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

TL;DR

This paper investigates whether a preference relation exists in preference-based argumentation frameworks that can produce a given argumentation graph and labelling, with implications for preference elicitation and explainability.

Contribution

It analyzes the inverse problem of preference-based reductions in argumentation, providing polynomial-time solutions for the most common reduction methods under complete semantics.

Findings

Most cases of the inverse problem can be answered in polynomial time.

The study focuses on four widely-used preference-based reductions.

Applications include preference elicitation and explainability in argumentation.

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.