An Imprecise Probability Approach for Abstract Argumentation Based on Credal Sets

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.

Imprecise abstract argumentation as a support for forensic engineering

“…PðAÞ is, therefore, a measure of evidence in favor of event A, or in other words, how much K(X) supports event A, while PðAÞ measures the lack of evidence against A. Morveli-Espinoza et al (2019) propose an extension of the PrAAF in the framework of the epistemic approach in which credal sets are used to model the uncertainty values of the arguments taking into consideration causal relationships between the arguments to estimate the lower and upper probabilities. Following along from their work, we propose an extension of the PrAAF, called an imprecise probability argumentation system (IPAS), based on the Possible worlds (w) Probability P(w)…”