Dung’s Argumentation Framework (AF) has been extended in several directions. An interesting extension, among others, is the Epistemic AF (EAF) which allows representing the agent’s belief by means of epistemic constraints. In particular, an epistemic constraint is a propositional formula over labeled arguments (e.g. in(a), out(c)) extended with the modal operators K and M that intuitively state that the agent believes that a given formula is certainly or possibly true, respectively. In this paper, focusing on EAF, we investigate the complexity of the possible and necessary variants of three canonical problems in abstract argumentation: verification, existence, and non-empty existence. Moreover, we explore the relationship between EAF and incomplete AF (iAF), an extension of AF where arguments and attacks may be uncertain. Our complexity analysis shows that the verification problem in iAF can be naturally reduced to the verification in EAF, while it turns out that a similar result cannot hold for the necessary (non-empty) existence problem.
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