Gentzen-style characterizations of Negation as Failure

  • Jan A. Plaza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 737)


We investigate Negation as Failure as incorporated in (nondeterministic) SLDNF-resolution and in (deterministic) PROLOG's resolution. We formulate three Gentzen-style systems which characterize prepositional SLDNF-resolution and propositional PROLOG's resolution in a sound and complete way (without assuming stratification or any other restrictions on programs.) Our analysis employs certain three-valued logics.

The results of this paper can be of interest for rule-based expert systems which represent knowledge in propositional logic, and for other AI-systems which use Negation as Failure for non-monotonic reasoning.


negation as failure SLDNF-resolution PROLOG logic programming Gentzen systems soundness and completeness many-valued logics nonmonotonic reasoning rule-based expert systems knowledge representation in logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jan A. Plaza
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of MiamiCoral GablesUSA

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