Classical methods in nonmonotonic reasoning
In this paper we present and compare some classical problem solving methods for computing the stable models of a general propositional logic program. In particular linear programming, propositional satisfiability, constraint satisfaction, and graph algorithms are considered. Central to our approach is the representation of a logic program by means of a graph.
Unable to display preview. Download preview PDF.
- 1.C. Bell, A. Nerode, R. Ng, and V. S. Subrahmanian. Implementing deductive databases by linear programming. In ACM, Principles of Database Systems, 1992.Google Scholar
- 2.C. Bell, A. Nerode, R. Ng, and V. S. Subrahmanian. Implementing stable semantics by linear programming. In Proc. of International Workshop on Logic Programming and Nonmonotonic Reasoning, 1993.Google Scholar
- 3.R. Ben-Eliyahu and R. Dechter. Default logic, propositional logic and constraints. In Proc. of AAAI-91, pages 379–385, 1991.Google Scholar
- 4.R. Ben-Eliyahu and R. Dechter. Propositional semantics for disjunctive logic programs. Technical Report 92-66, University of California, Irvine, 1992.Google Scholar
- 5.Chin-Liang Chang and Richard Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, 1973.Google Scholar
- 6.K. L. Clark. Negation as failure. In Gallaire and Minker, editors, Logic and databases, pages 293–322. Plenum Press, New York, 1978.Google Scholar
- 7.Y. Dimopoulos. Classical methods in nonmonotonic reasoning. Technical Report MPI-I-94-229, Max-Planck-Insitut für Informatik, 1994. forthcoming.Google Scholar
- 8.Y. Dimopoulos and V. Magirou. A graph-theoretic approach to default logic. To appear in Information and Computation, 1994.Google Scholar
- 9.Y. Dimopoulos, V. Magirou, and C. Papadimitriou. On kernels, defaults and even graphs. Technical Report MPI-I-93-226, Max-Planck-Institut für Informatik, 1993.Google Scholar
- 10.M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proc. Fifth International Conference and Symposium on Logic Programming, pages 1070–1080, Cambridge, Mass., 1988. MIT Press.Google Scholar
- 11.C. Papadimitriou and M. Yannakakis. Tie-breaking semantics and structural totality. In Proceedings Eleventh Symposium on Principles of Database Systems, pages 16–22, 1992.Google Scholar
- 12.R. Reiter. A logic for default reasoning. AI Journal, 13:81–132, 1980.Google Scholar
- 13.H. Zhang. Sato: A decision procedure for propositional logic. Association of Automated Reasoning Newsletters, 22, 1993.Google Scholar