Efficiently Estimating the Probability of Extensions in Abstract Argumentation

Probabilistic abstract argumentation combines Dung's abstract argumentation framework with probability theory to model uncertainty in argumentation. In this setting, we deal with the fundamental problem of computing the probability Pr-sem (S) that a set S of arguments is an extension according to a semantics sem. We focus on three popular semantics (i.e., complete, grounded, and preferred) for which the state-of-the-art approach is that of estimating Pr-sem (S) by using a Monte-Carlo simulation technique, as computing Pr-sem (S) has been proved to be intractable. In this paper, we detect and exploit some properties of these semantics to devise a new Monte-Carlo simulation approach which is able to estimate Pr-sem (S) using much fewer samples than the state-of-the-art approach, resulting in a significantly more efficient estimation technique.