Expressiveness of SETAFs and Support-Free ADFs under 3-valued Semantics
  Generalizing 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. Another approach is provided via abstract
dialectical frameworks (ADFs), where acceptance conditions specify the relation
between arguments; restricting these conditions naturally allows for so-called
support-free ADFs. The aim of the 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 discriminate the two
approaches.
