Abstract
The appropriateness of Autoepistemic Logic for the construction of knowledge representation systems is regarded as questionable due to its great computational complexity. Instead of resorting to incomplete interpreters, we propose a semantical characterization of approximate autoepistemic reasoning. It consists of a sequence of monotonically decreasing sets of belief states. Every autoepistemic expansion is a maximal fixpoint and is contained in the smallest fixpoint. For stratified knowledge bases the approach coincides with Autoepistemic Logic. For normal and disjunctive rules the construction can be reduced to iterated applications of a specialized consequence operator for the underlying monotonic logic. For normal rules the approximation coincides with the well-founded semantics on atomic propositions. Hence, it can be computed in quadratic time in this case.
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References
Chitta Baral and V. S. Subrahmanian. Dualities between alternative semantics for logic programming and nonmonotonic reasoning. In Proc. of the 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, pages 69–86. MIT Press, 1991.
Piero A. Bonatti. Beliefs as stable conjectures. In Proc. of the 1st Int. Workshop on Logic Programming and Non-monotonic Reasoning, pages 53–68. MIT Press, 1991.
Piero A. Bonatti. A family of three-valued autoepistemic logics. In E. Ardizzone, S. Gaglio, and F. Sorbello, editors, Trends in Artificial Intelligence, Proc. of the 2nd Congress of the Italian Association for Artificial Intelligence, pages 28–37. Springer, Lecture Notes in Artificial Intelligence 549, 1991.
Michael Gelfond and Vladimir Lifschitz. The stable model semantics for logic programming. In Proc. of the 5th Int. Conf. and Symp. on Logic Programming, pages 1070–1080. MIT Press, 1988.
Joseph Y. Halpern and Yoram Moses. Towards a theory of knowledge and ignorance: Preliminary report. In Krzysztof R. Apt, editor, Logics and Models of Concurrent Systems, pages 459–476. Springer, 1985.
Tomi Janhunen. Weakened negative introspection in autoepistemic reasoning. Technical Report Series A, No. 21, Helsinki University of Technology, Digital Systems Laboratory, February 1993.
Tomi Janhunen and Ilkka Niemelä. A scheme for weakened negative introspection in autoepistemic reasoning. In Proc. of the Kurt Gödel Colloquium. Springer, Lecture Notes in Computer Science (to be published), 1993.
Jürgen Kalinski. Autoepistemic expansions with incomplete belief introspection. In J. Dix, K.P. Jantke, and P.H. Schmitt, editors, Proc. of the 1st Int. Workshop on Nonmonotonic and Inductive Logic, pages 223–232. Springer, Lecture Notes in Artificial Intelligence 543, 1991.
H. A. Kautz and B. Selman. Hard problems for simple default logics. In Proc. of the 1st Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 189–197. Morgan Kaufmann, 1989.
Phokion G. Kolaitis. The expressive power of stratified logic programs. Information and Computation, 90:50–66, 1991.
Wiktor Marek and Miroslaw Truszczyński. Autoepistemic logic. Journal of the ACM, 38(3):588–619, 1991.
Jack Minker and Arcot Rajasekar. A fixpoint semantics for disjunctive logic programs. Journal of Logic Programming, 9:45–74, 1990.
Robert C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25(4):75–94, 1985.
Ilkka Niemelä. Decision procedure for autoepistemic logic. In Proc. of the 9th Conf. on Automated Deduction, pages 675–684. Springer, Lecture Notes in Computer Science 310, 1988.
Ilkka Niemelä and Jussi Rintanen. On the impact of stratification on the complexity of nonmonotonic reasoning. In Proc. of the 3rd Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 627–638. Morgan Kaufmann, 1992.
L. M. Pereira, J. N. Aparício, and J. J. Alferes. Non-monotonic reasoning with well founded semantics. In Proc. of the 8th Int. Conf. on Logic Programming, pages 475–489. MIT Press, 1991.
Teodor C. Przymusinski. Three-valued formalizations of non-monotonic reasoning and logic programming. In Proc. of the 1st Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 341–348. Morgan Kaufmann, 1989.
Alfred Tarski. A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics, 5:285–309, 1955.
M. H. van Emden and R. A. Kowalski. The semantics of predicate logic as a programming language. Journal of the ACM, 23(4):733–742, 1976.
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, 1991.
Allen Van Gelder. The alternating fixpoint of logic programs with negation. In Proc. of the 8th Symp. on Principles of Database Systems, pages 1–10, 1989.
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© 1994 Springer-Verlag Berlin Heidelberg
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Kalinski, J. (1994). Weak autoepistemic reasoning and well-founded semantics. In: Lakemeyer, G., Nebel, B. (eds) Foundations of Knowledge Representation and Reasoning. Lecture Notes in Computer Science, vol 810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58107-3_11
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DOI: https://doi.org/10.1007/3-540-58107-3_11
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