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.