Diversity of Extensions in Abstract Argumentation

2026-05-13

AI Summary

This work addresses the lack of effective measures for quantifying the degree of difference among extensions—i.e., sets of accepted arguments—in abstract argumentation. It formally introduces the notion of extension diversity, proposing a quantitative metric based on the symmetric difference between sets, and systematically investigates three fundamental problems: the existence of k-diverse extensions, the coverage of a given argument across diverse extensions, and the computation of the maximum achievable diversity level. Through a comprehensive computational complexity analysis, the study fully classifies these problems and develops prototype algorithms to compute diversity measures. Empirical evaluation demonstrates both the effectiveness and tractability of the proposed approach, offering new insights into the intrinsic extent of disagreement within argumentation frameworks.

Abstract

Argumentation is an important topic of AI for modelling and reasoning about arguments. In abstract argumentation, we consider directed graphs, so-called argumentation frameworks (AF), that express conflicts between arguments. The semantics is defined by the notion of extensions, which are sets of arguments that satisfy particular relationship conditions in the AF. Usually, standard reasoning in argumentation do not reveal how far apart extensions are. We introduce a quantitative notion of diversity of extensions based on the symmetric difference and provide a systematic complexity classification. Intuitively, diversity captures whether extensions of a framework (accepted viewpoints) differ only marginally or represent fundamentally incompatible sets of arguments. We study whether an AF admits k-diverse extensions, admits k-diverse extensions covering specific arguments, and to compute the largest k for which an AF admits k-diverse extensions. We outline a prototype and provide an evaluation for computing diversity levels.

Problem

• abstract argumentation
• extensions
• diversity
• symmetric difference
• argumentation frameworks

Innovation

• diversity of extensions
• abstract argumentation
• symmetric difference
• computational complexity
• argumentation frameworks