generating extensions starts by guessing a theory and using it in place of the background theory; what results from the process of extension generation is actually an extension only if it is equivalent to the theory guessed at the beginning. This variant of default logic is related in principle to autoepistemic logic, where a theory has the model in which is true just because, assuming true, the formula supports the initial assumption. Disjunctive default logic the consequence of a default is a set of formulae instead of a single formula. Whenever the default is applied, at least one of its consequences is nondeterministically chosen and made true. Priorities on defaults the relative priority of defaults can be explicitly specified; among the defaults that are applicable to a theory, only one of the most preferred ones can be applied. Some semantics of default logic do not require priorities to be explicitly specified; rather, more specific defaults (those that are applicable in fewer cases) are preferred over less specific ones. Statistical variant a statistical default is a default with an attached upper bound on its frequency of error; in other words, the default is assumed to be an incorrect inference rule in at most that fraction of times it is applied. Translations Default theories can be translated into theories in other logics and vice versa. The following conditions on translations have been considered: Consequence-Preserving the original and the translated theories have the same (propositional) consequences; Faithful this condition only makes sense when translating between two variants of default logic or between default logic and a logic in which a concept similar to extension exists, e.g., models in modal logic; a translation is faithful if there exists a mapping (typically, a bijection) between the extensions (or models) of the original and translated theories; Modular a translation from default logic to another logic is modular if the defaults and the background theory can be translated separately; moreover, the addition of formulae to the background theory only leads to adding the new formulae to the result of the translation; Same-Alphabet the original and translated theories are built on the same alphabet; Polynomial the running time of the translation or the size of the generated theory are required to be polynomial in the size of the original theory. Translations are typically required to be faithful or at least consequence-preserving, while the conditions of modularity and same