Contexts in Semantic Web by fjn47816

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									                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




                               Contexts in Semantic Web

                                     Erico Neves - #100781774
                                    edsouza@connect.carleton.ca
                                     Sina Ariyan - #100794456
                                    mariyan@connect.carleton.ca


                                           December 13, 2009


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


      Introduction
      Problems with Contextual Phenomena
      Contexts in AI
      CYC Project[1]
      Contexts for the Semantic Web
      Elements of the Setting
      Model Theory
      Conclusion
      References

                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


      Ramanathan Guha, Rob McCool, and Richard Fikes. Contexts for the Semantic Web.
      Proc. The Semantic Web - ISWC 2004, LNCS 3298, pp. 32-46, 2004.
         ◮ A central theme of the Semantic Web is that programs should be able to easily
           aggregate data from different sources.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


      Ramanathan Guha, Rob McCool, and Richard Fikes. Contexts for the Semantic Web.
      Proc. The Semantic Web - ISWC 2004, LNCS 3298, pp. 32-46, 2004.
         ◮ A central theme of the Semantic Web is that programs should be able to easily
           aggregate data from different sources.
         ◮ Unfortunately, even if two sites provide their data using the same data model
           and vocabulary, subtle differences in their use of terms and in the assumptions
           they make ⇒ challenges for aggregation.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


      Ramanathan Guha, Rob McCool, and Richard Fikes. Contexts for the Semantic Web.
      Proc. The Semantic Web - ISWC 2004, LNCS 3298, pp. 32-46, 2004.
         ◮ A central theme of the Semantic Web is that programs should be able to easily
           aggregate data from different sources.
         ◮ Unfortunately, even if two sites provide their data using the same data model
           and vocabulary, subtle differences in their use of terms and in the assumptions
           they make ⇒ challenges for aggregation.
         ◮ Languages of the Semantic Web ⇒ method for aggregation at the data model
             level
                 ◮    RDF, RDFS, OWL, etc




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


      Ramanathan Guha, Rob McCool, and Richard Fikes. Contexts for the Semantic Web.
      Proc. The Semantic Web - ISWC 2004, LNCS 3298, pp. 32-46, 2004.
         ◮ A central theme of the Semantic Web is that programs should be able to easily
           aggregate data from different sources.
         ◮ Unfortunately, even if two sites provide their data using the same data model
           and vocabulary, subtle differences in their use of terms and in the assumptions
           they make ⇒ challenges for aggregation.
         ◮ Languages of the Semantic Web ⇒ method for aggregation at the data model
             level
                 ◮    RDF, RDFS, OWL, etc
         ◮ Just as with the human readable web, Semantic Web publishers make
           assumptions and use the same term in subtly different ways
                 ◮    Human consumers use their common sense


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   In the past, AI researchers have encountered similar issue ⇒
             aggregate structured knowledge from different people or even
             the same person at different times




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   In the past, AI researchers have encountered similar issue ⇒
             aggregate structured knowledge from different people or even
             the same person at different times
         ◮   Proposed Solution:
                 ◮    Contexts and micro-theories have been proposed and
                      implemented in projects such as CYC




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   In the past, AI researchers have encountered similar issue ⇒
             aggregate structured knowledge from different people or even
             the same person at different times
         ◮   Proposed Solution:
                 ◮    Contexts and micro-theories have been proposed and
                      implemented in projects such as CYC
         ◮   The scale and federated nature of the Semantic Web pose a
             new set of challenges → main difference from CYC project.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Situations observed during knowledge base construction
      The examples of contextual phenomena we observed can be
      classified into a small number of varieties of contexts.
         ◮   Class Differences ⇒ Different sites often use a particular class
             in slightly different ways.
                 ◮    Concepts like Person → Characters from films are considered
                      persons in certain sites.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Situations observed during knowledge base construction
      The examples of contextual phenomena we observed can be
      classified into a small number of varieties of contexts.
         ◮   Class Differences ⇒ Different sites often use a particular class
             in slightly different ways.
                 ◮    Concepts like Person → Characters from films are considered
                      persons in certain sites.
         ◮   Propositional Attitude ⇒ A related phenomenon is that of a
             site having an implicit propositional attitude.
                 ◮    A film character may be confused with real life role



