Admissibility in the Abstract Dialectical Framework

The aim of this paper is to study the concept of admissibility in abstract dialectical frameworks ADFs. While admissibility is well-understood in Dung-style frameworks, a generalization to ADFs is not trivial. Indeed, the original proposal turned out to behave unintuitively at certain instances. A recent approach circumvented this problem by using a three-valued concept. In this paper, we propose a novel two-valued approach which more directly follows the original understanding of admissibility. We compare the two approaches and show that they behave differently on certain ADFs. Our results imply that for generalizations of Dung-style frameworks, establishing a precise correspondence between two-valued i.e. extension-based and three-value i.e. labeling-based characterizations of argumentation semantics is not easy and requires further investigations.