Abstract
In this paper, we present a method for embedding prioritized circumscription of a clausal theory into general disjunctive logic programs (GDP) with negation as failure in the head. In recent works, Sakama and Inoue show that parallel circumscription can be embedded in GDP. They also show that prioritized circumscription of a clausal theory can be represented in the framework of GDP extended with priorities. In our method, the priorities of minimization in the circumscription policy are translated into the syntactical form of logic program rules, and the models of the circumscription are precisely captured by the stable models of the program. Thus we show that prioritized circumscription can be directly embedded in GDP without extending the GDP logic programming framework. This result further asserts the expressive power of the class of general disjunctive programs and supports its use for knowledge representation in Artificial Intelligence.
Work supported in part by NSF grant IRI-9409370 and LEQSF grant LEQSF(RF/95-97) RDA-37
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J. Chen, Minimal Knowledge + Negation as Failure = Only Knowing (sometimes). Proceedings of the 2nd International Workshop on Logic Programming and Non-monotonic Reasoning, June 1993, pp. 132–150.
C. Sakama, K. Inoue, Embedding Circumscriptive Theories in General Disjunctive Programs, Proceedings of the 3rd International Workshop on Logic Programming and Non-monotonic Reasoning, June 1995, pp. 344–357.
C. Sakama, K. Inoue, Representing Priorities in Logic Programs, Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, pp. 82–96.
M. Gelfond and V. Lifschitz, Compiling Circumscriptive Theories in Logic Programs, Proceedings of 2nd International Workshop on Nonmonotonic Reasoning, 1988, LNAI 346, pp. 74–99.
M. Gelfond and V. Lifschitz, Classical Negation in Logic Programs and Disjunctive Databases. New Generation Computing, 9 (1991), pp. 365–385.
M. Gelfond, H. Przymusinska, and T. Przymusinski, On the Relationship between Circumscription and Negation as Failure, Artificial Intelligence, 38 (1989), pp. 75–94.
K. Inoue, C. Sakama, On Positive Occurrences of Negation as Failure, Proceedings of KR'94, pp. 293–304.
S. Kundu and J. Chen, A New Class of Theories for Which Circumscription Can Be Obtained via The Predicate Completion. Journal of Experimental and Theoretical AI, 8 (1996), pp. 191–205.
V. Lifschitz, Closed World Databases and Circumscription, Artificial Intelligence, 27 (1985), pp. 229–235.
V. Lifschitz, Computing Circumscription, Proceedings of IJCAI-85, pp. 121–127.
V. Lifschitz, On the Declarative Semantics of Logic Programs with Negation, In Foundations of Deductive Databases and Logic Programming (J. Minker ed.), Morgan Kaufmann, 1988, pp. 177–192.
V. Lifschitz, Minimal Belief and Negation As Failure. Artificial Intelligence, 70 (1-2), 1994, pp. 53–72.
V. Lifschitz, G. Schwarz, Extended Logic Programs as Autoepistemic Theories, Proceedings of the 2nd International Workshop on Logic Programming and Non-monotonic Reasoning, June 1993, pp. 101–114.
V. Lifschitz, T. Woo, Answer Sets in General Nonmonotonic Reasoning (preliminary report), Proceedings of KR'92, pp. 603–614.
W. Marek and M. Truszczynski, Reflexive Autoepistemic Logic and Logic Programming, Proceedings of the 2nd International Workshop on Logic Programming and Non-monotonic Reasoning, June 1993, pp. 115–131.
J. McCarthy, Circumscription-A Form of Non-monotonic Reasoning, Artificial Intelligence 13 (1-2), 1980, pp. 27–39.
R. Moore, Semantical Considerations on Nonmonotonic Logic, Artificial Intelligence, 25 (1), 1985, pp. 75–94.
T. Przymusinski, On the Declarative Semantics of Deductive Databases and Logic Programs, In Foundations of Deductive Databases and Logic Programming (J. Minker ed.), Morgan Kaufmann, 1988, pp. 193–216.
T. Przymusinski, An Algorithm to Compute Circumscription, Artificial Intelligence, 38 (1989), pp. 49–73.
R. Reiter, A Logic for Default Reasoning, Artificial Intelligence, 13 (1-2), 1980, pp. 81–132.
R. Reiter, Circumscription Implies Predicate Completion (sometimes), Proceedings of AAAI'82, pp. 418–420.
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© 1997 Springer-Verlag Berlin Heidelberg
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Chen, J. (1997). Embedding prioritized circumscription in logic programs. In: Raś, Z.W., Skowron, A. (eds) Foundations of Intelligent Systems. ISMIS 1997. Lecture Notes in Computer Science, vol 1325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63614-5_5
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DOI: https://doi.org/10.1007/3-540-63614-5_5
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