Tight Logic Programs

TL;DR

This paper explores the concept of tightness in logic programs, extending Fages' theorem to nested expressions and programs with transitive closure, enhancing understanding of stable models and program completion.

Contribution

It generalizes the notion of tightness and Fages' theorem to more complex logic programs with nested expressions and transitive closure.

Findings

Extended the definition of tightness to nested expressions

Generalized Fages' theorem to new classes of programs

Analyzed tight logic programs with transitive closure

Abstract

This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain syntactic condition, which is now called ``tightness,'' then its stable models can be characterized as the models of its completion. We extend the definition of tightness and Fages' theorem to programs with nested expressions in the bodies of rules, and study tight logic programs containing the definition of the transitive closure of a predicate.