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

2026-04-24

AI Summary

This study addresses the inverse problem in preference-based argumentation frameworks: given an argument graph, a target labeling, and a semantics, does there exist a preference relation over arguments such that, under a mainstream preference reduction method and complete semantics, the resulting extension yields precisely that labeling? For the first time, we systematically analyze the tractability of this inverse problem across four widely used preference reduction methods. By integrating insights from abstract argumentation theory, preference modeling, and computational complexity analysis, we demonstrate that—apart from a few exceptional cases—the problem is decidable in polynomial time. This result substantially enhances the computational feasibility of such reasoning tasks in preference-aware argumentation systems.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Natural Language Processing: Discourse, Pragmatics & Argument Mining
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• preference-based argumentation
• inverse problem
• argumentation frameworks
• preference elicitation
• explainability

Innovation

• preference-based argumentation
• inverse problem
• polynomial-time solvability
• argumentation frameworks
• preference elicitation