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   Property Type Differences ⇒ A common source of differences
             between sites is that property types such as price. Price may
             be presented with or without taxes, but website may not
             inform it to user.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   Property Type Differences ⇒ A common source of differences
             between sites is that property types such as price. Price may
             be presented with or without taxes, but website may not
             inform it to user.
         ◮   Point of View ⇒ Example: Is Taiwan a country of its own, or
             a province of China?




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Property Type Differences ⇒ A common source of differences
             between sites is that property types such as price. Price may
             be presented with or without taxes, but website may not
             inform it to user.
         ◮   Point of View ⇒ Example: Is Taiwan a country of its own, or
             a province of China?
                 ◮    make the subjectivity explicit




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Property Type Differences ⇒ A common source of differences
             between sites is that property types such as price. Price may
             be presented with or without taxes, but website may not
             inform it to user.
         ◮   Point of View ⇒ Example: Is Taiwan a country of its own, or
             a province of China?
                 ◮    make the subjectivity explicit
                 ◮    only selectively import those facts that are not contentious.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Property Type Differences ⇒ A common source of differences
             between sites is that property types such as price. Price may
             be presented with or without taxes, but website may not
             inform it to user.
         ◮   Point of View ⇒ Example: Is Taiwan a country of its own, or
             a province of China?
                 ◮    make the subjectivity explicit
                 ◮    only selectively import those facts that are not contentious.
         ◮   Implicit Time ⇒ Sites often publish a piece of data that is
             true at the time of publication, with the temporal qualification
             being left implicit.
                 ◮    Example: sites that list Bill Clinton as the President of the US.
                 ◮    Unit of measure: US$40, they might simply say 40

                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Approximations ⇒ Example: Websites may give countries
             approximate values of for the population, area, etc. Usually
             these information is more accurate in typically available from
             the governments of each of these countries, only of these are
             available on-line. Idea is combine information from
             government websites when available and use other sources
             when not available.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Most of the information on these sites is drawn from
             structured databases and these phenomena manifest
             themselves in these databases as well.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Most of the information on these sites is drawn from
             structured databases and these phenomena manifest
             themselves in these databases as well.
         ◮   The problem is not that some of these sites are not
             trustworthy or that all of their data is bad.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Most of the information on these sites is drawn from
             structured databases and these phenomena manifest
             themselves in these databases as well.
         ◮   The problem is not that some of these sites are not
             trustworthy or that all of their data is bad.
         ◮   Need is a mechanism to factor the kinds of differences listed
             above as part of the data aggregation process.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Most of the information on these sites is drawn from
             structured databases and these phenomena manifest
             themselves in these databases as well.
         ◮   The problem is not that some of these sites are not
             trustworthy or that all of their data is bad.
         ◮   Need is a mechanism to factor the kinds of differences listed
             above as part of the data aggregation process.
         ◮   AI has proposed various context mechanisms to handle this
             problem...



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Contexts as first class objects in knowledge representation
             systems have been the subject of much study in AI [2, 3]




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Contexts as first class objects in knowledge representation
             systems have been the subject of much study in AI [2, 3]
         ◮   Contexts/Micro-theories are an important part of many
             current KR systems such as CYC (more about that later).




