Stability in Abstract Argumentation

Abstract: The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away from the logical structure of arguments, and we transpose this notion of stability to the context of Dungean argumentation frameworks. In particular, we show how this problem can be translated into reasoning with Argument-Incomplete AFs. Then we provide preliminary complexity results for stability under four prominent semantics, in the case of both credulous and skeptical reasoning. Finally, we illustrate to what extent this notion can be useful with an application to argument-based negotiation.