Investigating subclasses of abstract dialectical frameworks

Dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures

Characterizing strongly admissible sets

The concept of strong admissibility plays an important role in dialectical proof procedures for grounded semantics allowing, as it does, concise proofs that an argument belongs to the grounded extension without having necessarily to construct this extension in full. One consequence of this property is that strong admissibility (in contrast to grounded semantics) ceases to be a unique status semantics. In fact it is straightforward to construct examples for which the number of distinct strongly admissible sets is exponential in the number of arguments. We are interested in characterizing properties of collections of strongly admissible sets in the sense that any system describing the strongly admissible sets of an argument framework must satisfy particular criteria. In terms of previous studies, our concern is the signature and with conditions ensuring realizability. The principal result is to demonstrate that a system of sets describes the strongly admissible sets of some framework if and only if that system has the property of being decomposable.</jats:p

On the Expressive Power of Collective Attacks

International audienceIn 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