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: Reiters, justified, constrained, rational, and cumulative. We prove that all the analyzed variants are ? 2 p -complete in the general case, and remains so even if all defaults are prerequisite-free and seminormal. Cumulative default logic is also ? 2 p -complete even if all defaults are normal and prerequisite-free. The other semantics are ? 2 p [ log n ] -complete and coNP-complete if all defaults are normal and prerequisites are allowed or not, respectively.
model checking default logic computational complexity nonmonotonic reasoning