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A non-preferential semantics of non-monotonic modal logic

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Abstract

We present a new semantical description of non-monotonic modal logic whose underlying (monotonic) modal logic S is characterized by a class of cluster-decomposable Kripke interpretations: it is shown that S-expansions coincide with the theories of isolated clusters of the canonical model of S.

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References

  1. Donini, F.M., Nardi, D., Rosati, R.: Ground nonmonotonic modal logics. J. Log. Comput. 7, 523–548 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fitting, M.: Basic modal logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 1: Logical Foundations, pp. 368–448. Oxford University Press, Oxford (1993)

    Google Scholar 

  3. Grimberg, B., Kaminski, M.: First-order ground non-monotonic modal logic. Fundam. Inform. 83, 253–276 (2008)

    MATH  MathSciNet  Google Scholar 

  4. Hughes, G.E., Cresswell, M.J.: A Companion to Modal Logic. Methuen and Co., London (1984)

    MATH  Google Scholar 

  5. Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge, New York, New York (1996)

    MATH  Google Scholar 

  6. Lemmon, E.J. (in collaboration with D. Scott): In: Segerberg, K. (ed.) The “Lemmon Notes”: An Introduction to Modal Logic. Basil Blackwell, Oxford (1977)

    Google Scholar 

  7. Konolige, K.: On the relation between default and autoepistemic logic. Artif. Intell. 35, 343–382 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Marek, W., Truszczyński, M.: Nonmonotonic Logic. Springer, Berlin (1993)

    MATH  Google Scholar 

  9. McDermott, D.: Non-monotonic logic II: Non-monotonic modal theories. J. ACM 29, 33–57 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. McDermott, D., Doyle, J.: Non-monotonic logic I. Artif. Intell. 13, 41–72 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  11. Moore, R.C.: Semantical considerations on non-monotonic logics. Artif. Intell. 25, 75–94 (1985)

    Article  MATH  Google Scholar 

  12. Moore, R.C.: Possible-world semantics for autoepistemic logic. In: Ginsberg, M.L. (ed.) Readings in Non-monotonic Reasoning, pp. 137–142. Morgan Kaufmann, Los Altos, California (1987)

    Google Scholar 

  13. Schwarz, G.: Minimal model semantics for nonmonotonic modal logics. In: Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science, pp. 34–43. IEEE Computer Society Press, Los Alamitos, California (1992)

    Chapter  Google Scholar 

  14. Segerberg, K.: An essay in classical modal logic. Filos. Stud. 13 (1971)

  15. Shvarts, G.: Autoepistemic modal logics. In: Parikh, R. (ed.) Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge, pp. 97–110. Morgan Kaufmann, Los Altos, California (1990)

    Google Scholar 

  16. Stalnaker, R.: A note on nonmonotonic modal logic. Artif. Intell. 64, 183–196 (1993)

    Article  MathSciNet  Google Scholar 

  17. Tiomkin, M., Kaminski, M.: The modal logic of cluster-decomposable Kripke interpretations. Notre Dame J. Form. Log. 48, 511–520 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Voorbraak, F.: The logic of objective knowledge and rational belief. In: van Eijck, J. (ed.) Proceedings of the European Workshop on Logics in Artificial Intelligence—JELIA’90, vol. 478 of Lecture Notes in Artificial Intelligence, pp. 499–515. Springer, Berlin (1990)

    Google Scholar 

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Correspondence to Michael Kaminski.

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Kaminski, M. A non-preferential semantics of non-monotonic modal logic. Ann Math Artif Intell 53, 205–223 (2008). https://doi.org/10.1007/s10472-009-9114-0

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