General Epistemic Abstract Argumentation Framework: Semantics and Complexity

Epistemic Abstract Argumentation Framework (EAAF) extends Dung's framework (AAF)-a central formalism in AI for modeling disputes among agents-by allowing the representation of epistemic knowledge. In particular, EAAF augments AAF with weak and strong epistemic attacks whose intuitive meaning is that an argument a defeats an argument b by means of a weak (resp. strong) epistemic attack if a is true in every (resp. at least one) extension. So far, the semantics of EAAF has been defined only for a restricted class of frameworks, namely acyclic EAAF, where epistemic attacks do not occur in any cycle. In this paper, we provide an intuitive semantics for (general) EAAF that naturally extends that for AAF as well as that for acyclic EAAF. After providing some fundamental properties and giving an algorithm that enables the computation of EAAF semantics, by relying on state-of-the-art AAF-solvers, we investigate the complexity of canonical argumentation problems.