Weak extensions for default theories

Extended abstract
  • F. Lévy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)


We propose a notion of weak extension of a default theory, motivated by a kind of paraconsistent view of default reasoning, and which coincides with Reiter's extensions when they exist. When the default theory is inconsistent, in the sense that it has no extension, we determine defaults which are not involved in the inconsistency, preserving the possibility to draw some default conclusions. Moreover, any finite default theory has weak extensions, though the question remains open for infinite default theories. Weak extensions correspond to some consistent labelings of the defaults, according to a notion of consistency close to the standard one in the TMS, so computing weak extensions may adapt standard methods of the TMS. We also compare weak extensions to propositions based on a maximal consistent set of defaults, and show that maximal consistency generate far more extensions. Finally, we briefly sketch how our results can be extended to Autoepistemic Logic and to Logic Programming.


Logic Program Default Theory Default Logic Nonmonotonic Reasoning Default Reasoning 
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. [Bara & Subr 90]
    C. R. Baral and V.S. Subrahmanian: “Stable and Extension Class Theory for Logic Programs and Default Logics” 3d International Workshop on Nonmonotonic Reasoning, South Lake Tahoe, Cal, May and June 1990Google Scholar
  2. [Besnard 83]
    P. Besnard: “Une procédure de décision en logique non monotone” Thesis, 1983 University of Rennes 1Google Scholar
  3. [Brewka 89]
    G. Brewka: “Nonmonotonic Reasoning: From Theoretical Foundation Toward Efficient Computation” PHD Dissertation University of HamburgGoogle Scholar
  4. [Brewka 91]
    G. Brewka: “Cumulative Default Logic: in defense of nonmonotonic inference rules” Artificial Intelligence n∘50 1991 183–205Google Scholar
  5. [Delgr & Jack 91]
    J. P. Delgrande and W. K. Jackson: “Default Logic Revisited” Proceedings KR 91 1991 118–127Google Scholar
  6. [Ether 87]
    D. W. Etherington: “Formalizing Nonmonotonic Reasoning Systems” Artificial Intelligence n∘31 1987Google Scholar
  7. [Froi & Meng 92]
    C. Froidevaux, J. Mengin: “A Framework for Default Logics” LRI Research Report n∘755 University of Paris Sud May 1992Google Scholar
  8. [Goodwin 87]
    J. Goodwin: “A Theory and System for Non Monotonic Reasoning” Linköping studies in science and technology 165, 1987Google Scholar
  9. [Junk & Kono 90]
    U. Junker, K. Konolige “Computing the Extensions of Autoepistemic and Default Logics with a Truth Maintenance System” AAAI 90.Google Scholar
  10. [Luka 85]
    W. Lukaszewicz: “Two Results on Default Logic” Proceedings IJCAI 85 Los Angeles 1985 459–461Google Scholar
  11. [Luka 88]
    W. Lukaszewicz: “Considerations on default logic — an alternative approach”. Computational Intelligence n∘4 1988 1–16Google Scholar
  12. [Moin 92]
    Y. Moinard: “Unifying varous approaches to Default Logic” Proceedings IPMU92 Palma de Mallorca July 1992 61–64Google Scholar
  13. [Moore 85]
    R.C. Moore: “Semantical Considerations on nonmonotonic Logic” Artificial Intelligence n∘25 1985 75–94Google Scholar
  14. [Poole 88]
    D. L. Poole: “A Logical Framework for Default Reasoning” Artificial Intelligence n∘ 36 1988 27–47Google Scholar
  15. [Reiter 80]
    Raymond Reiter: “A Logic for Default Reasoning” Artificial Intelligence n∘ 13 avril 1980 81–132Google Scholar
  16. [Schaub 91]
    T. Schaub: “Assertional Default Theories: a semantical View” Proceedings KR91 496–506Google Scholar
  17. [Schaub 92]
    T. Schaub:”On constrained Default Theories” Proceedings ECAI 92 304–308Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • F. Lévy
    • 1
  1. 1.LIPN CNRS-URA 1507University of ParisVilletaneuseFrance

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