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.

翻译：论辩是人工智能中用于建模和推理论证的重要课题。在抽象论辩中，我们考虑有向图，即所谓的论辩框架，用于表达论证之间的冲突。语义通过扩展的概念定义，扩展是论辩框架中满足特定关系条件的论证集合。通常，论辩中的标准推理无法揭示扩展之间的距离差异。本文基于对称差引入了扩展多样性的量化概念，并提供了系统性的复杂度分类。直观上，多样性捕捉的是框架的扩展（可接受观点）之间仅存在微小差异，还是代表根本不相容的论证集合。我们研究论辩框架是否承认k-多样性扩展、是否承认覆盖特定论证的k-多样性扩展，以及如何计算使论辩框架承认k-多样性扩展的最大k值。我们概述了一个原型系统，并对多样性水平的计算进行了评估。