Rejection in Abstract Argumentation: Harder Than Acceptance?
This work addresses a theoretical gap in argumentation frameworks for AI and logic, but it appears incremental as it extends existing frameworks with rejection conditions.
The paper tackles the problem of modeling argument rejection in abstract argumentation by introducing rejection conditions (RCs) and associating arguments with logic programs, resulting in high expressiveness that leads to problems in higher levels of the polynomial hierarchy.
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.