Weak Admissibility for ABA via Abstract Set-Attacks

Is an argument acceptable if all potential counter-arguments are unacceptable themselves? In standard models of argumentation, the answer to this question is counter-intuitively not necessarily yes. However, based on the notion of weak admissibility, a family of semantics has been established where these unreasonable attacks do not successfully counter otherwise strong arguments. While in the abstract setting weak admissibility is well-understood, a similar issue arises in the context of structured argumentation formalisms like assumption based argumentation (ABA). It is well known that under standard argumentation semantics, ABA frameworks can be reduced to abstract argumentation frameworks (AFs), however, it turns out that in the case of weak admissibility this approach surprisingly fails. We instead propose to utilize a recently published instantiation technique utilizing collective attacks (SETAFs). We first define weak admissibility for SETAFs and study basic properties; afterwards, we push our proposal to the structured setting. We show that via our approach the characteristic properties of weak admissibility carry over to ABA, and thus establish a basis for further studies of these common scenarios also in ABA and related structured argumentation formalisms.