Abstract
We extend Clark’s definition of a completed program and the definition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas. The concept of a tight program and Fages’ theorem are extended to disjunctive programs as well.
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References
Babovich, Y., Erdem, E., Lifschitz, V.: Fages’ theorem and answer set programming. In: Proc. Eighth Int’l. Workshop on Non-Monotonic Reasoning (2000), http://arxiv.org/abs/cs.ai/0003042
Baral, C., Gelfond, M.: Logic programming and knowledge representation. Journal of Logic Programming 20, 73–148 (1994)
Ben-Eliyahu, R., Dechter, R.: Propositional semantics for disjunctive logic programs. Annals of Mathematics and Artificial Intelligence 12, 53–87 (1996)
Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)
Eiter, T., Gottlob, G.: Complexity results for disjunctive logic programming and application to nonmonotonic logics. In: Miller, D.(ed.) Proc. ILPS 1993, pp. 266–278 (1993)
Erdem, E., Lifschitz, V.: Transformations of logic programs related to causality and planning. In: Gelfond, M., Leone, N., Pfeifer, G. (eds.) LPNMR 1999. LNCS (LNAI), vol. 1730, pp. 107–116. Springer, Heidelberg (1999)
Erdem, E., Lifschitz, V.: Tight logic programs. Theory and Practice of Logic Programming 3, 499–518 (2003)
Fages, F.: Consistency of Clark’s completion and existence of stable models. Journal of Methods of Logic in Computer Science 1, 51–60 (1994)
Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K., (eds.) Logic Programming: Proc. Fifth Int’l Conf. and Symp., pp. 1070–1080 (1988)
Inoue, K., Sakama, C.: Negation as failure in the head. Journal of Logic Programming 35, 39–78 (1998)
Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 369–389 (1999)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541 (2001)
Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Proc. AAAI 2002 (2002)
Lloyd, J., Topor, R.: Making Prolog more expressive. Journal of Logic Programming 3, 225–240 (1984)
Marek, V., Subrahmanian, V.S.: The relationship between logic program semantics and non-monotonic reasoning. In: Levi, G., Martelli, M., (eds.) Logic Programming: Proc. Sixth Int’l Conf., pp. 600–617 (1989)
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Lee, J., Lifschitz, V. (2003). Loop Formulas for Disjunctive Logic Programs. In: Palamidessi, C. (eds) Logic Programming. ICLP 2003. Lecture Notes in Computer Science, vol 2916. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24599-5_31
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DOI: https://doi.org/10.1007/978-3-540-24599-5_31
Publisher Name: Springer, Berlin, Heidelberg
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