A gradual semantics with imprecise probabilities for support argumentation frameworks

Support Argumentation Frameworks (SAFs) are a type of the Abstract Argumentation Framework, where the interactions between arguments have a positive nature. A quantitative way of evaluating the arguments in a SAF is by applying a gradual semantics, which assigns a numerical value to each argument with the aim of ranking or evaluate them. In the literature,studied gradual semantics determine precise probability values; however, in many applications there is the necessity of imprecise evaluations which consider a range of values for assessing an argument. Thus, the first contribution of this article is an imprecise gradual semantics (IGS) based on credal networks theory. The second contribution is a set of properties for evaluating IGSs, which extend some properties proposed for precise gradual semantics. Besides, we suggest a classification of semantics considering the set of properties and evaluate our proposed IGS according to the extended properties. Finally, the practical application of the results is discussed by using an example from Network Science, i.e, PageRank. We also discuss how gradual semantics benefit PageRank research by allowing to generate contrastive explanations about the scores in a more natural way