Advertisement

Cooperative combination of default logic and autoepistemic logic

  • Choh Man Teng
Reasoning with Changing and Incomplete Information
  • 206 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1359)

Abstract

When we work with information from multiple sources, the formats of the knowledge bases may not be uniform. It is desirable to be able to combine a knowledge base of default rules with one containing autoepistemic formulas. “Cooperative combination” refers to the integration of knowledge bases in different formats, in a way that retains as much of the individual characteristics of the component formalisms as possible. Previous work on relating default logic and autoepistemic logic mostly imposes some constraints on autoepistemic logic, and thus is not suitable for combining the two logics. We first present a fixed point formulation of autoepistemic logic analogous to that of default logic. Then we introduce a possible world framework with a partition structure, which corresponds to our intuitive notion of accessibility as linking alternate “possible” worlds. We show that both default logic and autoepistemic logic can be characterized using this common framework, which is important for developing a semantics applicable to the two logics, both separately and combined. We show one way of cooperatively integrating the two logics, and provide both a syntactic fixed point and a semantic possible partition sequence characterization.

Keywords

Modal Logic Modal System Accessibility Relation Default Rule Default Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Got93]
    Georg Gottlob. The power of beliefs or translating default logic into standard autoepistemic logic. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 570–575, 1993.Google Scholar
  2. [Kon88]
    Kurt Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343–382, 1988.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [Kon89]
    Kurt Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 41:115, 1989. Errata.MathSciNetCrossRefGoogle Scholar
  4. [Kon92]
    Kurt Konolige. Ideal introspective belief. In Proceedings of the Tenth National Conference on Artificial Intelligence, pages 635–641, 1992.Google Scholar
  5. [Kon94]
    Kurt Konolige. Autoepistemic logic. In Dov M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3: Nonmonotonic Reasoning and Uncertain Reasoning. Clarendon Press, 1994.Google Scholar
  6. [LS90]
    Fangzhen Lin and Yoav Shoham. Epistemic semantics for fixed-point nonmonotonic logics. In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge, pages 111–120, 1990.Google Scholar
  7. [Moo84]
    Robert C. Moore. Possible-world semantics for autoepistemic logic. In Proceedings of AAAI Non-monotonic Reasoning Workshop, pages 344–354, 1984.Google Scholar
  8. [Moo85]
    Robert C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [MT90]
    Wiktor Marek and Miroslaw Truszczyński. Modal logic for default reasoning. Annals of Mathematics and Artificial Intelligence, 1:275–302, 1990.zbMATHCrossRefGoogle Scholar
  10. [Poo94]
    David Poole. Default logic. In Dov M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 3: Nonmonotonic Reasoning and Uncertain Reasoning. Clarendon Press, 1994.Google Scholar
  11. [Rei80]
    R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.zbMATHMathSciNetCrossRefGoogle Scholar
  12. [Seg71]
    K. Segerberg. An essay in classical modal logic, 1971. Filosofiska Studier, Uppsala University, 13.Google Scholar
  13. [Shv90]
    Grigori Shvarts. Autoepistemic modal logics. In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge, pages 97–109, 1990.Google Scholar
  14. [Sta80]
    R. Stalnaker. A note on non-monotonic modal logic. Department of Philosophy, Cornell University, Ithaca, New York, U.S.A., 1980. Unpublished manuscript.Google Scholar
  15. [Tru91a]
    Miroslaw Truszczyński. Embedding default logics into modal nonmonotonic logics. In Proceedings of the First International Workshop on Logic Programming and Non-monotonic Reasoning, pages 151–165, 1991.Google Scholar
  16. [Tru91b]
    Miroslaw Truszczyński. Modal interpretations of default logic. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, pages 393–398, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Choh Man Teng
    • 1
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA

Personalised recommendations