Stable model checking for disjunctive logic programs
The stable model semantics is the most widely acknowledged semantics for disjunctive logic programs.
The paper investigates computational aspects related to the stable model semantics of (function-free) disjunctive logic programs. In particular, an efficient algorithm for solving the (co-NP-hard decision) problem of checking if a model is stable is provided. The correctness of the proposed method is formally proven, and its computational complexity is analyzed. In general, the algorithm runs in polynomial space and single exponential time (in the worst case). However, the algorithm runs in polynomial time on the class of head-cycle free programs and, in case of general disjunctive logic programs, it limits the inefficient part of the computation only to the components of the program which are not head-cycle free. Some optimization techniques are also employed to reduce the amount of computation to be performed in practice.
KeywordsLogic Program Stable Model Dependency Graph Ground Atom Naive Algorithm
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- 1.Baral, C., Gelfond, M., Logic Programming and Knowledge Representation Journal of Logic Programming, Vol. 19/20, May/July 1994, pp. 73–148.Google Scholar
- 2.Ben-Eliyahu, R., Dechter, R., Propositional Semantics for Disjunctive Logic Programs, Annals of Mathematics and Artificial Intelligence, Vol. 12, 1994, pp. 53–87.Google Scholar
- 3.Ben-Eliyahu, R., Palopoli, L., Reasoning with Minimal Models: Efficient Algorithms and Applications, Proc. Fourth International Conference on Principles of Knowledge Representation and Reasoning (KR-94), 1994, pp. 39–50.Google Scholar
- 4.Eiter, T., Gottlob, G., and Mannila, H., Adding Disjunction to Datalog, Proceedings ACM PODS-94, May 1994, pp. 267–278.Google Scholar
- 5.Eiter, T., Gottlob, G., On the Computational Cost of Disjunctive Logic Programming: Propositional Case, Annals of Mathematics and Artificial Intelligence, J. C. Baltzer AG, Science Publishers, Vol. 15, 1995, pp. 289–323.Google Scholar
- 6.Elkan, C., A rational Reconstruction of Nonmonotonic Truth Maintenance Systems, Artificial Intelligence, Vol. 43, 1990, pp. 219–234.Google Scholar
- 7.Gelfond, M., Lifschitz, V., The Stable Model Semantics for Logic Programming, Proceedings Fifth Logic Programming Symposium, MIT Press, Cambridge Mass., 1988, pp. 1070–1080.Google Scholar
- 8.Gelfond, M., Lifschitz, V., Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing, Vol. 9, 1991, pp. 365–385.Google Scholar
- 9.Gottlob, G., Complexity and Expressive Power of Disjunctive Logic Programming, In M. Bruynooghe, editor, Proc. of the International Logic Programming Symposium (ILPS-'94), Ithaca NY, MIT Press, 1994, pp. 23–42.Google Scholar
- 10.IFIP-GI Workshop: Disjunctive Logic Programming and Disjunctive Databases, 13th IFIP World Computer Congress.Google Scholar
- 11.Leone, N., Rullo, P., Scarcello, F., Declarative and Fixpoint Characterizations of Disjunctive Stable Models, Proceedings of International Logic Programming Symposium-ILPS'95, Portland, Oregon, December 4–7, 1995.Google Scholar
- 12.Leone, N., Rullo, P., Scarcello, F., On the Computation of Disjunctive Stable Models, Proc. DEXA '96, September 1996.Google Scholar
- 13.Lobo, J., Minker, J., Rajasekar, A., Foundations of disjunctive logic programming, The MIT Press, 1992.Google Scholar
- 14.Marek, W., Truszczyński, M., Autoepistemic Logic, Journal of the ACM, Vol. 38, No. 3, 1991, pp. 588–619.Google Scholar
- 15.Przymusinski, T., Stable Semantics for Disjunctive Programs, New Generation Computing, Vol. 9, 1991, pp. 401–424.Google Scholar
- 16.Sakama, C., Inoue, K., Embedding Circumscriptive Theories in General Disjunctive Programs, Proc. LPNMR '95, June 1995.Google Scholar
- 17.Van Gelder, A., Ross, K. A., Schlipf, J. S., The Well-Founded Semantics for General Logic Programs, Journal of ACM, Vol. 38, No. 3, 1991, pp. 620–650.Google Scholar
- 18.Vardi, M., Complexity of relational query languages, Proceedings 14th ACM STOC, 1982, pp. 137–146.Google Scholar