Diversity of Extensions in Abstract Argumentation

• URL: http://arxiv.org/abs/2605.13332v1
• Date: Wed, 13 May 2026 10:51:41 GMT
• Title: Diversity of Extensions in Abstract Argumentation
• Abstract summary: We introduce a notion of diversity of extensions based on the symmetric difference and provide a systematic complexity classification.<n>We study whether an argumentation framework (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.
• Score: 19.79760019224408
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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