# Gentzen-style characterizations of Negation as Failure

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## Abstract

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.

## Keywords

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## Preview

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© Springer-Verlag Berlin Heidelberg 1993