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(Towards) Compatibility Formalization
                              Between PR-OWL and OWL
                               Rommel Carvalho, Kathryn Laskey, and Paulo Costa
                                          George Mason University

                            Paper - First International Workshop on Uncertainty in Description Logics
                                                        UniDL - FLoC 2010




Thursday, July 15, 2010
Agenda




                                   2

Thursday, July 15, 2010
Agenda

            Introduction




                                    2

Thursday, July 15, 2010
Agenda

            Introduction
            Problem




                                    2

Thursday, July 15, 2010
Agenda

            Introduction
            Problem
            MEBN and PR-OWL




                                    2

Thursday, July 15, 2010
Agenda

            Introduction
            Problem
            MEBN and PR-OWL
            Mapping Concepts




                                    2

Thursday, July 15, 2010
Agenda

            Introduction
            Problem
            MEBN and PR-OWL
            Mapping Concepts
            Using Existing Types




                                     2

Thursday, July 15, 2010
Agenda

            Introduction
            Problem
            MEBN and PR-OWL
            Mapping Concepts
            Using Existing Types
            Conclusion



                                     2

Thursday, July 15, 2010
Introduction


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         3
                                                      Conclusion
Thursday, July 15, 2010
Introduction

                   An ontology is [5] 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.




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                           4
                                                      Conclusion
Thursday, July 15, 2010
Introduction
                   A probabilistic ontology is [5] 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;
                          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.


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                                    5
                                                      Conclusion
Thursday, July 15, 2010
Introduction




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         6
                                                      Conclusion
Thursday, July 15, 2010
Introduction
            MEBN
                  Represent and reason with uncertainty about any
                  propositions that can be expressed in first-order logic




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         6
                                                      Conclusion
Thursday, July 15, 2010
Introduction
            MEBN
                  Represent and reason with uncertainty about any
                  propositions that can be expressed in first-order logic
            PR-OWL
                  Uses MEBN logic to provide a framework for building
                  probabilistic ontologies




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         6
                                                      Conclusion
Thursday, July 15, 2010
Introduction
            MEBN
                  Represent and reason with uncertainty about any
                  propositions that can be expressed in first-order logic
            PR-OWL
                  Uses MEBN logic to provide a framework for building
                  probabilistic ontologies
            Simple fraud detection and prevention example for
            illustrating problems/solutions

                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         6
                                                      Conclusion
Thursday, July 15, 2010
Problem


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         7
                                                      Conclusion
Thursday, July 15, 2010
Problem




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         8
                                                      Conclusion
Thursday, July 15, 2010
Problem




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         8
                                                      Conclusion
Thursday, July 15, 2010
Problem




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         8
                                                      Conclusion
Thursday, July 15, 2010
Problem

                                                                                           ?


1. Mapping - winner
2.Types - value

                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         8
                                                      Conclusion
Thursday, July 15, 2010
MEBN and PR-OWL


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         9
                                                      Conclusion
Thursday, July 15, 2010
MEBN




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         10
                                                      Conclusion
Thursday, July 15, 2010
MEBN
        BN + FOL [15]
                   Procurement                 Procurement Directed MFrag
                  Fraud Detection
                    MTheory [2]




                                          Directed Procurement by Indices MFrag




                          Indices MFrag




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         10
                                                      Conclusion
Thursday, July 15, 2010
PR-OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         11
                                                      Conclusion
Thursday, July 15, 2010
PR-OWL
        MEBN + OWL [5]




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         11
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         12
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - OWL to PR-OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         13
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - OWL to PR-OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         13
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - OWL to PR-OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         13
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - PR-OWL to OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         14
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - PR-OWL to OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         14
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - PR-OWL to OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         14
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concepts - PR-OWL to OWL




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         14
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concept Instance




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         15
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concept Instance




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         15
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concept Instance




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         15
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concept Instance




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         15
                                                      Conclusion
Thursday, July 15, 2010
Mapping Concept Instance




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         15
                                                      Conclusion
Thursday, July 15, 2010
Using Existing Types


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         16
                                                      Conclusion
Thursday, July 15, 2010
Using Existing Types




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         17
                                                      Conclusion
Thursday, July 15, 2010
Using Existing Types




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         17
                                                      Conclusion
Thursday, July 15, 2010
Using Existing Types




