  Argumentation Frameworks (AFs) are a key formalism in AI research. Their
semantics have been investigated in terms of principles, which define
characteristic properties in order to deliver guidance for analysing
established and developing new semantics. Because of the simple structure of
AFs, many desired properties hold almost trivially, at the same time hiding
interesting concepts behind syntactic notions. We extend the principle-based
approach to Argumentation Frameworks with Collective Attacks (SETAFs) and
provide a comprehensive overview of common principles for their semantics. Our
analysis shows that investigating principles based on decomposing the given
SETAF (e.g. directionality or SCC-recursiveness) poses additional challenges in
comparison to usual AFs. We introduce the notion of the reduct as well as the
modularization principle for SETAFs which will prove beneficial for this kind
of investigation. We then demonstrate how our findings can be utilized for
incremental computation of extensions and give a novel parameterized
tractability result for verifying preferred extensions.

Artificial Intelligence