Diversity of Extensions in Abstract Argumentation

TL;DR

This paper introduces a quantitative measure of diversity among extensions in abstract argumentation frameworks, analyzing its complexity and providing a prototype for computation.

Contribution

It defines a new notion of diversity based on symmetric difference, classifies its computational complexity, and offers a prototype implementation.

Findings

Diversity captures how much extensions differ in argumentation frameworks.

Complexity classification for deciding k-diverse extensions is provided.

A prototype tool for computing diversity levels is outlined and evaluated.

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.