Computing the Extensions of an Argumentation Framework Based on Its Strongly Connected Components

Currently, only some argumentation frameworks (AFs) with special topologies have been identified as tractable classes. By taking advantage of the tractability of some parts of a general AF, this paper proposes a method to compute the extensions of an AF based on its strongly connected components (SCCs). In this method, an AF is partitioned into a set of sub frameworks (by a linear time algorithm) according to its SCCs. Under an argumentation semantics that satisfies the criterion of directionality, sets of extensions of all sub-frameworks can be computed locally, and combined incrementally to form the extensions of the original AF. The analysis shows that by using this method the complexity of computing the extensions of an AF may be reduced to a greater or a lesser extent, depending on the size and the topology of a dominant sub-framework of the AF, as well as the number of extensions of the AF.