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         17
                                                      Conclusion
Thursday, July 15, 2010
Using Existing Types




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         17
                                                      Conclusion
Thursday, July 15, 2010
Conclusion


                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         18
                                                      Conclusion
Thursday, July 15, 2010
Conclusion




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         19
                                                      Conclusion
Thursday, July 15, 2010
Conclusion
                 Described the main compatibility issues between
                 PR-OWL and OWL
                          Lack of mapping between deterministic and probabilistic
                          concepts
                          Lack of use of existing types




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         19
                                                      Conclusion
Thursday, July 15, 2010
Conclusion
                 Described the main compatibility issues between
                 PR-OWL and OWL
                          Lack of mapping between deterministic and probabilistic
                          concepts
                          Lack of use of existing types
                 Provided qualitative descriptions of possible
                 solutions
                          Random Variable closely related to Properties
                          Substitution of PR-OWL’s types by OWL’s types

                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         19
                                                      Conclusion
Thursday, July 15, 2010
Conclusion




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         20
                                                      Conclusion
Thursday, July 15, 2010
Conclusion

                 Future work




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         20
                                                      Conclusion
Thursday, July 15, 2010
Conclusion

                 Future work
                          Define new syntax for PR-OWL 2




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         20
                                                      Conclusion
Thursday, July 15, 2010
Conclusion

                 Future work
                          Define new syntax for PR-OWL 2
                          Define semantics for PR-OWL 2




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         20
                                                      Conclusion
Thursday, July 15, 2010
Conclusion

                 Future work
                          Define new syntax for PR-OWL 2
                          Define semantics for PR-OWL 2
                          Present problem and possible solutions for consistency
                          checking between OWL axioms and PR-OWL local
                          probability distributions




                  Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types -
                                                                                                         20
                                                      Conclusion
Thursday, July 15, 2010
Obrigado!




                                      21

Thursday, July 15, 2010

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UniDL 2010 - Compatibility Formalization Between PR-OWL and OWL

