Comparative Expressivity for Structured Argumentation Frameworks with Uncertain Rules and Premises

TL;DR

This paper investigates the expressivity of structured argumentation frameworks with uncertain rules and premises, comparing them to abstract models to understand their capabilities and limitations in representing uncertainty.

Contribution

It introduces a formal notion of expressivity for structured and abstract argumentation models and provides comparative results, advancing the theoretical understanding of uncertain argumentation.

Findings

Structured models can express more nuanced uncertainty than abstract models.

Certain formal frameworks are shown to have equivalent expressivity levels.

Results include both positive and negative comparisons of expressivity.

Abstract

Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following a recent trend in the literature, we tackle the open question of studying plausible instantiations of these abstract models. To do so, we ground the uncertainty of arguments in their components, structured within rules and premises. Our main technical contributions are: i) the introduction of a notion of expressivity that can handle abstract and structured formalisms, and ii) the presentation of both negative and positive expressivity results, comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results affect incomplete abstract argumentation frameworks, and their extension with dependencies, on the abstract side, and ASPIC+, on the structured side.