# Revisiting initial sets in abstract argumentation

arXiv: https://arxiv.org/abs/2204.09985 · HTML: https://mlsanity.com/paper/2204.09985/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 49 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 2 of 2)

- [On the Intertranslatability of Argumentation Semantics](https://mlsanity.com/paper/1401.3895/) (2014)
- [Verifiability of Argumentation Semantics](https://mlsanity.com/paper/1603.09502/) (2016)

## Built on by (most cited first, 1 of 1)

- [Online Handbook of Argumentation for AI: Volume 4](https://mlsanity.com/paper/2401.09444/) (2023)

## Abstract (arXiv)

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.