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A preference semantics for ground nonmonotonic modal logics

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Book cover Progress in Artificial Intelligence (EPIA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 990))

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Abstract

In this paper we provide a semantic characterization of ground logics, a family of nonmonotonic modal logics obtained by means of a variant of the well known Mc Dermott and Doyle fixed point equation. The term ground logics carries the idea of restricting the negative introspection capabilities of the reasoning agent to the objective (i.e. non modal) part of the theory. This intuition was nicely formalized for modal logic S5 by a semantic definition based on a preference relation on Kripke models, which was obtained as the semantic counterpart to the notion of minimal knowledge initially defined by Halpern and Moses. We have then found a preference relation on Kripke models that both generalizes this notion of minimal knowledge and provides a semantic characterization for a significant subset of ground logics.

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References

  1. F. M. Donini, D. Nardi and R. Rosati. Ground Nonmonotonic Modal Logics for Knowledge Representation. To appear in Proceedings of WOCFAI-95.

    Google Scholar 

  2. F. M. Donini, D. Nardi and R. Rosati. Non-first-order features in concept languages. To appear in Proceedings of AI *IA-95 — Fourth congress of the Italian Association for Artificial Intelligence.

    Google Scholar 

  3. J. Halpern and Y. Moses. Towards a theory of knowledge and ignorance: preliminary report. In K. Apt editor, Logics and models of concurrent systems, pages 459–476, Springer-Verlag, 1985.

    Google Scholar 

  4. M. Kaminski. Embedding a default system into nonmonotonic logic. Fundamenta Informaticae, 14:345–354, 1991.

    Google Scholar 

  5. K. Konolige. On the relationship between default and autoepistemic logic. Artificial Intelligence Journal, 35:343–382, 1988.

    Article  Google Scholar 

  6. H. J. Levesque. All I know: a study in autoepistemic logic. Artificial Intelligence, 42:263–310, 1990.

    Article  Google Scholar 

  7. V. Lifschitz. Nonmonotonic databases and epistemic queries. In Proc. of the 12th Int. Joint Conf. on Artificial Intelligence IJCAI-91, Sydney, 1991.

    Google Scholar 

  8. V. Lifschitz. Minimal belief and negation as failure. Artificial Intelligence Journal, 70:53–72, 1994.

    Article  Google Scholar 

  9. F. Lin and Y. Shoham. Epistemic semantics for fixed-point non-monotonic logics. Artificial Intelligence Journal, 57:271–289, 1992.

    Article  Google Scholar 

  10. W. Marek, G.F. Shvarts and M. Truszczyński. Modal nonmonotonic logics: ranges, characterization, computation. In Proceedings of the 2nd international conference on principles of knowledge representation and reasoning (KR-91), pages 395–404, Morgan Kaufmann, 1992.

    Google Scholar 

  11. W. Marek and M. Truszczyński. Autoepistemic logic. Journal of the ACM, 38:588–619, 1991.

    Article  Google Scholar 

  12. V.W. Marek and M. Truszczyński. Nonmonotonic logic. Context-dependent reasoning. Springer-Verlag, 1993.

    Google Scholar 

  13. D. McDermott. Non-monotonic logic II: Non-monotonic modal theories. Journal of the ACM, 29:33–57, 1982.

    Article  Google Scholar 

  14. D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence Journal. 13:41–72. 1980.

    Google Scholar 

  15. R. C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence Journal, 25:75–94, 1985.

    Google Scholar 

  16. R. Reiter, A Logic for Default Reasoning. Artificial Intelligence Journal, 13:81–132, 1980.

    Google Scholar 

  17. G. Schwarz. Autoepistemic logic of knowledge. In A. Nerode, W. Marek and V.S. Subrahmanian editors, Logic programming and nonmonotonic reasoning, pages 260–274, MIT press, 1991.

    Google Scholar 

  18. G. Schwarz. Minimal model semantics for nonmonotonic modal logics. In Proceedings of LICS-92, pages 34–43, IEEE Computer Society Press, 1992.

    Google Scholar 

  19. G. Schwarz. Bounding introspection in nonmonotonic logics. In Proceedings of the 3rd international conference on principles of knowledge representation and reasoning (KR-92), pages 581–590, Morgan Kaufmann, 1992.

    Google Scholar 

  20. G. Schwarz and M. Truszczyński. Modal logic S4f and the minimal knowledge paradigm. In Proceedings of the Fourth Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-92), pages 184–198, 1992.

    Google Scholar 

  21. G. Schwarz and M. Truszczynski. Minimal knowledge problem: a new approach. Artificial Intelligence Journal, 67:113–141, 1994.

    Google Scholar 

  22. Y. Shoham. Nonmonotonic logics: meaning and utility. In Proc. of the 10th Int. Joint Conf. on Artificial Intelligence IJCAI-87, Milan, 1987.

    Google Scholar 

  23. M. Tiomkin and M. Kaminski. Nonmonotonic default modal logics. In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-90), pages 73–84, 1990.

    Google Scholar 

  24. M. Truszczyński. Modal interpretations of default logic. In Proc. of the 12th Int. Joint Conf. on Artificial Intelligence IJCAI-91, Sydney, 1991.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, I-00198, Roma, Italy

    Daniele Nardi & Riccardo Rosati

Authors
  1. Daniele Nardi
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  2. Riccardo Rosati
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Editor information

Carlos Pinto-Ferreira Nuno J. Mamede

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© 1995 Springer-Verlag Berlin Heidelberg

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Nardi, D., Rosati, R. (1995). A preference semantics for ground nonmonotonic modal logics. In: Pinto-Ferreira, C., Mamede, N.J. (eds) Progress in Artificial Intelligence. EPIA 1995. Lecture Notes in Computer Science, vol 990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60428-6_19

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  • DOI: https://doi.org/10.1007/3-540-60428-6_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60428-0

  • Online ISBN: 978-3-540-45595-0

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