Expressiveness of SETAFs and Support-Free ADFs under 3-valued Semantics
This work addresses a theoretical problem in computational argumentation for researchers, but it is incremental as it builds on existing formalisms without introducing new methods.
The paper investigates the relationship between SETAFs and support-free ADFs in argumentation frameworks under 3-valued semantics, finding that the key difference lies in the presence of unsatisfiable acceptance conditions in support-free ADFs.
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.