Logic programming and autoepistemic logics: New relations and complexity results

  • Marco Schaerf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 728)

Abstract

In recent years, many authors have pointed out the strict correlation between non-Horn logic programs and non-monotonic reasoning. As a result, many studies on the relations between various semantics for negation and non-monotonic logics have appeared in the literature. The analysis of these relations helps understanding the properties of the various systems and allows importing analysis from one formalism into another one. In this paper we show a one-to-one mapping between the positivistic models and moderately-grounded expansions of autoepistemic logic and a one-to-one correspondence between the minimally-supported models and the stable parsimonious expansions. These relations are then used to prove the computational complexity of reasoning with the positivistic and minimally-supported model semantics, as well as new complexity results for restricted subsets of autoepistemic logic.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. R. Apt, H. A. Blair, and A. Walker. Towards a theory of declarative knowledge. In J. Minker, editor, Foundation of Deductive Databases and Logic Programming, pages 89–142. Morgan Kaufmann, 1988.Google Scholar
  2. 2.
    N. Bidoit and C. Froidevaux. General logic databases and programs: default logic semantics and stratification. Information and Computation, 91:15–54, 1991.Google Scholar
  3. 3.
    N. Bidoit and R. Hull. Positivism versus minimalism in deductive databases. In Proceedings of the Fifth Conference on Principle Of Database Systems (PODS-86), pages 123–132, 1986.Google Scholar
  4. 4.
    N. Bidoit and R. Hull. Minimalism, justification and non-monotonicity in deductive databases. Journal of Computer and System Sciences, 38:290–325, 1989.Google Scholar
  5. 5.
    K. L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Data Bases, pages 293–322. Plenum, 1978.Google Scholar
  6. 6.
    T. Eiter and G. Gottlob. Propositional circumscription and extended closed world reasoning are II 2p-complete. Technical Report CD-TR 91/20, Technische Universität Wien, Vienna Austria, Christian Doppler Labor für Expertensysteme, May 1991. To appear in Theoretical Computer Science.Google Scholar
  7. 7.
    T. Eiter and G. Gottlob. Reasoning with parsimonious and moderately grounded expansions. Fundamenta Informaticae, 17(1,2):31–54, 1992.Google Scholar
  8. 8.
    M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proceedings of the Fifth Logic Programming Symposium, pages 1070–1080. MIT Press, 1988.Google Scholar
  9. 9.
    K. Konolige. On the relationship between default and autoepistemic logic. Artificial Intelligence Journal, 35:343–382, 1988.Google Scholar
  10. 10.
    W. Marek and V. S. Subrahmanian. The relationship between logic program, semantics and non-monotonic reasoning. In Proceedings of the Sixth International Conference on Logic Programming (ICLP-89), pages 600–617, 1989.Google Scholar
  11. 11.
    W. Marek and M. Truszczyński. Autoepistemic logic. Journal of the ACM, 38(3):588–619, 1991.Google Scholar
  12. 12.
    W. Marek and M. Truszczyński. Computing intersection of autoepistemic expansions. In Proceedings of the First International Workshop on Logic Programming and Non Monotonic Reasoning, pages 37–50. The MIT press, 1991.Google Scholar
  13. 13.
    R. C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence Journal, 25:75–94, 1985.Google Scholar
  14. 14.
    R. Reiter. A logic for default reasoning. Artificial Intelligence Journal, 13:81–132, 1980.Google Scholar
  15. 15.
    L. J. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3:1–22, 1976.Google Scholar
  16. 16.
    A. van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38:620–650, 1991.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Marco Schaerf
    • 1
    • 2
  1. 1.Istituto di ElettrotecnicaUniversità di CagliariCagliariItalia
  2. 2.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItalia

Personalised recommendations