# Diversity of Extensions in Abstract Argumentation

arXiv: https://arxiv.org/abs/2605.13332 · HTML: https://mlsanity.com/paper/2605.13332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 10 of 10)

- [Argumentative XAI: A Survey](https://mlsanity.com/paper/2105.11266/) (2021)
- [Counting Complexity for Reasoning in Abstract Argumentation](https://mlsanity.com/paper/1811.11501/) (2018)
- [Fudge: A light-weight solver for abstract argumentation based on SAT reductions](https://mlsanity.com/paper/2109.03106/) (2021)
- [The pyglaf argumentation reasoner (ICCMA2021)](https://mlsanity.com/paper/2109.03162/) (2021)
- [Facets in Argumentation: A Formal Approach to Argument Significance](https://mlsanity.com/paper/2505.10982/) (2025)
- [Parameterized Complexity of Logic-Based Argumentation in Schaefer's Framework](https://mlsanity.com/paper/2102.11782/) (2021)
- [Computing Repairs Under Functional and Inclusion Dependencies via Argumentation](https://mlsanity.com/paper/2312.01973/) (2023)
- [Combining Voting and Abstract Argumentation to Understand Online Discussions](https://mlsanity.com/paper/2402.05895/) (2024)
- [Dung's Argumentation Framework: Unveiling the Expressive Power with Inconsistent Databases](https://mlsanity.com/paper/2412.11617/) (2024)
- [Structure-Aware Encodings of Argumentation Properties for Clique-width](https://mlsanity.com/paper/2511.10767/) (2025)

## Abstract (arXiv)

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.