alphabet are sometimes ignored. The translatability between propositional default logic and the following logics have been studied: classical propositional logic; autoepistemic logic; propositional default logic restricted to seminormal theories; alternative semantics of default logic; circumscription. Translations exist or not depending on which conditions are imposed. Translations from propositional default logic to classical propositional logic cannot always generate a polynomially sized propositional theory, unless the polynomial hierarchy collapses. Translations to autoepistemic logic exist or not depending on whether modularity or the use of the same alphabet is required. Complexity The computational complexity of the following problems about default logic is known: Existence of extensions deciding whether a propositional default theory has at least one extension is -complete; Skeptical entailment deciding whether a propositional default theory skeptically entails a propositional formula is -complete; Credulous entailment deciding whether a propositional default theory credulously entails a propositional formula is -complete; Extension checking deciding whether a propositional formula is equivalent to an extension of a propositional default theory is -complete; Model checking deciding whether a propositional interpretation is a model of an extension of a propositional default theory is -complete. Implementations Four systems implementing default logics are DeReS, XRay, GADeL, and Catala. See also Answer set programming Defeasible logic Non-monotonic logic References G. Antoniou (1999). A tutorial on default logics. ACM Computing Surveys, 31(4):337-359. M. Cadoli, F. M. Donini, P. Liberatore, and M. Schaerf (2000). Space efficiency of propositional knowledge representation formalisms. Journal of Artificial Intelligence Research, 13:1-31. P. Cholewinski, V. Marek, and M. Truszczynski (1996). Default reasoning system DeReS. In Proceedings of the Fifth International Conference on the Principles of Knowledge Representation and Reasoning (KR'96), pages 518-528. J. Delgrande and T. Schaub (2003). On the relation between Reiter's default logic and its (major) variants. In Seventh European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2003), pages 452-463. J. P. Delgrande, T. Schaub, and W. K. Jackson (1994). Alternative approaches to default logic. Artificial Intelligence, 70:167-237. G. Gottlob (1992). Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2:397-425. G. Gottlob (1995). Translating default logic into standard autoepistemic logic. Journal of the ACM, 42:711-740. T. Imielinski (1987). Results on translating defaults to circumscription. Artificial Intelligence, 32:131-146. T. Janhunen (1998). On the intertranslatability of autoepistemic, default and priority logics, and parallel circumscription. In Proceedings of the Sixth European Workshop on Logics in Artificial Intelligence (JELIA'98), pages 216-232. T. Janhunen (2003). Evaluating