Computing Preferred Labellings by Exploiting SCCs and Most Sceptically Rejected Arguments

The computation of preferred labellings of an abstract argumentation framework (or briefly, AF) is generally intractable. The existing decomposition-based approach by exploiting strongly connected components (SCCs) of a general AF is promising to cope with this problem. However, the efficiency of this approach is highly limited by the maximal SCC of an AF. This paper presents a further solution by exploiting the most sceptically rejected arguments of an AF. Given an AF, its grounded labelling is first generated. Then, the attacks between the undecided arguments and the rejected arguments are removed. It turns out that the modified AF has the same preferred labellings as the original AF, but the maximal SCC in it could be much smaller than that of the original AF. Empirical results show that this new method dramatically reduce the computation time for some sparse AFs (when the ratio of the number of edges to the number of nodes of an AF is between 1:1 and 1.8:1).