# On the Existence of an Inverse Solution for Preference-Based Reductions in Argumentation

arXiv: https://arxiv.org/abs/2604.22958 · HTML: https://mlsanity.com/paper/2604.22958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [On the Acceptability of Arguments in Preference-Based Argumentation](https://mlsanity.com/paper/1301.7358/) (2013)
- [Preference Elicitation in Assumption-Based Argumentation](https://mlsanity.com/paper/2005.05721/) (2020)
- [Analytical Solutions for the Inverse Problem within Gradual Semantics](https://mlsanity.com/paper/2203.01201/) (2022)
- [Inferring Attack Relations for Gradual Semantics](https://mlsanity.com/paper/2211.16118/) (2022)
- [The Effect of Preferences in Abstract Argumentation Under a Claim-Centric View](https://mlsanity.com/paper/2204.13305/) (2022)
- [An Extension-based Approach for Computing and Verifying Preferences in Abstract Argumentation](https://mlsanity.com/paper/2403.17653/) (2024)

## Abstract (arXiv)

Preference-based argumentation frameworks (PAFs) extend Dung's approach to abstract argumentation (AAFs) by encoding preferences over arguments. Such preferences control the transformation of attacks into defeats, and different approaches to doing so result in different reductions from a PAF to an AAF. In this paper we consider a PAF inverse problem which takes an argumentation graph, a labelling and a semantics as an input, and outputs a ``yes" or ``no" as to whether there is a preference relation between the arguments which can yield the desired labelling. This inverse problem has applications in areas including preference elicitation and explainability. We consider this problem in the context of the four most widely-used preference based reductions under the complete semantics. We show that in most cases, the problem can be answered in polynomial time.