Realizability of three-valued semantics for abstract dialectical frameworks

摘要

We investigate fundamental properties of three-valued semantics for abstract dialectical frameworks (ADFs). In particular, we deal with realizability, i.e., the question whether there exists an ADF that has a given set of interpretations as its semantics. We provide necessary and sufficient conditions that hold for a set of three-valued interpretations whenever there is an ADF realizing it under admissible, complete, grounded, or preferred semantics. Moreover, we show how to construct such an ADF in case of realizability. Our results lay the ground for studying the expressiveness of ADFs under three-valued semantics. Since ADFs generalize many existing approaches, our results have immediate impact on many argumentation formalisms including abstract argumentation frameworks. As first applications, we study implications of our results on the existence of certain join operators on ADFs. Furthermore, we exploit our (exact) characterizations to obtain realizability results also for a more relaxed setting, where realizing ADFs may contain hidden statements.