Taking into account ?who said what? in abstract argumentation: Complexity results

We propose a new paradigm for reasoning over abstract argumentation frameworks where the "who said what" relation, associating each argument with the set of agents who claimed it, is taken into account, along with possible information on the trustworthiness of the agents. Specifically, we extend the traditional reasoning based on the classical verification and acceptance problems and introduce a reasoning paradigm investigating how the "robustness" of a set of arguments S (in terms of being an extension or not) or of an argument a (in terms of being accepted or not) can change if what has been claimed by some agents is ignored (as if these agents were removed from the dispute modeled by the argumentation framework). In this regard, we address the problems of searching the "minimum extent" of the removal of agents that makes a set S an extension or an argument a accepted. Compared with the case where only the "yes/no" answer of the traditional verification and acceptance problems are available, the knowledge of such a minimum provides the analyst with further insights allowing them to better judge the robustness of S and a. We consider the above minimization problems in two variants, where the agents are associated with a measure of their trustworthiness or not and provide a thorough characterization of their complexities.(c) 2023 Elsevier B.V. All rights reserved.