A query answering algorithm for Lukaszewicz' general open default theory

  • Viorica Ciorba
Default Logics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1126)


In this paper, we present a new query answering algorithm for Lukaszewicz' general open default theory. This algorithm, instead of computing all the extensions of the theory, computes only a set of defaults which proves the query. The advantages of our approach in comparison with other existent methods is that it is oriented by the query, it deals with open defaults and it can be easily adapted both for credulous and skeptical reasoning.

The strong point of our algorithm is that we do not perform the initial step of the instanciation of open defaults. The free variables of open defaults will be instanciated during our algorithm by the unification mechanism.

Firstly, we translate a default logic into a new variant of Poole's formalism. In this translation, we associate to every default of the theory, a default's name which is a simple literal parameterized by the free variables of the default. Thus, the defaults can be easily manipulated. In this context, answering a query requires the computation of a sequence of defaults which proves the formula and satisfies some properties (groundness and regularity). Concerning the provability of the query and the groundness property, we propose a modification of Inoue's production algorithm. Concerning the regularity property, we show how Poole's method can be adapted to check it.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Viorica Ciorba
    • 1
  1. 1.Laboratoire de Recherche en InformatiqueUniversité de Paris SudOrsay CedexFrance

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