The Inverse Problem for Argumentation Gradual Semantics

TL;DR

This paper investigates the inverse problem in weighted argumentation semantics, proposing an algorithm to determine initial weights that produce a desired argument ranking, along with theoretical characterization and empirical evaluation.

Contribution

It introduces an algorithm for the inverse problem in weighted semantics, characterizes necessary properties of semantics for the algorithm, and provides empirical results.

Findings

The algorithm can effectively find initial weights for certain semantics.

Characterization of semantics properties necessary for the algorithm.

Empirical evaluation demonstrates the algorithm's practical applicability.

Abstract

Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each following different principles and producing different argument rankings. A sub-class of such semantics, the so-called weighted semantics, takes, in addition to the graph structure, an initial set of weights over the arguments as input, with these weights affecting the resultant argument ranking. In this work, we consider the inverse problem over such weighted semantics. That is, given an argumentation framework and a desired argument ranking, we ask whether there exist initial weights such that a particular semantics produces the given ranking. The contribution of this paper are: (1) an algorithm to answer this problem, (2) a characterisation of the properties that a gradual semantics must satisfy for the algorithm to operate, and (3) an empirical evaluation of the proposed algorithm.