Graph Based Answer Set Programming Solver Systems

TL;DR

This paper introduces a novel dependency graph-based method for answer set programming that enables explicit goal conjunction representation and causal justification, improving interpretability and uniformity in answer set computation.

Contribution

It proposes a new dependency graph approach that explicitly models conjunctions and causal relationships, addressing limitations of previous graph-based methods in ASP.

Findings

The graph representation allows for explicit goal conjunction modeling.

Causal relationships enable easier justification of literals.

Two approaches (bottom-up and top-down) are explored for answer set computation.

Abstract

Answer set programming (ASP) is a popular nonmonotonic-logic based paradigm for knowledge representation and solving combinatorial problems. Computing the answer set of an ASP program is NP-hard in general, and researchers have been investing significant effort to speed it up. The majority of current ASP solvers employ SAT solver-like technology to find these answer sets. As a result, justification for why a literal is in the answer set is hard to produce. There are dependency graph based approaches to find answer sets, but due to the representational limitations of dependency graphs, such approaches are limited. This paper proposes a novel dependency graph-based approach for finding answer sets in which conjunction of goals is explicitly represented as a node which allows arbitrary answer set programs to be uniformly represented. Our representation preserves causal relationships allowing for justification for each literal in the answer set to be elegantly found. In this paper, we explore two different approaches based on the graph representation: bottom-up and top-down. The bottom-up approach finds models by assigning truth values along with the topological order, while the top-down approach generates models starting from the constraints.