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The power of beliefs or translating default logic into standard autoepistemic logic

  • Georg Gottlob
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 810)

Abstract

Since Konolige's translation of default logic into strongly grounded autoepistemic logic, several other variants of Moore's original autoepistemic logic that embody default logic have been studied. All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show, that a modular translation is not possible. However, we exhibit a a faithful polynomial-time translation from propositional default logic into standard AEL which is nonmodular. It follows that the expressive power of standard AEL is strictly greater than that of default logic. Our translation uses as important intermediate step an embedding of Marek's and Truszczyński's nonmonotonic logic N into standard AEL.

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References

  1. 1.
    J. Delgrande and W. Jackson. Default Logic Revisited. In Proc. KR-91 Google Scholar
  2. 2.
    Th. Eiter and G. Gottlob Reasoning with Parsimonious and Moderately Grounded Expansions. Fundamenta Informaticae, 17:31–53, 1992.Google Scholar
  3. 3.
    M.C. Fitting, W. Marek, and M. Truszczyński. The Pure Logic of Necessitation. The Journal of Logic and Computation, 2(3):349–373, 1992.Google Scholar
  4. 4.
    G. Gottlob. The Power of Beliefe: Translating Default Logic Into Standard Autoepistemic Logic (Extended Report). Report CD-TR-92/34, TU Wien, Paniglgasse 16, A-1040 Wien, Austria, 1992.Google Scholar
  5. 5.
    G. Gottlob. Complexity Results for Nonmonotonic Logics. The Journal of Logic and Computation, 2:3:397–425, June 1992.Google Scholar
  6. 6.
    T. Imielinski. Results on Translating Defaults to Circumscription. In Proc. IJCAI-1985, 1985.Google Scholar
  7. 7.
    M. Kaminski. Embedding a Default System into Nonmonotonic Logic. Fundamenta Informaticae, 14:345–354, 1991.Google Scholar
  8. 8.
    K. Konolige. On the Relationship between Default and Autoepistemic Logic. AIJ, 35:343–382, 1988. (+ Errata, vol 41(1989/90), p.115, 1989).Google Scholar
  9. 9.
    F. Lin and Y. Shoham. Epistemic Semantics for Fixed-Point Non-Monotonic Logics. In Proc. TARK-90, pp. 111–120. 1990.Google Scholar
  10. 10.
    W. Marek, G.F. Schwartz, and M. Truszczynski. Modal Nonmonotonic Logics: Ranges, Characterization, Computation. Proc. KR-91.Google Scholar
  11. 11.
    W. Marek and M. Truszczynski. Relating Autoepistemic and Default Logics. In Proc. KR-89.Google Scholar
  12. 12.
    W. Marek and M. Truszczyński. Modal logic for default reasoning. Annals of Mathematics and Artificial Intelligence, 1:275–302, 1990.Google Scholar
  13. 13.
    D. McDermott. Non-Monotonic Logic II: Nonmonotonic Modal Theories. JACM, 29:33–57, 1982.Google Scholar
  14. 14.
    R.C. Moore. Semantical Considerations on Nonmonotonic Logic. AIJ, 25:75–94, 1985.Google Scholar
  15. 15.
    I. Niemelä. Constructive Tightly Grounded Autoepistemic Reasoning. In Proc. IJCAI-1991, 1991.Google Scholar
  16. 16.
    R. Reiter. A Logic for Default Reasoning. AIJ, 13:81–132, 1980.Google Scholar
  17. 17.
    G. Shvarts. Autoepistemic Modal Logics. In Proc. TARK-90, pp. 97–109. 1990.Google Scholar
  18. 18.
    P. Siegel. A Modal Language for Nonmonotonic Logic. In Proc. Workshop DRUM-S/'CEE, Marseille, France, 1990, 1990.Google Scholar
  19. 19.
    M. Truszczynski. Modal Interpretations of Default Logic. In Proc. IJCAI-1991, 1991.Google Scholar
  20. 20.
    M. Truszczynski. Embedding Default Logic into Modal Nonmonotonic Logics. Proc. Workshop on Nonmon. Reas. and LP, Washington, July 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Georg Gottlob
    • 1
  1. 1.Institut für InformationssystemeTechnische Universität WienWienAustria

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