Complexity of semi-stable and stage semantics in argumentation frameworks

In this work, we answer two questions about the complexity of semi-stable semantics for abstract argumentation frameworks: we show -completeness for the problem of deciding whether an argument is skeptically accepted, and respectively, -completeness for the problem of deciding whether an argument is credulously accepted under the semi-stable semantics. Furthermore, we extend these complexity bounds to the according decision problems for stage semantics and discuss two approaches towards tractability.