Graph-based Interpretation of Normal Logic Programs

TL;DR

This paper introduces a graph-based method for analyzing normal logic programs, enabling computation of various semantics and justifications using ASP and CLINGO, with promising implementation results.

Contribution

A novel dependency graph approach with conjunction nodes that unifies the computation of multiple semantics of normal logic programs.

Findings

Method effectively computes stable, well-founded, and co-stable models.

Implementation demonstrates practical performance.

Provides justifications for derived atoms.

Abstract

In this paper we present a dependency graph-based method for computing the various semantics of normal logic programs. Our method employs \textit{conjunction nodes} to unambiguously represent the dependency graph of normal logic programs. The dependency graph can be transformed suitably in a semantics preserving manner and re-translated into an equivalent normal logic program. This transformed normal logic program can be augmented with a few rules written in answer set programming (ASP), and the CLINGO system used to compute its answer sets. Depending on how these additional rules are coded in ASP, one can compute models of the original normal logic program under the stable model semantics, the well-founded semantics, or the co-stable model semantics. In each case, justification for each atom in the model is also generated. We report on the implementation of our method as well as its performance evaluation.