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PR-OWL 2.0 - Bridging the gap to OWL semantics

Rommel Carvalho, profile picture
Rommel Carvalho

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.

Technology
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Semantic Web
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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
Agenda 2 Sunday, December 19, 2010
Agenda Introduction 2 Sunday, December 19, 2010
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
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
Introduction Introduction - PR-OWL 2.0 - Conclusion 3 Sunday, December 19, 2010
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
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
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
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
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
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
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
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
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
PR-OWL *reproduced with permission from [3] - extended version Introduction - PR-OWL 2.0 - Conclusion 6 Sunday, December 19, 2010
Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7 Sunday, December 19, 2010
Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7 Sunday, December 19, 2010
Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7 Sunday, December 19, 2010
Mapping problem ? 1. Mapping - winner 2.Types - value Introduction - PR-OWL 2.0 - Conclusion 7 Sunday, December 19, 2010
PR-OWL 2.0 Introduction - PR-OWL 2.0 - Conclusion 8 Sunday, December 19, 2010
Mapping is incomplete OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9 Sunday, December 19, 2010
Mapping is incomplete OWL winnerOf winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9 Sunday, December 19, 2010
Mapping is incomplete OWL winnerOf Procurement winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9 Sunday, December 19, 2010
Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9 Sunday, December 19, 2010
Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL Procurement Enterprise Introduction - PR-OWL 2.0 - Conclusion 9 Sunday, December 19, 2010
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
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
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
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
Simple solution OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10 Sunday, December 19, 2010
Simple solution OWL winnerOf winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10 Sunday, December 19, 2010
Simple solution OWL winnerOf Procurement winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10 Sunday, December 19, 2010
Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10 Sunday, December 19, 2010
Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 10 Sunday, December 19, 2010
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
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
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
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
What about n-ary relations? PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11 Sunday, December 19, 2010
What about n-ary relations? PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11 Sunday, December 19, 2010
What about n-ary relations? OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11 Sunday, December 19, 2010
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
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
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
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
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
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
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
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
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
What changed? OWL winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 13 Sunday, December 19, 2010
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
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
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
The bridge Introduction - PR-OWL 2.0 - Conclusion 14 Sunday, December 19, 2010
Conclusion Introduction - PR-OWL 2.0 - Conclusion 15 Sunday, December 19, 2010
Conclusion Introduction - PR-OWL 2.0 - Conclusion 16 Sunday, December 19, 2010
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
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
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
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
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
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
Future work Introduction - PR-OWL 2.0 - Conclusion 17 Sunday, December 19, 2010
Future work Formally define the semantics of the schematic proposed Introduction - PR-OWL 2.0 - Conclusion 17 Sunday, December 19, 2010
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
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
Obrigado! 18 Sunday, December 19, 2010

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PR-OWL 2.0 - Bridging the gap to OWL semantics

  • 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