A modal semantics for the negation as failure and the closed world assumption rules

  • Philippe Balbiani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)


In this paper we show how to syntactically represent the relation of cause and effect between a predicate name and the bodies of the clauses which define this predicate in a logic program. In so doing, we prove that we can logically express many properties about SLD-trees, especially the absence or the presence of an empty leaf and/or an infinite branch. This relation of cause and effect is linked to the execution of the program. Thus it is a temporal relation. Modal logics have shown in the past their ability to deal with temporal concepts and temporal properties of sequential or parallel programs. Consequently we naturally define in modal logic a completion formula of logic programs. This formula is a modal version of Clark's formula. It gives soundness and completeness results of two nononotonic inference rules : the negation as failure and the closed world assumption.


logic programming with negation declarative semantics modal logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Philippe Balbiani
    • 1
  1. 1.Institute de Recherche en Informatique de ToulouseUniversité Paul SabatierToulouse Cedex

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