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

Abstract

AbstractGeneralising 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.Keywords: Abstract argumentation frameworksabstract dialectical frameworkscollective attack Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 We note this concept does not allow for auxiliary arguments that simulate certain behaviours, see e.g. Modgil and Bench-Capon (Citation2011).2 As discussed in Polberg (Citation2017), in general, SETAFs translate to bipolar ADFs that contain attacking and redundant links. However, when we first remove redundant attacks from the SETAF we obtain a SFADF.3 Recent work Dvořák et al. (Citation2021a) studies different types of symmetry in SETAFs. Our notion of symmetry corresponds the notion of primal-symmetric SETAFs without self-attacks in Dvořák et al. (Citation2021a)Additional informationFundingThis research has been supported by Austrian Science Fund (FWF) through projects I2854, P30168. The second researcher is supported by 1- the Netherlands Organisation for Scientific Research (NWO) through the Hybrid Intelligence Gravitation Programme, And 2- the Netherlands eScience Center project “The Eye of theBeholder”.