Graduality in Probabilistic Argumentation Frameworks

Gradual semantics are methods that evaluate overall strengths of individual arguments in graphs. In this paper, we investigate gradual semantics for extended frameworks in which probabilities are used to quantify the uncertainty about arguments and attacks belonging to the graph. We define the likelihoods of an argument's possible strengths when facing uncertainty about the topology of the argumentation framework. We also define an approach to compare the strengths of arguments in this probabilistic setting. Finally, we propose a method to calculate the overall strength of each argument in the framework, and we evaluate this method against a set of principles.