Explaining Non-Acceptability in Abstract Argumentation

Argumentation frameworks (AFs) provide a central approach to perform reasoning in many formalisms within argumentation in Artificial Intelligence (AI). Semantics for AFs specify criteria under which sets of arguments can be deemed acceptable, with the notion of admissibility being at the core of main semantics for AFs. A fundamental reasoning task is to find an admissible set containing a queried argument, called credulous acceptance under admissibility. While such a set explains how to argue in favour of a queried argument, finding an explanation in the negative case, i.e., answering why a queried argument is not credulously accepted under admissibility, is less immediate. In this paper, we approach this problem by considering subframeworks of a given AF as witnesses for non-acceptability. Due to the non-monotonicity of semantics for AFs, this requires that every expansion of the witnessing subframework must preserve non-acceptance of the argument-otherwise the subframework would not give sufficient reason for rejection. Among our main contributions (i) we show that this notion of witnessing subframeworks is connected to strong admissibility of AFs, (ii) we investigate the complexity of finding small such subframeworks, and (iii) we extend a recently proposed framework for abstraction in the declarative answer set programming paradigm in order to compute rejecting subframeworks. The resulting system is thus able to deliver explanations also in the case of non-acceptance and we provide a first empirical study that shows the feasibility of our approach.