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Contexts as first class objects in knowledge representation
             systems have been the subject of much study in AI [2, 3]
         ◮   Contexts/Micro-theories are an important part of many
             current KR systems such as CYC (more about that later).
         ◮   They have been used in natural language understanding to
             model indexicals and other issues that arise at the semantic
             and pragmatic processing layers




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Contexts as first class objects in knowledge representation
             systems have been the subject of much study in AI [2, 3]
         ◮   Contexts/Micro-theories are an important part of many
             current KR systems such as CYC (more about that later).
         ◮   They have been used in natural language understanding to
             model indexicals and other issues that arise at the semantic
             and pragmatic processing layers
         ◮   The scope and complexity of the AI problems are substantially
             more than anything we expect to encounter in Semantic Web.



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Primary role for contexts on the Semantic Web is to factor
             the differences → between data sources when aggregating
             data from them.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Primary role for contexts on the Semantic Web is to factor
             the differences → between data sources when aggregating
             data from them.
         ◮   No need for nested contexts, ephemeral contexts and the
             ability to transcend contexts.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Primary role for contexts on the Semantic Web is to factor
             the differences → between data sources when aggregating
             data from them.
         ◮   No need for nested contexts, ephemeral contexts and the
             ability to transcend contexts.
         ◮   Semantic Web highly distributed = AI systems smaller and
             centralized.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   Primary role for contexts on the Semantic Web is to factor
             the differences → between data sources when aggregating
             data from them.
         ◮   No need for nested contexts, ephemeral contexts and the
             ability to transcend contexts.
         ◮   Semantic Web highly distributed = AI systems smaller and
             centralized.
         ◮   Therefore, there is place for stronger constraints on the
             computational complexity and ease of use of the context
             mechanism.


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   CYC is the largest experiment yet in symbolic AI.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   CYC is the largest experiment yet in symbolic AI.
         ◮   Project began in 1984 under the auspices of the
             Microelectronics and Computer Technology Corporation, a
             consortium of computer, semiconductor, and electronics
             manufacturers.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   CYC is the largest experiment yet in symbolic AI.
         ◮   Project began in 1984 under the auspices of the
             Microelectronics and Computer Technology Corporation, a
             consortium of computer, semiconductor, and electronics
             manufacturers.
         ◮   1995 Douglas Lenat, the CYC project director, spun off the
             project as Cycorp, Inc.




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   CYC is the largest experiment yet in symbolic AI.
         ◮   Project began in 1984 under the auspices of the
             Microelectronics and Computer Technology Corporation, a
             consortium of computer, semiconductor, and electronics
             manufacturers.
         ◮   1995 Douglas Lenat, the CYC project director, spun off the
             project as Cycorp, Inc.
         ◮   The most ambitious goal of Cycorp was to build a KB
             containing a significant percentage of the commonsense
             knowledge of a human being.



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   CYC is the largest experiment yet in symbolic AI.
         ◮   Project began in 1984 under the auspices of the
             Microelectronics and Computer Technology Corporation, a
             consortium of computer, semiconductor, and electronics
             manufacturers.
         ◮   1995 Douglas Lenat, the CYC project director, spun off the
             project as Cycorp, Inc.
         ◮   The most ambitious goal of Cycorp was to build a KB
             containing a significant percentage of the commonsense
             knowledge of a human being.
         ◮   A projected 100 million commonsense assertions, or rules,
             were to be coded into CYC.
                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   The expectation was that this “critical mass” would allow the
             system itself to extract further rules directly from ordinary
             prose → foundation for future generations of expert systems.




      More informations can be found in http://www.cyc.com/cyc



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




         ◮   The expectation was that this “critical mass” would allow the
             system itself to extract further rules directly from ordinary
             prose → foundation for future generations of expert systems.
         ◮   Among the outstanding remaining problems are issues in
             searching and problem solving → how to search the KB
             automatically for information that is relevant to a given
             problem
      More informations can be found in http://www.cyc.com/cyc



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Context mechanism setting:
         ◮   Semantic web contents from a number of different URLs
         ◮   Content from different URLs may contain differences like the
             ones described earlier
         ◮   We would like to create an internally consistent aggregate of
             the data
         ◮   The aggregate should be maximal
                 ◮    It should incorporate as much of the data from different URLs




