On the realisability of weak argumentation semantics

Abstract We analyse representatives of the class of non-admissible semantics, particularly the undisputed, strongly undisputed, weakly admissible and weakly preferred semantics, in terms of realisability and their signatures. More specifically, we determine properties of the extension sets they produce, as well as structural features of frameworks that realize extension sets under these semantics. We describe two classes of extension sets for which we show that they are not realisable under undisputed semantics. We also identify approaches that have proven to be useful in the construction of frameworks that aim to realize given extension sets under classical semantics and transfer them to the non-admissible case. While a full characterisation of the signatures of the non-admissible semantics remains elusive, we provide plausible upper bounds and discuss the challenges in establishing concrete lower bounds.