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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 1997: Logic Programming And Nonmonotonic Reasoning pp 132–151Cite as

Separating disbeliefs from beliefs in autoepistemic reasoning

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1265))

Abstract

This paper investigates separated autoepistemic logic which is a generalization of Moore's autoepistemic logic with separate modalities for belief and disbelief. Along the separation of beliefs and disbeliefs, the relationship between autoepistemic logic and default logic becomes very intuitive. Straightforward ways of translating default theories into separated autoepistemic theories and back are presented. These translations are shown to preserve a variety of semantics of default theories such as those based on default extensions, weak extensions and stationary extensions. These classes of extensions are captured by their analogs in separated autoepistemic logic, and vice versa. A particular novelty of the approach is that a reasonable notion of separated stationary expansions can be established.

The reported research has been financed by Academy of Finland and Helsinki Graduate School in Computer Science and Engineering.

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References

  1. K.R. Apt, H.A. Blair, and A. Walker. Towards a theory of declarative knowledge. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 89–148. Morgan Kaufmann Publishers, Los Altos, 1988.

    Google Scholar 

  2. C. R. Baral and V.S. Subrahmanian. Stable and extension class theory for logic programs and default logics. Journal of Automated Reasoning, 8:345–366, 1992.

    Google Scholar 

  3. P. Bonatti. Autoepistemic logics as a unifying framework for the semantics of logic programs. Journal of Logic Programming, 22(2):91–149, 1995.

    Google Scholar 

  4. D.M. Gabbay, C.J. Hogger, and J.A. Robinson, editors. Handbook of Logic and Artificial Intelligence and Logic Programming, Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning. Oxford University Press, Oxford, 1994.

    Google Scholar 

  5. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proceedings of the 5th International Conference on Logic Programming, pages 1070–1080, Seattle, USA, August 1988. The MIT Press.

    Google Scholar 

  6. G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2(3):397–425, June 1992.

    Google Scholar 

  7. T. Janhunen. Representing autoepistemic introspection in terms of default rules. In Proceedings of the European Conference on Artificial Intelligence, pages 70–74, Budapest, Hungary, August 1996. John Wiley.

    Google Scholar 

  8. K. Konolige. On the relation between default and autoepistemic logic. Artificial Intelligence, 35:343–382, 1988.

    Article  Google Scholar 

  9. V. Lifschitz. Computing circumscription. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, pages 121–127, Los Angeles, California, USA, August 1985. Morgan Kaufmann Publishers.

    Google Scholar 

  10. V. Lifschitz. Nonmonotonic databases and epistemic queries. In Proceedings of the 12th International Joint Conference on Artificial Intelligence, pages 381–386, Sydney, Australia, August 1991. Morgan Kaufmann Publishers.

    Google Scholar 

  11. F. Lin and Y. Shoham. A logic of knowledge and justified assumptions. Artificial Intelligence, 57:271–289, 1992.

    Google Scholar 

  12. W. Marek, G.F. Schwarz, and M. Truszczyński. Modal nonmonotonic logics: Ranges, characterization, computation. Journal of the ACM, 40(4):963–990, 1993.

    Google Scholar 

  13. W. Marek and M. Truszczyński. Modal logic for default reasoning. Annals of Mathematics and Artificial Intelligence, 1:275–302, 1990.

    Google Scholar 

  14. W. Marek and M. Truszczyński. Nonmonotonic Logic: Context-Dependent Reasoning. Springer-Verlag, Berlin, 1993.

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. R.C. Moore. Autoepistemic logic. In P. Smets, E.H. Mamdani, and D. Dubois, editors, Non-Standard Logics for Automated Reasoning, pages 105–136. Academic Press, London, 1988.

    Google Scholar 

  18. I. Niemelä. Towards automatic autoepistemic reasoning. In Proceedings of the European Workshop on Logics in Artificial Intelligence-JELIA '90, pages 428–443, Amsterdam, The Netherlands, September 1990. Springer-Verlag.

    Google Scholar 

  19. I. Niemelä. A unifying framework for nonmonotonic reasoning. In Proceedings ofthe 10th European Conference on Artificial Intelligence, pages 334–338, Vienna, Austria, August 1992. John Wiley.

    Google Scholar 

  20. I. Niemelä. A decision method for nonmonotonic reasoning based on autoepistemic reasoning. Journal of Automated Reasoning, 14:3–42, 1995.

    Google Scholar 

  21. I. Niemelä. Towards efficient default reasoning. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 312–318, Montreal, Canada, August 1995. Morgan Kaufmann Publishers.

    Google Scholar 

  22. H. Przymusinska and T.C. Przymusinski. Stationary default extensions. In Working Notes of the 4th International Workshop on on Nonmonotonic Reasoning, pages 179–193, Plymouth, Vermont, USA, May 1992.

    Google Scholar 

  23. T. C. Przymusinski. Static semantics for normal and disjunctive logic programs. Annals of Mathematics and Artificial Intelligence, 14:323–357, 1995.

    Google Scholar 

  24. T.C. Przymusinski. Autoepistemic logics of closed beliefs and logic programming. In Proceedings of the 1st International Workshop on Logic Programming and Nonmonotonic Reasoning, pages 3–20, Washington, D.C., USA, July 1991. The MIT Press.

    Google Scholar 

  25. T.C. Przymusinski. Three-valued nonmonotonic formalisms and semantics of logic programming. Artificial Intelligence, 49:309–343, 1991.

    Google Scholar 

  26. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    Article  Google Scholar 

  27. R. Stalnaker. A note on non-monotonic modal logic. Artificial Intelligence, 64:183–196, 1993.

    Google Scholar 

  28. M. Truszczyński. Embedding default logic into modal nonmonotonic logics. In Proceedings of the 1st International Workshop on Logic Programming and Nonmonotonic Reasoning, pages 151–165, Washington, D.C., USA, July 1991. The MIT Press.

    Google Scholar 

  29. A. Van Gelder, K.A. Ross, and J.S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620–650, July 1991.

    Google Scholar 

  30. J. You and L. Yuan. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences, 49:334–361, 1994.

    Google Scholar 

  31. L. Yuan. Autoepistemic logic of first order and its expressive power. Journal of Automated Reasoning, 13(1):69–82, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Digital Systems Laboratory, Helsinki University of Technology, P.O.Box 1100, FIN-02015 HUT, Finland

    Tomi Janhunen

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  1. Tomi Janhunen
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Editor information

Jürgen Dix Ulrich Furbach Anil Nerode

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© 1997 Springer-Verlag Berlin Heidelberg

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Janhunen, T. (1997). Separating disbeliefs from beliefs in autoepistemic reasoning. In: Dix, J., Furbach, U., Nerode, A. (eds) Logic Programming And Nonmonotonic Reasoning. LPNMR 1997. Lecture Notes in Computer Science, vol 1265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63255-7_10

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  • DOI: https://doi.org/10.1007/3-540-63255-7_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63255-9

  • Online ISBN: 978-3-540-69249-2

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