On the Complexity of Probabilistic Abstract Argumentation Frameworks

Probabilistic abstract argumentation combines Dung's abstract argumentation framework with theory in order to model uncertainty in argumentation. In this setting, we address the fundamental of computing the probability that a set of arguments is an extension according to a given semantics. We on the most popular semantics (i.e., admissible, stable, complete, grounded, preferred, ideal-set, ideal, and semistable) and show the following dichotomy result: computing the probability that a set of is an extension is either FP or FP#P-complete depending on the semantics adopted. Our polynomial-results are particularly interesting, as they hold for some semantics for which no polynomial-time was known so far.