On the Existence of an Inverse Solution for Preference-Based Reductions in Argumentation
Provides a theoretical foundation for preference elicitation and explainability in argumentation, but the results are incremental (polynomial-time algorithms for known reductions).
The paper defines an inverse problem for preference-based argumentation frameworks: given an argumentation graph, a labelling, and a semantics, determine whether a preference relation exists that yields that labelling under a given reduction. They show that for four common reductions under complete semantics, the problem is solvable in polynomial time.
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.