Bijective faithful translations among default logics

In this article, we report results about translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can introduce new variables and that the result of translating a theory can either be produced in time polynomial in the size of the theory or its output is of size polynomial in the size of the theory; we restrict to the case in which the original theory has extensions. This study fills a gap between two previous works, one studying bijective translations among restrictions of default logics and one studying non-bijective translations between default variants of default logic.