The complexity of model checking for propositional default logics

We analyze the complexity of deciding whether a propositional interpretation is a model of a default theory for some of the variants of default logic presented in the literature: Reiter's, justified, constrained, rational, and cumulative. We prove that all the analyzed variants are Σ2p-complete in the general case, and remains so even if all defaults are prerequisite-free and seminormal. Cumulative default logic is also Σ2p-complete even if all defaults are normal and prerequisite-free. The other semantics are Δ2p[logn]-complete and coNP-complete if all defaults are normal and prerequisites are allowed or not, respectively.