Revisiting initial sets in abstract argumentation
This work provides incremental insights into conflict analysis in abstract argumentation, primarily for researchers in formal argumentation.
The paper revisits initial sets in abstract argumentation, analyzing their structure and devising a construction principle for admissible sets, which helps explain extensions in admissibility-based semantics.
We revisit the notion of initial sets by Xu and Cayrol, i.e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to explain why certain arguments can be accepted. We contribute with new insights on the structure of initial sets and devise a simple non-deterministic construction principle for any admissible set, based on iterative selection of initial sets of the original framework and its induced reducts. In particular, we characterise many existing admissibility-based semantics via this construction principle, thus providing a constructive explanation on the structure of extensions. We also investigate certain problems related to initial sets with respect to their computational complexity.