Abstract
In this paper we present and compare some classical problem-solving methods for computing the stable models of logic programs with negation. Using a graph theoretic representation of logic programs and their stable models, we discuss and compare linear programming, propositional satisfiability, constraint satisfaction, and graph methods.
Similar content being viewed by others
References
Brass, S. and Dix, J.: A general approach to bottom-up computation of disjunctive semantics, in J. Dix, L. Pereira, and T. Przymusinski (eds), Nonmonotonic Extensions of Logic Programming, LNAI 927, Springer, Berlin, 1995, pp. 127–155.
Ben-Eliyahu, R. and Dechter, R.: Default logic, propositional logic and constraints, in Proc. of AAAI-91, 1991, pp. 379–385.
Ben-Eliyahu, R. and Dechter, R.: Propositional semantics for default logic, in Fourth International Workshop on Nonmonotonic Reasoning, Plymouth, VT, 1992, pp. 13–27.
Ben-Eliyahu, R. and Dechter, R.: Propositional Semantics for Disjunctive Logic Programs, Technical Report 92-66, University of California, Irvine, 1992.
Bell, C., Nerode, A., Ng, R., and Subrahmanian, V. S.: Implementing deductive databases by linear programming, in ACM, Principles of Database Systems, 1992.
Bell, C., Nerode, A., Ng, R., and Subrahmanian, V.S.: Implementing stable semantics by linear programming, in Proc. of International Workshop on Logic Programming and Nonmonotonic Reasoning, 1993.
Chang, Chin-Liang and Lee, Richard: Symbolic Logic and Mechanical Theorem Proving, Academic Press, 1973.
Clark, K. L.: Negation as failure, in Gallaire and Minker (eds), Logic and Databases, Plenum Press, New York, 1978, pp. 293–322.
Cholewinski, P., Marek, V., Mikitiuk, A. and Truszczynski, M.: Experimenting with nonmonotonic reasoning, in Proc. ICLP'95, 1995.
Constantini, S.: Contributions to the stable model semantics of logic programs with negation, in A. Nerode (ed.), Proc. of the Second Intern. Workshop on Logic Programming and Nonmonotonic Reasoning, MIT Press, 1993.
Chen, W. and Warren, D. S.: Computation of Stable Models and Its Integration with Logical Query Processing, Technical Report, Department of Computer Science, SUNY at Stony Brook, 1993.
Dimopoulos, Y. and Magirou, V.: A graph theoretic approach to default logic, Information and Computation 112(2) (1994), 239–256.
Dimopoulos, Y., Magirou, V., and Papadimitriou, C. H.: On kernels, defaults and even graphs, Annals of Mathematics and Artificial Intelligence, 1995, to appear.
Dimopoulos, Y. and Torres, A.: Graph-theoretic structures in logic programs and default theories, Theoretical Computer Science, 1996, to appear.
Gelfond, M. and Lifschitz, V.: The stable model semantics for logic programming, in Proc. Fifth International Conference and Symposium on Logic Programming, Cambridge, MA, MIT Press, 1988, pp. 1070–1080.
Gelfond, M. and Lifschitz, V.: Classical negation in logic programs and disjunctive databases, New Generation Computing 9 (1991), 365–387.
Johnson, D., Papadimitriou, C. H., and Yannakakis, M.: On generating all maximal independent sets, Information Processing Letters 27(3) (1988), 119–123.
Kunen, K.: Signed data dependencies in logic program, Journal of Logic Programming 7 (1989), 231–145.
Marek, A. and Truszczynski, M.: Autoepistemic logic, Journal of the ACM 38(3) (1991), 588–619.
Papadimitriou, C. and Yannakakis, M.: Tie-breaking semantics and structural totality, in Proceedings Eleventh Symposium on Principles of Database Systems, 1992, pp. 16–22.
Reiter, R.: A logic for default reasoning, AI Journal 13 (1980), 81–132.
Sato, T.: Completed logic programs and their consistency, Journal of Logic Programming 9 (1990), 33–44.
Subrahmanian, V. S., Nau, D., and Vago, C.: WFS + branch and bound = stable models, IEEE Transactions on Knowledge and Data Engineering 7 (1995), 362–377.
Saccà, D. and Zaniolo, C.: Stable models and non-determinism in logic programs with negation, in Proceedings Ninth Symposium on Principles of Database Systems, 1990, pp. 205–217.
Zhang, H.: Sato: A decision procedure for propositional logic, Association of Automated Reasoning Newsletter 22 (1993).
Zhang, H.: SAtisfiability Testing Optimized (SATO), version 2.0. Available by ftp from herky.cs.uiowa.edu: public/sato, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dimopoulos, Y. On computing logic programs. J Autom Reasoning 17, 259–289 (1996). https://doi.org/10.1007/BF00283131
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00283131