Advertisement

Revision of non-monotonic theories

Some postulates and an application to logic programming
  • Cees Witteveen
  • Wiebe van der Hoek
  • Hans de Nivelle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 838)

Abstract

We present some revision systems for non-monotonic theories and we concentrate on the revision of logic programs whenever they are classically consistent, but do not have an acceptable (non-monotonic) model. The revision method we propose is to expand an original theory (program) in order to obtain an acceptable model.

We distinguish between weak revision, conservative revision and strong revision systems. These systems differ to the extent the revision affects the set of classical models of the original theory.

We then show that there exist weak, conservative and strong expansion systems for normal logic programs using the stable model semantics.

In particular, we present a strong expansion method which makes it possible to construct for an arbitrary (incoherent) normal logic program P a -classically- equivalent expanded program P′ such that P′ always has a stable model.

Keywords

Revision Non-monotonic Reasoning Logic Programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Alchourrón, P. Gärdenfors and D. Makinson, On the Logic of Theory Change: Partial Meet Contraction and Revision Functions, Journal of Symbolic Logic, 50, 510–530, 1985Google Scholar
  2. 2.
    P. Gärdenfors, Knowledge in Flux, MIT Press, Cambridge, MA, 1988Google Scholar
  3. 3.
    M. Gelfond and V. Lifschitz, The Stable Model Semantics for Logic Programming. In: Fifth International Conference Symposium on Logic Programming, pp. 1070–1080, 1988.Google Scholar
  4. 4.
    L. Giordano and A. Martelli, Generalized Stable Models, Truth Maintenance and Conflict Resolution, in: D. Warren and P. Szeredi (eds) Proceedings of the 7th International Conference on Logic Programming, pp. 427–441, 1990.Google Scholar
  5. 5.
    K. Inoue, Hypothetical Reasoning in Logic Programs, Journal of Logic Programming, 18, 3, 191–227, 1994Google Scholar
  6. 6.
    J. W. Lloyd, Foundations of Logic Programming, Springer Verlag, Heidelberg, 1987.Google Scholar
  7. 7.
    W. Marek, V.S. Subrahmanian, The relationship between stable, supported, default and auto-epistemic semantics for general logic programs, Theoretical Computer Science 103 (1992) 365–386.Google Scholar
  8. 8.
    V. W. Marek and M. Truszczyński, Nonmonotonic Logic, Springer Verlag, Heidelberg, 1993.Google Scholar
  9. 9.
    L. M. Pereira, J. J. Alferes and J. N. Aparicio, Contradiction Removal within well-founded semantics. In: A. Nerode, W. Marek and V. S. Subrahmanian, (eds.), First International Workshop on Logic Programming and Non-monotonic Reasoning, MIT Press, 1991.Google Scholar
  10. 10.
    L. M. Pereira, J. J. Alferes and J. N. Aparicio, The Extended Stable Models of Contradiction Removal Semantics. In: P. Barahona, L.M. Pereira and A. Porto, (eds.), Proceedings-EPIA 91, Springer Verlag, Heidelberg, 1991.Google Scholar
  11. 11.
    H. Rott, Modellings for Belief Change: Base Contraction, Multiple Contraction, and Epistemic Entrenchment, in: D. Pearce and G. Wagner, Logics in AI, Springer Verlag Berlin, 1992.Google Scholar
  12. 12.
    C. Witteveen and G. Brewka, Skeptical Reason Maintenance and Belief Revision, Artificial Intelligence, 61 (1993) 1–36.Google Scholar
  13. 13.
    C. Witteveen and W. van der Hoek, Belief Revision by Expansion, in: M. Clarke et al. (eds), Symbolic and Quantitative Approaches to Reasoning and Uncertainty, LNCS 747, Springer, Heidelberg, 1993, pp. 380–388.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Cees Witteveen
    • 1
  • Wiebe van der Hoek
    • 2
  • Hans de Nivelle
    • 1
  1. 1.Dept of Mathematics and Computer ScienceDelft University of TechnologyAJ DelftThe Netherlands
  2. 2.Dept of Computer ScienceUtrecht UniversityUtrechtThe Netherlands

Personalised recommendations