Abstract
We use Kripke structures of autoepistemic logic to classify various semantics for disjunctive logic programs with default negation. We have observed that nonmonotonic reasoning can be characterized by Kripke structures whose beliefs are justified. We also observed that two different types of negative introspection in autoepistemic reasoning present two different interpretations of default negation: consistency-based and minimal-model-based; we further observed that all logic program semantics fall into three semantical points of view: the skeptical, stable, and partial-stable. Based on these observations, we classify disjunctive logic program semantics into six different categories, and discuss the relationships among various semantics.
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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.
S. Brass and J. Dix. A disjunctive semantics based on unfolding and bottom-up evaluation. In Bernd Wofiner, editor, IFIP '94-Congress, Workshop FG2: Disjunctive Logic Programming and Disjunctive Databases), pages 83–91, 1994.
S. Brass, J. Dix, I. Niemela, and T. Przymusinski. A comparison of the static and the disjunctive well-founded semantics and its implementation. In Proc. of Knowledge Representation, 1998.
P. M. Dung. Negations as hypotheses: An abductive foundation for logic programming. In Proceedings of the 8th ICLP, pages 3–17, 1991.
T. Eiter, N. Leone, and D. Sacc. The expressive power of partial models in disjunctive deductive databases. In Logic in Databases, pages 245–264, 1996.
A. Van Gelder, K. Ross, and J. Schlipf. The well-founded semantics for general logic programs. JACM, 38:620–650, 1991.
M. Gelfond. On stratified autoepistemic theories. In Proceedings of AAAI-87, pages 207–211. Morgan Kaufmann Publishers, 1987.
M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proc. of the 5th ICLP, pages 1070–1080, 1988.
M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, 9:365–386, 1991.
J.Y. Halpern and Y. Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379, 1992.
Jaakko Hintikka. Knowledge and Belief: An introduction to the logic of the two notions. Cornell University Press, 1962.
H. J. Levesque. All I know: A study in autoepistemic logic. AI, 42:263–309, 1990.
R. C. Moore. Semantic considerations on non-monotonic logic. AI, 25:75–94, 1985.
T. C. Przymusinski. Stable semantics for disjunctive programs. New Generation Computing, 9:401–424, 1991.
T. C. Przymusinski. Static semantics for normal and disjunctive logic programs. Annals of Mathematics and Artificial Intelligence, 14:323–357, 1995.
D. Saccà and C. Zaniolo. Stable models and non-determinism in logic programs with negation. In Proceedings of the 9th ACM PODS, pages 205–217, 1990.
J.-H. You, X. Wang, and L.-Y. Yuan. Disjunctive logic programming as constrained inferences. In Proc. of ICLP, 1997.
J.-H. You and L.-Y. Yuan. A three-valued semantics of deductive databases and logic programs. Journal of Computer and System Sciences, 49:334–361, 1994.
J.-H. You and L.-Y. Yuan. On the equivalence of semantics for normal logic programs. Journal of Logic Programming, 22(3):209–219, 1995.
L.-Y. Yuan. Autoepistemic logic of first order and its expressive power. Journal of Automated Reasoning, 13(1):69–82, 1994.
L.-Y. Yuan and J.-H. You. Autoepistemic circumscription and logic programming. Journal of Automated Reasoning, 10:143–160, 1993.
L.-Y. Yuan and J.-H. You. On the extension of logic programming with negation though uniform proofs. In Proc. of LPNMR'95, LNAI Vol. 928, 1995.
L.-Y. Yuan and J.-H. You. An introspective logic of belief. In Proc. of the Workshop on LP&KR, ILPS'97, pages 157–170, 1997.
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© 1998 Springer-Verlag Berlin Heidelberg
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Yuan, LY., You, JH., Goebel, R. (1998). Disjunctive logic programming and possible model semantics. In: Wobcke, W., Pagnucco, M., Zhang, C. (eds) Agents and Multi-Agent Systems Formalisms, Methodologies, and Applications. DAI 1997. Lecture Notes in Computer Science, vol 1441. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055020
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DOI: https://doi.org/10.1007/BFb0055020
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