On the expressive power of collective attacks

In this paper, we consider SETAFs due to Nielsen and Parsons, an exten-sion of Dung’s abstract argumentation frameworks that allow for collective attacks.We first provide a comprehensive analysis of the expressiveness of SETAFs un-der conflict-free, naive, stable, complete, admissible and preferred semantics. Ouranalysis shows that SETAFs are strictly more expressive than Dung AFs. Towardsa uniform characterization of SETAFs and Dung AFs we provide general resultson expressiveness which take the maximum degree of the collective attacks intoaccount. Our results show that, for eachk>0, SETAFs that allow for collectiveattacks ofk+1 arguments are more expressive than SETAFs that only allow forcollective attacks of at mostkarguments.

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