# Rejection in Abstract Argumentation: Harder Than Acceptance?

arXiv: https://arxiv.org/abs/2408.10683 · HTML: https://mlsanity.com/paper/2408.10683/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 3 of 3)

- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [Lower Bounds for QBFs of Bounded Treewidth](https://mlsanity.com/paper/1910.01047/) (2019)
- [Treewidth-Aware Complexity in ASP: Not all Positive Cycles are Equally Hard](https://mlsanity.com/paper/2007.04620/) (2020)

## Abstract (arXiv)

Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with acceptance conditions on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for rejecting an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.