Capturing Non-flat Assumption-based Argumentation with Bipolar SETAFs

While the flat fragment of assumption-based argumentation (ABA) is widely studied in the literature, the general, non-flat case has mostly been neglected so far. Until recently, there was no possible way to instantiate non-flat ABA in terms of an abstract argumentation framework. While this gap has been closed for complete-based ABA semantics, capturing admissible-based semantics cannot yet be achieved by looking at the relation between the instantiated arguments only; it requires augmenting arguments with their premises, hence being a semi-abstract instantiaiton. In this paper, we provide a compact and fully abstract instantiation by making use of both collective attack and support relations. Then, inspired by fundamental properties of abstract formalisms, we identify flaws of native ABA semantics in the non-flat case and provide refinements thereof, utilizing our novel instatiation.