On the different types of collective attacks in abstract argumentation: equivalence results for SETAFs

Abstract

Abstract Argumentation frameworks with collective attacks are a prominent extension of Dung’s abstract argumentation frameworks, where an attack can be drawn from a set of arguments to another argument. These frameworks are often abbreviated as SETAFs. Although SETAFs have received increasing interest recently, a thorough study on the actual behaviour of collective attacks has not been carried out yet. In particular, the richer attack structure SETAFs provide can lead to different forms of redundant attacks, i.e. attacks that are subsumed by attacks involving less arguments. Also the notion of strong equivalence, which is fundamental in nonmonotonic formalisms to characterize equivalent replacements, has not been investigated for SETAFs so far. In this paper, we first provide a classification of different types of collective attacks and analyse for which semantics they can be proven redundant. We do so for eleven well-established abstract argumentation semantics. We then study how strong equivalence between SETAFs can be decided with respect to the considered semantics and also consider variants of strong equivalence. Our results show that removing redundant attacks in a suitable way provides direct means to characterize strong equivalence by syntactical equivalence of so-called kernels, thus generalizing well-known results on strong equivalence between Dung AFs.