Revisiting initial sets in abstract argumentation

TL;DR

This paper explores the structure and computational aspects of initial sets in abstract argumentation frameworks, offering new insights and a constructive method to understand admissible sets and semantics.

Contribution

It introduces a non-deterministic construction principle for admissible sets and characterizes many semantics through this approach.

Findings

Characterizes many admissibility-based semantics.

Provides a simple construction principle for admissible sets.

Investigates computational complexity of initial set problems.

Abstract

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.