On Efficiently Enumerating Semi-Stable Extensions via Dynamic Programming on Tree Decompositions

Many computational problems in the area of abstract argumentation are intractable. For some semantics like preferred and semi-stable, important decision problems can even be hard for classes of the second level of the polynomial hierarchy. One approach to deal with this inherent difficulty is to exploit structure of argumentation frameworks. In particular, algorithms that run in linear time for argumentation frameworks of bounded tree width have been proposed for several semantics. In this paper, we contribute to this line of research and propose a novel algorithm for the semi-stable semantics. We also present an implementation of the algorithm and report on some experimental results.