originOf enterpriseOf priceOf
domain
Contract contractOf
Procurement Enterprise Price range
PR-OWL
Introduction - PR-OWL 2.0 - Conclusion 12
Sunday, December 19, 2010

51. Solution for n-ary mapping
OWL enterpriseOf priceOf
contractOf
Contract _:id1 range domain domain range
Enterprise _:id1 Price
originOf enterpriseOf priceOf
domain
Contract contractOf
Procurement Enterprise Price range
priceOf_RV
PR-OWL “1”^^int hasArgument “2”^^int hasArgument
hasArgNumber hasArgNumber
priceOf_RV_contract priceOf_RV_enterprise
hasArgTerm hasArgTerm
hasPossibleValues
_MFrag.contract _MFrag.enterprise
isSubsBy isSubsBy defineUncertaintyOf
Contract Enterprise Price
isObjectIn isObjectIn
range range range
contractOf enterpriseOf priceOf
domain domain domain
_:id1
Introduction - PR-OWL 2.0 - Conclusion 12
Sunday, December 19, 2010

52. What changed?
OWL
winnerOf
Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 13
Sunday, December 19, 2010

53. What changed?
OWL
winnerOf
Procurement Enterprise
winnerOf
winnerOf_RV
winnerOf_RV_procurement
_MFrag.procurement
*No mapping to
OWL properties
Procurement Enterprise
Introduction - PR-OWL 2.0 - Conclusion 13
Sunday, December 19, 2010

54. What changed?
OWL
winnerOf
Procurement Enterprise
winnerOf
winnerOf_RV winnerOf_RV
winnerOf_RV_procurement winnerOf_RV_procurement
_MFrag.procurement _MFrag.procurement
*Added mapping
*No mapping to for RVs
OWL properties winnerOf
Procurement Enterprise Procurement Enterprise
winnerOf
Introduction - PR-OWL 2.0 - Conclusion 13
Sunday, December 19, 2010

55. What changed?
OWL
winnerOf
Procurement Enterprise
winnerOf
winnerOf_RV winnerOf_RV winnerOf_RV
winnerOf_RV_procurement winnerOf_RV_procurement winnerOf_RV_procurement
_MFrag.procurement _MFrag.procurement _MFrag.procurement
*Added mapping
*Added mapping
*No mapping to for RVs
for RVs’ arguments
OWL properties winnerOf winnerOf
Procurement Enterprise Procurement Enterprise Procurement Enterprise
winnerOf winnerOf
Introduction - PR-OWL 2.0 - Conclusion 13
Sunday, December 19, 2010

56. The bridge
Introduction - PR-OWL 2.0 - Conclusion 14
Sunday, December 19, 2010

57. Conclusion
Introduction - PR-OWL 2.0 - Conclusion 15
Sunday, December 19, 2010

58. Conclusion
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

59. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

60. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
A formal mapping between OWL concepts and PR-OWL
random variables
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

61. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
A formal mapping between OWL concepts and PR-OWL
random variables
Justified the importance of a formal mapping through an example
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

62. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
A formal mapping between OWL concepts and PR-OWL
random variables
Justified the importance of a formal mapping through an example
Presented a simple solution sufficient for binary relations
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

63. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
A formal mapping between OWL concepts and PR-OWL
random variables
Justified the importance of a formal mapping through an example
Presented a simple solution sufficient for binary relations
Presented a complex and robust solution for n-ary relations
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

64. Conclusion
Provided both the syntax and a more in depth
description of one of the major changes in PR-
OWL 2.0
A formal mapping between OWL concepts and PR-OWL
random variables
Justified the importance of a formal mapping through an example
Presented a simple solution sufficient for binary relations
Presented a complex and robust solution for n-ary relations
Presented a schematic for how to do the mapping back and forth
between PR-OWL random variables and OWL triples (both
predicates and functions)
Introduction - PR-OWL 2.0 - Conclusion 16
Sunday, December 19, 2010

65. Future work
Introduction - PR-OWL 2.0 - Conclusion 17
Sunday, December 19, 2010

66. Future work
Formally define the semantics of the schematic
proposed
Introduction - PR-OWL 2.0 - Conclusion 17
Sunday, December 19, 2010

67. Future work
Formally define the semantics of the schematic
proposed
Propose an algorithm for performing the mapping
from OWL concepts to PR-OWL RVs, and vice-
versa
Introduction - PR-OWL 2.0 - Conclusion 17
Sunday, December 19, 2010

68. Future work
Formally define the semantics of the schematic
proposed
Propose an algorithm for performing the mapping
from OWL concepts to PR-OWL RVs, and vice-
versa
In addition, PR-OWL 2 will address other issues
described in [2]
Replace the meta-entity definition in PR-OWL
Use of existing types in OWL, RDF(S), and XML as
possible values for RVs (including data types)
Introduction - PR-OWL 2.0 - Conclusion 17
Sunday, December 19, 2010

69. Obrigado!
18
Sunday, December 19, 2010