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.
| Comments: | Technical Report to the paper accepted at IJCAI 2026 |
| Subjects: | Artificial Intelligence (cs.AI); Computational Complexity (cs.CC) |
| Cite as: | arXiv:2605.13332 [cs.AI] |
| (or arXiv:2605.13332v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2605.13332 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yasir Mahmood [view email]
[v1]
Wed, 13 May 2026 10:51:41 UTC (542 KB)