Default logic: Orderings and extensions

  • Mike Hopkins
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)


An ordering on default rules is defined that formalises intuitive relationships between rules. Unlike Etherington's [Eth88] orderings on literals which were only used to guarantee the existence of a computable extension, ours are defined proof-theoretically and used as an integral part of an algorithm that efficiently calculates all extensions for several useful sub-classes of default logic. The algorithm represents a significant reduction in complexity over other existing methods, especially for large multi-domain examples where indepeneant partial extensions can be calculated for different groups of unrelated rules which can be combined to produce complete extensions. Also, by changing the definition of the orderings without altering the underlying algorithm, extensions can be calculated for variants of default logic that have been proposed since Reiter's original paper.


Network Theory Rule Application Extension Calculation Default Rule Default Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Bre90]
    G. Brewka. Cumulative default logic: In defense of nonmonotonic inference rules (draft). GMD, Postfach 1240, D5205 Sankt Augustin 1, Fed. Rep. of Germany, 1990.Google Scholar
  2. [Eth88]
    D. W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.Google Scholar
  3. [Fro86]
    C. Froidevaux. Taxonomic default theories. In ECAI, pages 123–129, 1986.Google Scholar
  4. [Hop90]
    M. S. Hopkins. The Implementation of a Plausible Inference System. PhD thesis, Queen Mary and Westfield, University of London, 1990.Google Scholar
  5. [JK90]
    U. Junker and K. Konolige. Computing the extensions of autoepistemic and default logics with a tms. In AAAI-90, pages 278–283, 1990.Google Scholar
  6. [KS89]
    H. A. Kautz and B. Selman. Hard problems for simple default logics. In Proc. 1st Int. Conf. on Principle of Knowledge Representation and Reasoning, pages 189–197, Toronto, 1989.Google Scholar
  7. [Lev91]
    F. Levy. Computing extensions of default theories. In European Conference on Symbolic and Quantitative Approaches to Uncertainty, pages 219–226, Marseille, 1991. Springer-Verlag. Lecture Notes in Computer Science 548.Google Scholar
  8. [Luk88]
    W. Lukaszewicz. Considerations on default logic — an alternative approach. Computational Intelligence, 4:1–16, 1988.Google Scholar
  9. [Poo88]
    D. Poole. A logical framework for default reasoning. Artificial Intelligence, 36:27–47, 1988.Google Scholar
  10. [Rei80]
    R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Mike Hopkins
    • 1
  1. 1.Department of Computer Science, Queen Mary and Westfield CollegeUniversity of LondonUK

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