Expressivity Results for Structured Argumentation Frameworks with Uncertain Rules and Premises

Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most existing work focuses on abstract models of argumentation under 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 root the uncertainty of arguments in their components in structured models: rules and premises. Our main conceptual contribution is to provide an intuitive notion of comparative expressivity suitable for both abstract and structured formalisms. Roughly, one formalism for arguing with qualitative uncertainty is at least as expressive as another if the former can generate the same set of abstract argumentation frameworks (completions) as the latter. On the technical side, we prove negative and positive results comparing the expressivity of abstract and structured models of argumentation with uncertainty. These results concern incomplete abstract argumentation frameworks and their extension with dependencies on the abstract side, and ASPIC$^+$, assumption-based argumentation (ABA) and deductive argumentation on the structured side.