Structure-Aware Encodings of Argumentation Properties for Clique-width
🤖 AI Summary
This paper addresses the high computational complexity of reasoning tasks in abstract argumentation frameworks (directed graphs). We propose a structural encoding method based on clique-width—a graph parameter capturing structural sparsity. For the first time, we design (Q)SAT encodings that preserve clique-width linearity: decision problems for major semantics—including stable, preferred, and grounded—are translated into structure-aware logical formulas whose size grows linearly with clique-width. Leveraging clique-width decompositions, structure-preserving reductions, and tight complexity analysis, we establish theoretical lower bounds on encoding overhead, proving asymptotic optimality under reasonable assumptions. Experimental evaluation demonstrates significant speedups, particularly on dense graphs, where traditional approaches falter. Our work thus provides both a novel theoretical foundation and a practical toolset for structurally informed argumentation solving.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Explores compact SAT encodings for argumentation problems using clique-width
Develops structure-aware reductions preserving clique-width for computational reasoning
Investigates encoding limitations for argumentation semantics including counting problems
Innovation
Methods, ideas, or system contributions that make the work stand out.
DDG reductions linearly preserve clique-width
Novel argumentation to (Q)SAT encodings
Directed decomposition-guided structural encodings
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