# Stability in Abstract Argumentation

arXiv: https://arxiv.org/abs/2012.12588 · HTML: https://mlsanity.com/paper/2012.12588/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 2 of 2)

- [Online Handbook of Argumentation for AI: Volume 4](https://mlsanity.com/paper/2401.09444/) (2023)
- [Relevance for Stability of Verification Status of a Set of Arguments in Incomplete Argumentation Frameworks (with Proofs)](https://mlsanity.com/paper/2505.16507/) (2025)

## Abstract (arXiv)

The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away from the logical structure of arguments, and we transpose this notion of stability to the context of Dungean argumentation frameworks. In particular, we show how this problem can be translated into reasoning with Argument-Incomplete AFs. Then we provide preliminary complexity results for stability under four prominent semantics, in the case of both credulous and skeptical reasoning. Finally, we illustrate to what extent this notion can be useful with an application to argument-based negotiation.