Splitting Argumentation Frameworks with Collective Attacks

Abstract

A recurring notion in the abstract argumentation community is that of collective attacks, whereby a set of arguments, rather than a single one, attacks another argument. The resulting frameworks capturing this phenomenon are referred to as SETAFs. Given the possibility of facing an exponential runtime in the size of the framework, techniques have been presented to compute extensions of a given framework incrementally, i.e. restricting the search space to sub-frameworks only, and then combining the obtained results. Existing research has primarily focused on approaches based on SCC-recursiveness, where SETAFs are evaluated along their strongly connected components (SCCs) using generalized semantics and dedicated algorithms. Splitting approaches are more general in this regard, as they do not have to consider SCCs individually and can be used on top of arbitrary argumentation solvers. Splitting techniques have been successfully applied in abstract argumentation but have been neglected for SETAFs so far. Towards lling this gap our work investigates the concept of (modication-based) splitting for SETAFs. We show that a splitting-based approach is possible for common semantics (such as admissible, complete, grounded, preferred, and stable), generalizing corresponding results of AFs, which can be seen as a restricted class of SETAFs. Along the way, we point out intricate details that are obvious or trivial for AFs, but help us to understand the underlying ideas in greater detail than before.