Computing extensions' probabilities in probabilistic abstract argumentation: Beyond independence

We characterize the complexity of the problem of computing the probabilities of the extensions in probabilistic abstract argumentation. We consider all the most popular semantics of extensions (admissible, stable, preferred, complete, grounded, ideal-set, ideal and semi-stable) and different forms of correlations that can be defined between arguments and defeats. We show that the complexity of the problem ranges from FP to FP#P -complete, with FP||NPcomplete cases, depending on the semantics of the extensions and the imposed correlations.