An Imprecise Probability Approach for Abstract Argumentation based on Credal Sets
This work provides a method for handling imprecise probabilities in argumentation frameworks, which is incremental as it extends existing precise probability models to more realistic uncertain scenarios.
The paper addresses the problem of calculating uncertainty in abstract argumentation extensions when argument probabilities are imprecise, using credal sets to compute lower and upper bounds and demonstrating the approach with a decision-making scenario.
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.