Michael Kaminski
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Abstract
In this article, we introduce first-order autoepistemic logic. Our definition is semantical and is based on the intuition similar to that lying behind the definition of first-order default logic. Thus, our definition of first-order autoepistemic logic well complies with that of first-order default logic and circumscription, providing a substantial evidence for its acceptance.
- Blair, H. and Marek, V. 1998. Henkin algebras with application to default logic. Presented at the 7th International Workshop on Nonmonotonic Reasoning.]]Google Scholar
- Gottlob, G. 1995. Translating default logic into standard autoepistemic logic. J. ACM 42, 711--740.]] Google Scholar
- Guerreiro, R. and Casanova, M. 1990. An alternative semantics for default logic. Presented at the 3th International Workshop on Nonmonotonic Reasoning.]]Google Scholar
- Hughes, G. and Cresswell, M. 1984. A Companion to Modal Logic. Methuen and Co, London.]]Google Scholar
- Janhunen, T. 1996. Representing autoepistemic introspection in terms of default rules. In Proceedings of the 12th European Conference on Artificial Intelligence -- ECAI'96, W. Wahlster, Ed. Wiley, Chichister, England, 70--74.]]Google Scholar
- Janhunen, T. 1998. On the intertranslatability of autoepistemic, default and priority logics, and parallel circumscription. In Proceedings of the 6th European Workshop on Logics in Artificial Intelligence -- JELIA'98, L. d. C. J. Dix and U. Furbach, Eds. Lecture Notes in Artificial Intelligence, vol. 1489. Springer, Berlin, 216--232.]] Google Scholar
- Janhunen, T. 1999. On the intertranslatability of non-monotonic logics. Ann. Math. Artif. Int. 27, 79--128.]] Google Scholar
- Kaminski, M. 1995. A comparative study of open default theories. Artif. Int. 77, 285--319.]] Google Scholar
- Kaminski, M. 1997a. The elimination of de re formulas. J. Philos. Logic 26, 411--422.]]Google Scholar
- Kaminski, M. 1997b. A note on the stable model semantics for logic programs. Artif. Int. 97, 467--479.]] Google Scholar
- Kaminski, M. 1999. Open default theories over closed domains. J. IGPL 7, 577--589.]]Google Scholar
- Kaminski, M., Makowsky, J., and Tiomkin, M. 1998. Extensions for open default theories via the domain closure assumption. J. Logic Comput. 8, 169--187.]]Google Scholar
- Kaminski, M. and Rey, G. 2000. First-order non-monotonic modal logics. Funda. Inf. 42, 303--333.]] Google Scholar
- Konolige, K. 1988. On the relation between default and autoepistemic logic. Artif. Int. 35, 343--382.]] Google Scholar
- Konolige, K. 1991. Quantification in autoepistemic logic. Funda. Inf. XV, 275--300.]] Google Scholar
- Konolige, K. 1994. Autoepistemic logic. In Handbook of Logic in Artificial Intelligence and Logic Programming, D. Gabbay, C. Hogger, and J. Robinson, Eds. Vol. 3. Oxford University Press, Oxford, England, 217--295.]] Google Scholar
- Lakemeyer, G. 1992. On perfect introspection with quantifying-in. Funda. Inf. 17, 75--98.]] Google Scholar
- Levesque, H. 1990. All I know: A study in autoepistemic logic. Artif. Int. 42, 263--309.]] Google Scholar
- Lifschitz, V. 1987. Computing circumscription. In Proceedings of the 9th International Joint Conference on Artificial Intelligence. Morgan-Kaufmann, San Mateo, California, 121--127.]]Google Scholar
- Lifschitz, V. 1990. On open defaults. In Computational Logic: Symposium Proceedings, J. Lloyd, Ed. Springer-Verlag, Berlin, 80--95.]]Google Scholar
- Lloyd, J. 1993. Foundations of Logic Programming, 2nd extended edition. Springer-Verlag, Berlin, Germany.]] Google Scholar
- Marek, W. and Truszczyński, M. 1989. Relating autoepistemic and default logics. In Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, R. Brachman, H. Levesque, and R. Reiter, Eds. Morgan-Kaufmann, Los Altos, California, 276--288.]] Google Scholar
- Marek, W. and Truszczyński, M. 1993. Nonmonotonic Logic. Springer-Verlag, Berlin, Germany.]]Google Scholar
- McCarthy, J. 1980. Circumscription---A form of non-monotonic reasoning. Artif. Int. 13, 27--39.]]Google Scholar
- Mendelson, E. 1987. Introduction to Mathematical Logic. Wadsworth and Brooks, Monterey, Calif.]] Google Scholar
- Moore, R. 1985. Semantical considerations on non-monotonic logics. Artif. Int. 25, 75--94.]] Google Scholar
- Moore, R. 1987. Possible-world semantics for autoepistemic logic. In Readings in Non--monotonic Reasoning, M. Ginsberg, Ed. Morgan-Kaufmann, Los Altos, Calif. 137--142.]] Google Scholar
- Niemelä, I. 1988. Autoepistemic predicate logic. In Proceedings of the 8th European Conference on Artificial Intelligence, B. Radig, Y. Kodratoff, B. Überreiter, and K.-P. Wimmer, Eds. Pitman Publishing, London, England, 595--600.]]Google Scholar
- Reiter, R. 1978. On closed world databases. In Logic and Databases, H. Gallaire and J. Minker, Eds. Plenum Press, New York, 55--76.]]Google Scholar
- Reiter, R. 1980. A logic for default reasoning. Artif. Int. 13, 81--132.]]Google Scholar
- Shvarts, G. 1990. Autoepistemic modal logics. In Proceedings of the 3rd Conference on Theoretical Aspects of Reasoning about Knowledge, R. Parikh, Ed. Morgan-Kaufmann, Los Altos, Calif. 97--110.]] Google Scholar
Index Terms
- Revisiting quantification in autoepistemic logic
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