An Imprecise Probability Approach for Abstract Argumentation based on Credal Sets

TL;DR

This paper introduces an imprecise probability method for abstract argumentation using credal sets, enabling the calculation of uncertainty bounds of extensions when exact probabilities are unknown or aggregated from multiple sources.

Contribution

It proposes a novel approach that models argument uncertainty with credal sets, providing bounds on extensions in abstract argumentation frameworks.

Findings

The approach effectively computes lower and upper bounds of extensions.

It handles aggregation of probabilities from multiple sources.

The method is demonstrated through a decision-making scenario.

Abstract

Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making.