Classical methods in nonmonotonic reasoning

  • Yannis Dimopoulos
Communications Logic for Artificial Intelligence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 869)


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.


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  1. 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. 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. 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. 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. 5.
    Chin-Liang Chang and Richard Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, 1973.Google Scholar
  6. 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. 7.
    Y. Dimopoulos. Classical methods in nonmonotonic reasoning. Technical Report MPI-I-94-229, Max-Planck-Insitut für Informatik, 1994. forthcoming.Google Scholar
  8. 8.
    Y. Dimopoulos and V. Magirou. A graph-theoretic approach to default logic. To appear in Information and Computation, 1994.Google Scholar
  9. 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. 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. 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. 12.
    R. Reiter. A logic for default reasoning. AI Journal, 13:81–132, 1980.Google Scholar
  13. 13.
    H. Zhang. Sato: A decision procedure for propositional logic. Association of Automated Reasoning Newsletters, 22, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Yannis Dimopoulos
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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