A divide-and-conquer method for computing preferred extensions of argumentation frameworks

In this paper, we propose a divide-and-conquer method for solving the preferred extensions enumeration prob-lem, which is computationally intractable in argumentation frameworks. The rationale is to take advantage of the fact that for acyclic argumentation frameworks the computation becomes tractable with polynomial time. Concretely, we identify sufficient conditions for decomposing an argumentation framework into sub-frameworks based on certain cycles, where the soundness and completeness in computing preferred extensions are proved. Based on this conclusion, we devise the partitioning algorithm and carry out an evaluation on the International Competition on Computational Models of Argumentation (ICCMA) 2019 dataset. The results show that for the complex, time-consuming tasks our method could reduce running time when compared with the state-of-the-art solver in ICCMA. This is our first attempt in tackling the complex argumentative knowledge and many directions are yet to be explored, both theoretical and empirical.