Representation theory for default logic

  • V. Wiktor Marek
  • Jan Treur
  • Mirosław Truszczyński


Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, non-normal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories.


Representation Theory Propositional Atom Countable Family Default Theory Default Logic 
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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • V. Wiktor Marek
    • 1
  • Jan Treur
    • 2
  • Mirosław Truszczyński
    • 3
  1. 1.Department of Computer ScienceUniversity of KentuckyLexingtonUSA
  2. 2.Department of Mathematics and Computer Science, Artificial Intelligence Group, De Boelelaan 1081aFree University AmsterdamAmsterdamThe Netherlands
  3. 3.Department of Computer ScienceUniversity of KentuckyLexingtonUSA

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