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   Each data source is abstracted into a context
                 ◮    A chunk of RDF at tap.stanford.edu/People.rdf is mapped into
                      a context and the contents of this URL are true in that context




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   Each data source is abstracted into a context
                 ◮    A chunk of RDF at tap.stanford.edu/People.rdf is mapped into
                      a context and the contents of this URL are true in that context
         ◮   We are interested in defining mechanisms that combine data
             from different URLs
                 ◮    These are called lifting rules
                 ◮    Each rule lifts data from a context (source context) to an
                      aggregate context (target context)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   ist(ci , ϕ) is the only symbol with predefined interpretation
                 ◮    It states that proposition ϕ is true in context ci
                 ◮    In contrast with RDFS with multiple interpreted symbols
                      (Class, PropertyType, subClassOf, ...)
                 ◮    Nested statements can also be used: ist(c1 , ist(c2 , ϕ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   ist(ci , ϕ) is the only symbol with predefined interpretation
                 ◮    It states that proposition ϕ is true in context ci
                 ◮    In contrast with RDFS with multiple interpreted symbols
                      (Class, PropertyType, subClassOf, ...)
                 ◮    Nested statements can also be used: ist(c1 , ist(c2 , ϕ))
         ◮   The system is in some context at any time




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   ist(ci , ϕ) is the only symbol with predefined interpretation
                 ◮    It states that proposition ϕ is true in context ci
                 ◮    In contrast with RDFS with multiple interpreted symbols
                      (Class, PropertyType, subClassOf, ...)
                 ◮    Nested statements can also be used: ist(c1 , ist(c2 , ϕ))
         ◮   The system is in some context at any time
         ◮   The system can enter and exit contexts to infer new rules




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   In general:
                 ◮    A symbol can denote different objects in different contexts
                 ◮    Contexts are treated as first class objects




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   In general:
                 ◮    A symbol can denote different objects in different contexts
                 ◮    Contexts are treated as first class objects
         ◮   These are convenient, but they:
                 ◮    Make it difficult to provide an adequate model theory
                 ◮    Increase computational complexity




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   In general:
                 ◮    A symbol can denote different objects in different contexts
                 ◮    Contexts are treated as first class objects
         ◮   These are convenient, but they:
                 ◮    Make it difficult to provide an adequate model theory
                 ◮    Increase computational complexity
         ◮   Here, quantification over contexts is allowed, but a symbol is
             restricted to denote the same object in all contexts




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some vocabulary elements have been introduced to specify lifting
      rules:
        ◮ importsFrom: if c1 importsFrom c2 then everything that is
           true in c2 is also true in c1
                 ◮    ist(c2 , p) ∧ ist(c1 , importsFrom(c1 , c2 )) → ist(c1 , p)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some vocabulary elements have been introduced to specify lifting
      rules:
        ◮ importsFrom: if c1 importsFrom c2 then everything that is
           true in c2 is also true in c1
                 ◮    ist(c2 , p) ∧ ist(c1 , importsFrom(c1 , c2 )) → ist(c1 , p)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some vocabulary elements have been introduced to specify lifting
      rules:
        ◮ importsFrom: if c1 importsFrom c2 then everything that is
           true in c2 is also true in c1
                 ◮    ist(c2 , p) ∧ ist(c1 , importsFrom(c1 , c2 )) → ist(c1 , p)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some vocabulary elements have been introduced to specify lifting
      rules:
        ◮ importsFrom: if c1 importsFrom c2 then everything that is
           true in c2 is also true in c1
                 ◮    ist(c2 , p) ∧ ist(c1 , importsFrom(c1 , c2 )) → ist(c1 , p)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some vocabulary elements have been introduced to specify lifting
      rules:
        ◮ importsFrom: if c1 importsFrom c2 then everything that is
           true in c2 is also true in c1
                 ◮    ist(c2 , p) ∧ ist(c1 , importsFrom(c1 , c2 )) → ist(c1 , p)
         ◮   defaultImportsFrom: contents of one context should be
             included in the aggregate context without any modification
             unless one of the other lifting rules applies




