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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-24599-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20642-2
Online ISBN: 978-3-540-24599-5
eBook Packages: Springer Book Archive