Rejection in Abstract Argumentation: Harder Than Acceptance?

TL;DR

This paper explores rejection conditions in abstract argumentation frameworks, analyzing their complexity and expressiveness, especially when associated with logic programs and structural parameters like treewidth.

Contribution

It introduces rejection conditions for argument rejection, linking them with logic programming and complexity analysis, expanding the expressiveness of argumentation frameworks.

Findings

Rejection AFs are highly expressive.

Complexity reaches higher levels of the polynomial hierarchy.

Analysis includes structural parameters like treewidth.

Abstract

Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with \emph{acceptance conditions} on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for \emph{rejecting} an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.