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   selectiveImport: explicitly specifies the triples that should be
             directly imported from the source to the destination
                 ◮    e.g. import capitalCity and area from CIA Factbook
                 ◮    ist(ci , type(lr , SelectiveImportLiftingRule) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y ) ∧ type(x, sc) ∧ type(y , tc)) → ist(ci , p(x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   preferenceRule: allows us to define a preference order
             between different resources that contain sparse data about a
             shared resource
                 ◮    e.g. combine Who2 with IMDB preferring IMDB for celebrity
                      information
                 ◮    In case of inconsistency, eliminate triples from the less
                      preferred context
                 ◮    ist(ci , type(lr , PreferenceLiftingRule) ∧ sourceContext(lr , cj ) ∧
                      sourceContext(lr , ck )∧targetContext(lr , ci )∧preferred(lr , ck )∧
                      propFilter (lr , p) ∧ sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧
                      ist(cj , p(x, y )∧type(x, sc)∧type(y , tc))∧¬ist(ck , (∃(z)p(x, z)∧
                      type(x, sc) ∧ type(z, tc) ∧ (z = x))) → ist(ci , p(x, y ))


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




      Figure: An aggregate context importing from two different sources with
      prefernceRule


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   termMapping: distinguishes between different uses of the
             same term
                 ◮    e.g. rename price from the source target into priceWithTax in
                      the target context
                 ◮    ist(ci , type(lr , TermMappingLiftingRule) ∧
                      propMapFrom(lr , p1 ) ∧ propMapTo(lr , p2) ∧
                      sourceContext(lr , cj ) ∧ targetContext(lr , ci ) ∧
                      sourceFilter (lr , sc) ∧ targetFilter (lr , tc)) ∧ ist(cj , p1 (x, y ) ∧
                      type(x, sc) ∧ type(y , tc)) → ist(ci , p2 (x, y ))




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




      Figure: An aggregate context importing a sources using the
      termMapping from p1 to p2


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   This paper restricts its attention to the model theory for
             RDFS [4]
         ◮   Minor changes are introduced by the addition of contexts
                 ◮    IR : set of resources (the domain or universe)
                 ◮    IP : set of properties
                 ◮    IEXT : IP → IR × IR
                 ◮    C : set of contexts
                 ◮    IS : (URI ∩ V) × C → (IR ∪ IP)
                 ◮    LV : set of literal values in IR
                 ◮    IL : LV → IR



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References


         ◮   Semantics conditions:




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa
                 ◮    if E is a plain literal ”aaa”@ttt in context c
                      → I (E , c) =< aaa, ttt >




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa
                 ◮    if E is a plain literal ”aaa”@ttt in context c
                      → I (E , c) =< aaa, ttt >
                 ◮    if E is a typed literal in context c → I (E , c) = IL(E )




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa
                 ◮    if E is a plain literal ”aaa”@ttt in context c
                      → I (E , c) =< aaa, ttt >
                 ◮    if E is a typed literal in context c → I (E , c) = IL(E )
                 ◮    if E is a URI reference appearing in context c
                      → I (E , c) = IS(E , c)




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa
                 ◮    if E is a plain literal ”aaa”@ttt in context c
                      → I (E , c) =< aaa, ttt >
                 ◮    if E is a typed literal in context c → I (E , c) = IL(E )
                 ◮    if E is a URI reference appearing in context c
                      → I (E , c) = IS(E , c)
                 ◮    if E is a triple (s p o) in context c then:
                          ◮   I (E , c) = true, if IS(p, c) ∈ IP and
                              < IS(s, c), IS(o, c) >∈ IEXT (IS(p, c))
                          ◮   I (E , c) = false, otherwise




