A comprehensive study of argumentation frameworks with sets of attacking arguments

It has been argued that Dung's classical Abstract Argumentation Framework (AAF) model is not appropriate for capturing "joint attacks", a feature that is inherent in several contexts and applications. The model proposed by Nielsen and Parsons in [1], often referred to as "framework with sets of attacking arguments" (SETAF), fills this gap by introducing joint attacks as a generalisation of the standard attack relationship of AAFs, thus constituting a faithful generalization of Dung's model. Building on that work, we provide a more complete characterization of these frameworks, which includes the treatment of various semantics not considered in the original publication, a more fine-grained representation of all acceptability semantics using labellings, and two functions allowing the transition between extensions and labellings along with their properties. Moreover, we show that a variety of well-known results that apply to AAF can be migrated to the SETAF setting. To further associate the two frameworks, we provide a natural way to represent a SETAF as a Dung-style AAF, and show how the generated AAF behaves. (C) 2019 Elsevier Inc. All rights reserved.