Abstract
An efficient algorithm for the computation of the stable model semantics of disjunctive logic programs is designed. Both soundness and completeness of the proposed method is formally proven. The computational complexity of the algorithm is also analyzed. In general, the algorithm runs in single exponential time and polynomial space (in the worst case); moreover, on some known tractable classes of programs it runs in polynomial time.
Work partially supported by Christian Doppler Lab. for Expert Systems, Istituto per la Sistemistica e I'Informatica, ISI-CNR, the EC-US project ”DEUS EX MACHINA” and by a MURST grant (40% share) under the project ”Sistemi formali e strumenti per basi di dati evolute”.
Preview
Unable to display preview. Download preview PDF.
References
Bell, C., Nerode, A., Ng, R., Subrahmanian, V. S., Implementing Stable Semantics by Linear Programming, Proceedings of LPNMR '93, MIT Press, Lisbon, Portugal, July, 1993, pp. 23–42.
Bell, C., Nerode, A., Ng, R., Subrahmanian, V. S., Mixed Integer Programming Methods for Computing Nonmonotonic Deductive Databases, Journal ACM, Vol.41, N.6, Nov. 1994, pp.1178–1215.
Buccafurri, F., Leone, N., Rullo, P., Stable Models and their Computation for Logic Programming with Inheritance and True Negation, Journal of Logic Programming, Vol 27(1), April 96, pp. 5–43.
Cho Le Winski, P., Marek, W., Mikitiuk, A., Truszczyński, M., Experimenting with Nonmonotonic Reasoning, Proc. 12th International Conference on Logic Programming, MIT Press, 1995.
Cuadrado, J., Pimentel, S., A Truth Maintenance System Based on Stable Models, Proc. 1989 North American Conf. on Logic Programming, pp. 274–290, 1989.
Dix, J. and Müller, M., Implementing Semantics of Disjunctive Logic Program s Using Fringes and Abstract Properties, Proceedings of LPNMR'93, MIT Press, Lisbon, Portugal, July, 1993, pp. 43–59.
Fernández, J.A., and Minker, J., Semantics of Disjunctive Deductive Databases, Proc. 4th Intl. Conference on Database Theory (ICDT-92), pp. 21–50, Berlin, October, 1992.
Fuentes, L.O., Applying Uncertainty Formalisms to Well-Defined Problems, manuscript, 1991.
Gelfond, M., Lifschitz, V., Classical Negation in Logic Programs and Disjunctive Databases, New Generation Computing, 9:365–385, 1991.
Inoue, K, Koshimura, M., Hasegawa, R., Embedding Negation as Failure into a Model Generation Theorem Prover, Proc. of CADE'92, June 1992, pp. 400–415.
Leone, N., Rullo, P., Safe Computation of the Well-Founded Semantics of DATA-LOG Queries, Information Systems, Vol. 17, N. 1, Pergamon Press, Gennaio 1992, pp. 17–31.
Leone, N., Rullo, P., Scarcello, F., Declarative and Fixpoint Characterizations of Disjunctive Stable Models, Proc. of ILPS'95, Portland, Oregon, December 4–7, 1995, pp. 399–413.
Leone, N., Rullo, P., Scarcello, F., Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics and Computation, Technical Report TR 96-14 ISI-CNR, 1996.
Minker, J., On Indefinite Data Bases and the Closed World Assumption, Proceedings of the 6th Conference on Automated Deduction (CADE-82), pp. 292–308, 1982.
Przymusinski, T. C., On the Declarative Semantics of Stratified Deductive Databases and Logic Programs, in Found. of deductive databases and logic programming, Morgan Kaufman, 1987, pp. 193–216
Przymusinska, H., Przymusinski, T. C., Weakly Perfect Model Semantics for Logic Programs, Proc. Fifth Int. Conf. and Symp. on Logic Programming, 1988.
Przymusinski, T., Stable Semantics for Disjunctive Programs, New Gen. Comp., 9:401–424, 1991.
Ross, K.A., Modular Stratification and Magic Sets for Datalog Programs with Negation, Proc. ACM Symposium on Principles of Database Systems 1990., 1990.
Ruiz, C., Minker, J., Computing Stable and Partial Stable Models of Extended Disjunctive Logic Programs, in Nonmonotonic Extensions of Logic Programming, LNCS, Springer, pp.205–229, 1995.
Saccá, D., Zaniolo, C., Stable Models and Nondeterminism in Logic Programs with Negation, Proc. ACM PODS, 1990.
Seipel, D., Minker, J., Ruiz., C., Model Generation and State Generation for Disjunctive Logic Programs, Tech. Rep. CS-TR-3546 UMIACS-TR-95-99, Dept. of Computer Science and Institute for Advanced Computer Studies, University of Maryland, U.S.A., 1995.
Stuber, J., Computing Stable Models by Program Transformation, Proc. ICLP'94, pp. 58–73.
Subrahmanian, V.S., Nau, D., Vago, C., WFS + Branch and Bound=Stable Models, IEEE Transactions on Knowledge and Data Engineering, 1995.
Van Gelder, A., Ross, K. A., Schlipf, J. S., The Well-Founded Semantics for General Logic Programs, Journal of ACM, 38(3):620–650, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Leone, N., Rullo, P., Scarcello, F. (1996). On the computation of disjunctive stable models. In: Wagner, R.R., Thoma, H. (eds) Database and Expert Systems Applications. DEXA 1996. Lecture Notes in Computer Science, vol 1134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034719
Download citation
DOI: https://doi.org/10.1007/BFb0034719
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61656-6
Online ISBN: 978-3-540-70651-9
eBook Packages: Springer Book Archive