Graphs and colorings for answer set programming

TL;DR

This paper explores how rule dependency graphs and their colorings can characterize and compute answer sets in logic programming, offering new operational methods and insights into rule interactions.

Contribution

It introduces a novel operational framework using graph colorings and operators to analyze answer sets, connecting graph-theoretical and proof-theoretic approaches.

Findings

Operational characterizations of answer sets via colorings

Identification of strategies used by the noMoRe system

Distinction of operations related to Fitting's operator and well-founded semantics

Abstract

We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fitting's operator as well as to well-founded semantics. (To appear in Theory and Practice of Logic Programming (TPLP))