Abstract Argumentation Frameworks with Marginal Probabilities

In the context of probabilistic AAFs, we introduce AAFs with marginal probabilities (mAAFs) requiring only marginal probabilities of arguments/attacks to be specified and not relying on the independence assumption. Reasoning over mAAFs requires taking into account multiple probability distributions over the possible worlds, so that the probability of extensions is not determined by a unique value, but by an interval. We focus on the problems of computing the max and min probabilities of extensions over mAAFs under Dung's semantics, characterize their complexity, and provide closed formulas for polynomial cases.