Justifying Argument Acceptance with Collective Attacks: Discussions and Disputes

In formal argumentation one aims for intuitive and concise justifications for the acceptance of arguments. Discussion games and dispute trees are established methods to obtain such a justification. However, so far these techniques are based on instantiating the knowledge base into graph-based Dung style abstract argumentation frameworks (AFs). These instantiations are known to produce frameworks with a large number of arguments and thus also yield long discussion games and large dispute trees. To obtain more concise justifications for argument acceptance, we propose to instantiate the knowledge base as an argumentation framework with collective attacks (SETAF). Remarkably, this approach yields smaller frameworks compared to traditional AF instantiation, while exhibiting increased expressive power. We then introduce discussion games and dispute trees tailored to SETAFs, show that they correspond to credulous acceptance w.r.t. the well-known preferred semantics, analyze and tune them w.r.t. the size, and compare the two notions. Finally, we illustrate how our findings apply to assumption-based argumentation.