On efficiently estimating the probability of extensions in abstract argumentation frameworks

Probabilistic abstract argumentation is an extension of Dung's abstract argumentation framework with probability theory. In this setting, we address the problem of computing the probability Prsem(S) that a set S of arguments is an extension according to a semantics sem. We focus on four popular semantics (i.e., complete, grounded, preferred and ideal-set) for which the state-of-the-art approach is that of estimating Prsem(S) by using a Monte-Carlo simulation technique, as computing Prsem(S) has been proved to be intractable. In this paper, we propose a new Monte-Carlo simulation approach which exploits some properties of the above-mentioned semantics for estimating Prsem(S) using much fewer samples than the state-of-the-art approach, resulting in a significantly more efficient estimation technique.