On Strong and Weak Admissibility in Non-Flat Assumption-Based Argumentation

In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playground since they concisely capture the relations between assumptions and are expressive enough to represent general non-flat ABA frameworks, as recently shown. While weak admissibility has been recently investigated for a restricted fragment of ABA in which assumptions cannot be derived (flat ABA), strong admissibility has not been investigated for ABA so far. We introduce strong admissibility for ABA and investigate desirable properties. We furthermore extend the recent investigations of weak admissibility in the flat ABA fragment to the non-flat case. We show that the central modularization property is maintained under classical, strong, and weak admissibility. We also show that strong and weakly admissible semantics in non-flat ABA share some of the shortcomings of standard admissible semantics and discuss ways to address these.