Expressiveness of SETAFs and support-free ADFs under 3-valued semantics

Abstract

Generalising the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Among the generalisations of AFs, abstract dialectical frameworks (ADFs) allow for a systematic and flexible generalisation of AFs in which different kinds of logical relations, e.g. attack and support, among arguments can be represented. Restricting the logical relations among arguments leads to different subclasses of ADFs of interest. In this work, we consider so-called support-free ADFs that allow for all kinds of attacks but no support or other relations and SETADFs that embed SETAFs in the ADF setting. The aim of this paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminates the two approaches.