Data and Knowledge Engineering
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 Sigma2-complete in the general case, and remains so even if all defaults are prerequisite-free and seminormal. Cumulative default logic is also Sigma2-complete even if all defaults are normal and prerequisite-free. The other semantics are Delta-log2-complete and coNP-complete if all defaults are normal and prerequisites are allowed or not, respectively.
@article{libe-scha-06-b, title = {The Complexity of Model Checking for Propositional Default Logics}, year = {2005}, author = {Liberatore, Paolo and Schaerf, Marco}, journal = {Data and Knowledge Engineering}, pages = {189-202}, number = {2}, volume = {55}, }doi: 10.1016/j.datak.2005.03.002