Structure-Aware Encodings of Argumentation Properties for Clique-width

TL;DR

This paper explores how to encode argumentation problems into (Q)SAT efficiently by leveraging the graph parameter clique-width, introducing reductions that preserve this property and analyzing their computational implications.

Contribution

It introduces novel clique-width-preserving reductions from argumentation problems to (Q)SAT, advancing understanding of encoding capabilities for dense graphs.

Findings

Reductions linearly preserve clique-width.

Established new results for all argumentation semantics.

Overhead of reductions cannot be significantly improved.

Abstract

Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small treewidth. Since these solvers are widely applied, research interests in compact encodings into (Q)SAT for solving and to understand encoding limitations. Even more general is the graph parameter clique-width, which unlike treewidth can be small for dense graphs. Although algorithms are available for clique-width, little is known about encodings. We initiate the quest to understand encoding capabilities with clique-width by considering abstract argumentation, which is a robust framework for reasoning with conflicting arguments. It is based on directed graphs and asks for computationally challenging properties, making it a natural candidate to study computational properties. We design novel reductions from argumentation problems to (Q)SAT. Our reductions linearly preserve the clique-width, resulting in directed decomposition-guided (DDG) reductions. We establish novel results for all argumentation semantics, including counting. Notably, the overhead caused by our DDG reductions cannot be significantly improved under reasonable assumptions.