PR-OWL 2.0 - Bridging the gap to OWL semantics

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Presentation given by Rommel Carvalho at the 6th Uncertainty Reasoning for the Semantic Web Workshop at the 9th International Semantic Web Conference in November 7, 2010.

Paper: PR-OWL 2.0 - Bridging the gap to OWL semantics

Abstract: The past few years have witnessed an increasingly mature body of research on the Semantic Web, with new standards being developed and more complex use cases being proposed and explored. As complexity increases in SW applications, so does the need for principled means to cope with uncertainty inherent to real world SW applications. Not surprisingly, several approaches addressing uncertainty representation and reasoning on the Semantic Web have emerged [3, 4, 6, 7, 10, 11, 13, 14]. For example, PR-OWL [3] provides OWL constructs for representing Multi-Entity Bayesian Network (MEBN) [8] theories. This paper reviews some shortcomings of PR-OWL 1 [2] and describes how they will be addressed in PR-OWL 2. A method is presented for mapping back and forth from triples into random variables (RV). The method applies to triples representing both predicates and functions. A complex example is given for mapping an n-ary relation using the proposed schematic.

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PR-OWL 2.0 - Bridging the gap to OWL semantics

  1. 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) 11/07/2010Sunday, December 19, 2010
  2. 2. Agenda 2Sunday, December 19, 2010
  3. 3. Agenda Introduction 2Sunday, December 19, 2010
  4. 4. Agenda Introduction PR-OWL 2.0 What’s missing? Mapping binary relations Mapping n-ary relations The bridge joining OWL and PR-OWL 2Sunday, December 19, 2010
  5. 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 2Sunday, December 19, 2010
  6. 6. Introduction Introduction - PR-OWL 2.0 - Conclusion 3Sunday, December 19, 2010
  7. 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 4Sunday, December 19, 2010
  8. 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 4Sunday, December 19, 2010
  9. 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 4Sunday, December 19, 2010
  10. 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 4Sunday, December 19, 2010
  11. 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 4Sunday, December 19, 2010
  12. 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 5Sunday, December 19, 2010
  13. 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 5Sunday, December 19, 2010
  14. 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 5Sunday, December 19, 2010
  15. 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 5Sunday, December 19, 2010
  16. 16. PR-OWL*reproduced with permission from [3] - extended version Introduction - PR-OWL 2.0 - Conclusion 6Sunday, December 19, 2010
  17. 17. Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7Sunday, December 19, 2010
  18. 18. Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7Sunday, December 19, 2010
  19. 19. Mapping problem Introduction - PR-OWL 2.0 - Conclusion 7Sunday, December 19, 2010
  20. 20. Mapping problem ?1. Mapping - winner2.Types - value Introduction - PR-OWL 2.0 - Conclusion 7Sunday, December 19, 2010
  21. 21. PR-OWL 2.0 Introduction - PR-OWL 2.0 - Conclusion 8Sunday, December 19, 2010
  22. 22. Mapping is incomplete OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  23. 23. Mapping is incomplete OWL winnerOf winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  24. 24. Mapping is incomplete OWL winnerOf Procurement winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  25. 25. Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  26. 26. Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL Procurement Enterprise Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  27. 27. Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf_RV Procurement Enterprise Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  28. 28. Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf_RV Procurement Enterprise Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  29. 29. Mapping is incomplete OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf_RV winnerOf_RV_procurement Procurement Enterprise Introduction - PR-OWL 2.0 - Conclusion 9Sunday, December 19, 2010
  30. 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 9Sunday, December 19, 2010
  31. 31. Simple solution OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  32. 32. Simple solution OWL winnerOf winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  33. 33. Simple solution OWL winnerOf Procurement winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  34. 34. Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  35. 35. Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  36. 36. Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf_RV winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  37. 37. Simple solution OWL winnerOf Procurement Enterprise winnerOf PR-OWL winnerOf_RV winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 10Sunday, December 19, 2010
  38. 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 10Sunday, December 19, 2010
  39. 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 10Sunday, December 19, 2010
  40. 40. What about n-ary relations? PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11Sunday, December 19, 2010
  41. 41. What about n-ary relations? PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11Sunday, December 19, 2010
  42. 42. What about n-ary relations? OWL PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11Sunday, December 19, 2010
  43. 43. What about n-ary relations? OWL Procurement hasContract Price Contract Enterprise hasPrice hasEnterprise PR-OWL Introduction - PR-OWL 2.0 - Conclusion 11Sunday, December 19, 2010
  44. 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 11Sunday, December 19, 2010
  45. 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 11Sunday, December 19, 2010
  46. 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 11Sunday, December 19, 2010
  47. 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 11Sunday, December 19, 2010
  48. 48. Solution for n-ary mapping OWL contractOf Contract _:id1 originOf enterpriseOf priceOf Procurement Enterprise Price PR-OWL Introduction - PR-OWL 2.0 - Conclusion 12Sunday, December 19, 2010
  49. 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 12Sunday, December 19, 2010
  50. 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 12Sunday, December 19, 2010
  51. 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 12Sunday, December 19, 2010
  52. 52. What changed? OWL winnerOf Procurement Enterprise winnerOf Introduction - PR-OWL 2.0 - Conclusion 13Sunday, December 19, 2010
  53. 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 13Sunday, December 19, 2010
  54. 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 13Sunday, December 19, 2010
  55. 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 13Sunday, December 19, 2010
  56. 56. The bridge Introduction - PR-OWL 2.0 - Conclusion 14Sunday, December 19, 2010
  57. 57. Conclusion Introduction - PR-OWL 2.0 - Conclusion 15Sunday, December 19, 2010
  58. 58. Conclusion Introduction - PR-OWL 2.0 - Conclusion 16Sunday, December 19, 2010
  59. 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 16Sunday, December 19, 2010
  60. 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 16Sunday, December 19, 2010
  61. 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 16Sunday, December 19, 2010
  62. 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 16Sunday, December 19, 2010
  63. 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 16Sunday, December 19, 2010
  64. 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 16Sunday, December 19, 2010
  65. 65. Future work Introduction - PR-OWL 2.0 - Conclusion 17Sunday, December 19, 2010
  66. 66. Future work Formally define the semantics of the schematic proposed Introduction - PR-OWL 2.0 - Conclusion 17Sunday, December 19, 2010
  67. 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 17Sunday, December 19, 2010
  68. 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 17Sunday, December 19, 2010
  69. 69. Obrigado! 18Sunday, December 19, 2010

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