Positive Dependency Graphs Revisited

TL;DR

This paper revisits the concept of positive dependency graphs in answer set programming, proposing a modification that strengthens existing theoretical results in the field.

Contribution

It introduces a modified positive dependency graph concept that enhances the theoretical framework of stable models in logic programming.

Findings

Strengthened results in stable model theory

New understanding of positive dependency graphs

Potential improvements in logic programming analysis

Abstract

Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results. Under consideration in Theory and Practice of Logic Programming (TPLP).