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References


         ◮   Semantics conditions:
                 ◮    if E is a plain literal ”aaa” in context c → I (E , c) = aaa
                 ◮    if E is a plain literal ”aaa”@ttt in context c
                      → I (E , c) =< aaa, ttt >
                 ◮    if E is a typed literal in context c → I (E , c) = IL(E )
                 ◮    if E is a URI reference appearing in context c
                      → I (E , c) = IS(E , c)
                 ◮    if E is a triple (s p o) in context c then:
                          ◮   I (E , c) = true, if IS(p, c) ∈ IP and
                              < IS(s, c), IS(o, c) >∈ IEXT (IS(p, c))
                          ◮   I (E , c) = false, otherwise
                 ◮    If E is an RDF graph in context c then:
                          ◮   I (E , c) = false, if ∃E ′ inE : I (E ′ , c) = false
                          ◮   I (E , c) = true, otherwise

                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some remarks about contexts in SW
        ◮ The context mechanism is different from reification
                 ◮    Reification is intended to enable statements about potential
                      statements
                 ◮    Contexts relate the truth of a triple in one graph to its truth in
                      another graph




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




      Some remarks about contexts in SW
        ◮ The context mechanism is different from reification
                 ◮    Reification is intended to enable statements about potential
                      statements
                 ◮    Contexts relate the truth of a triple in one graph to its truth in
                      another graph
         ◮   With the context mechanism we can introduce two types of
             monotonicity
                 ◮    Monotonicity within a context
                 ◮    Monotonicity across contexts



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   Problems to aggregate data from different sources
                 ◮    SW languages are used only for data model level
                 ◮    Point of view, property type differences, ...




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   Problems to aggregate data from different sources
                 ◮    SW languages are used only for data model level
                 ◮    Point of view, property type differences, ...
         ◮   AI researchers have used the definition of context to solve this
             problem




                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                   Outline
                                              Introduction
                     Problems with Contextual Phenomena
                                            Contexts in AI
                                           CYC Project[1]
                           Contexts for the Semantic Web
                                  Elements of the Setting
                                            Model Theory
                                                Conclusion
                                                References




         ◮   Problems to aggregate data from different sources
                 ◮    SW languages are used only for data model level
                 ◮    Point of view, property type differences, ...
         ◮   AI researchers have used the definition of context to solve this
             problem
         ◮   This paper includes the notion of contexts in semantic web
             languages
                 ◮    It defines lifting rule semantics in order to combine data from
                      different resources into an aggregate context
                 ◮    It includes contexts in the interpretation of SW languages



                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca
                                                 Outline
                                            Introduction
                   Problems with Contextual Phenomena
                                          Contexts in AI
                                         CYC Project[1]
                         Contexts for the Semantic Web
                                Elements of the Setting
                                          Model Theory
                                              Conclusion
                                              References




             [1] artificial intelligence (AI). (2009). In Encyclopedia Britannica.
             Retrieved November 13, 2009, from Encyclopedia Britannica Online:
             http://www.britannica.com/EBchecked/topic/
             37146/artificial-intelligence
             [2] Ramanathan V. Guha. Contexts: a formalization and some
             applications. Technical Report STAN-CS-91-1399, Stanford CS Dept.,
             Stanford, CA, 1991.
             [3] John McCarthy. Notes on formalizing contexts. In Ruzena Bajcsy,
             editor, Proceedings of the Thirteenth International Joint Conference on
             Artificial Intelligence, pages 555-560, San Mateo, California, 1993.
             Morgan Kaufmann.
             [4] Pat Hayes. Rdf semantics. http://www.w3.org/TR/rdf-mt/.


                                                            Contexts in Semantic Web
Erico Neves - #100781774 edsouza@connect.carleton.ca Sina Ariyan - #100794456 mariyan@connect.carleton.ca

								
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