Complexity in finitary argumentation (extended version)

TL;DR

This paper explores the computational complexity of infinite but finitary argumentation frameworks, revealing that certain semantics become significantly more tractable under finitary constraints, balancing expressiveness and computational feasibility.

Contribution

It provides a detailed complexity analysis of finitary infinite AFs, highlighting a key combinatorial property that reduces complexity for admissibility-based semantics.

Findings

Finitary constraints do not always reduce complexity in infinite AFs.

A combinatorial property significantly decreases complexity for admissibility semantics.

Finitary infinite AFs offer a practical balance between expressiveness and computational tractability.

Abstract

Abstract argumentation frameworks (AFs) provide a formal setting to analyze many forms of reasoning with conflicting information. While the expressiveness of general infinite AFs make them a tempting tool for modeling many kinds of reasoning scenarios, the computational intractability of solving infinite AFs limit their use, even in many theoretical applications. We investigate the complexity of computational problems related to infinite but finitary argumentations frameworks, that is, infinite AFs where each argument is attacked by only finitely many others. Our results reveal a surprising scenario. On one hand, we see that the assumption of being finitary does not automatically guarantee a drop in complexity. However, for the admissibility-based semantics, we find a remarkable combinatorial constraint which entails a dramatic decrease in complexity. We conclude that for many forms of reasoning, the finitary infinite AFs provide a natural setting for reasoning which balances well the competing goals of being expressive enough to be applied to many reasoning settings while being computationally tractable enough for the analysis within the framework to be useful.