  • 1. (Towards) Compatibility Formalization Between PR-OWL and OWL Rommel Carvalho, Kathryn Laskey, and Paulo Costa George Mason University Paper - First International Workshop on Uncertainty in Description Logics UniDL - FLoC 2010 Thursday, July 15, 2010
  • 2. Agenda 2 Thursday, July 15, 2010
  • 3. Agenda Introduction 2 Thursday, July 15, 2010
  • 4. Agenda Introduction Problem 2 Thursday, July 15, 2010
  • 5. Agenda Introduction Problem MEBN and PR-OWL 2 Thursday, July 15, 2010
  • 6. Agenda Introduction Problem MEBN and PR-OWL Mapping Concepts 2 Thursday, July 15, 2010
  • 7. Agenda Introduction Problem MEBN and PR-OWL Mapping Concepts Using Existing Types 2 Thursday, July 15, 2010
  • 8. Agenda Introduction Problem MEBN and PR-OWL Mapping Concepts Using Existing Types Conclusion 2 Thursday, July 15, 2010
  • 9. Introduction Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 3 Conclusion Thursday, July 15, 2010
  • 10. Introduction An ontology is [5] 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. Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 4 Conclusion Thursday, July 15, 2010
  • 11. Introduction A probabilistic ontology is [5] 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; 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. Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 5 Conclusion Thursday, July 15, 2010
  • 12. Introduction Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 6 Conclusion Thursday, July 15, 2010
  • 13. Introduction MEBN Represent and reason with uncertainty about any propositions that can be expressed in first-order logic Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 6 Conclusion Thursday, July 15, 2010
  • 14. Introduction MEBN Represent and reason with uncertainty about any propositions that can be expressed in first-order logic PR-OWL Uses MEBN logic to provide a framework for building probabilistic ontologies Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 6 Conclusion Thursday, July 15, 2010
  • 15. Introduction MEBN Represent and reason with uncertainty about any propositions that can be expressed in first-order logic PR-OWL Uses MEBN logic to provide a framework for building probabilistic ontologies Simple fraud detection and prevention example for illustrating problems/solutions Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 6 Conclusion Thursday, July 15, 2010
  • 16. Problem Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 7 Conclusion Thursday, July 15, 2010
  • 17. Problem Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 8 Conclusion Thursday, July 15, 2010
  • 18. Problem Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 8 Conclusion Thursday, July 15, 2010
  • 19. Problem Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 8 Conclusion Thursday, July 15, 2010
  • 20. Problem ? 1. Mapping - winner 2.Types - value Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 8 Conclusion Thursday, July 15, 2010
  • 21. MEBN and PR-OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 9 Conclusion Thursday, July 15, 2010
  • 22. MEBN Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 10 Conclusion Thursday, July 15, 2010
  • 23. MEBN BN + FOL [15] Procurement Procurement Directed MFrag Fraud Detection MTheory [2] Directed Procurement by Indices MFrag Indices MFrag Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 10 Conclusion Thursday, July 15, 2010
  • 24. PR-OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 11 Conclusion Thursday, July 15, 2010
  • 25. PR-OWL MEBN + OWL [5] Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 11 Conclusion Thursday, July 15, 2010
  • 26. Mapping Concepts Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 12 Conclusion Thursday, July 15, 2010
  • 27. Mapping Concepts - OWL to PR-OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 13 Conclusion Thursday, July 15, 2010
  • 28. Mapping Concepts - OWL to PR-OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 13 Conclusion Thursday, July 15, 2010
  • 29. Mapping Concepts - OWL to PR-OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 13 Conclusion Thursday, July 15, 2010
  • 30. Mapping Concepts - PR-OWL to OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 14 Conclusion Thursday, July 15, 2010
  • 31. Mapping Concepts - PR-OWL to OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 14 Conclusion Thursday, July 15, 2010
  • 32. Mapping Concepts - PR-OWL to OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 14 Conclusion Thursday, July 15, 2010
  • 33. Mapping Concepts - PR-OWL to OWL Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 14 Conclusion Thursday, July 15, 2010
  • 34. Mapping Concept Instance Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 15 Conclusion Thursday, July 15, 2010
  • 35. Mapping Concept Instance Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 15 Conclusion Thursday, July 15, 2010
  • 36. Mapping Concept Instance Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 15 Conclusion Thursday, July 15, 2010
  • 37. Mapping Concept Instance Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 15 Conclusion Thursday, July 15, 2010
  • 38. Mapping Concept Instance Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 15 Conclusion Thursday, July 15, 2010
  • 39. Using Existing Types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 16 Conclusion Thursday, July 15, 2010
  • 40. Using Existing Types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 17 Conclusion Thursday, July 15, 2010
  • 41. Using Existing Types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 17 Conclusion Thursday, July 15, 2010
  • 42. Using Existing Types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 17 Conclusion Thursday, July 15, 2010
  • 43. Using Existing Types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 17 Conclusion Thursday, July 15, 2010
  • 44. Conclusion Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 18 Conclusion Thursday, July 15, 2010
  • 45. Conclusion Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 19 Conclusion Thursday, July 15, 2010
  • 46. Conclusion Described the main compatibility issues between PR-OWL and OWL Lack of mapping between deterministic and probabilistic concepts Lack of use of existing types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 19 Conclusion Thursday, July 15, 2010
  • 47. Conclusion Described the main compatibility issues between PR-OWL and OWL Lack of mapping between deterministic and probabilistic concepts Lack of use of existing types Provided qualitative descriptions of possible solutions Random Variable closely related to Properties Substitution of PR-OWL’s types by OWL’s types Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 19 Conclusion Thursday, July 15, 2010
  • 48. Conclusion Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 20 Conclusion Thursday, July 15, 2010
  • 49. Conclusion Future work Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 20 Conclusion Thursday, July 15, 2010
  • 50. Conclusion Future work Define new syntax for PR-OWL 2 Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 20 Conclusion Thursday, July 15, 2010
  • 51. Conclusion Future work Define new syntax for PR-OWL 2 Define semantics for PR-OWL 2 Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 20 Conclusion Thursday, July 15, 2010
  • 52. Conclusion Future work Define new syntax for PR-OWL 2 Define semantics for PR-OWL 2 Present problem and possible solutions for consistency checking between OWL axioms and PR-OWL local probability distributions Introduction - Problem - MEBN and PR-OWL - Mapping Concepts - Using Existing Types - 20 Conclusion Thursday, July 15, 2010
  • 53. Obrigado! 21 Thursday, July 15, 2010