Defining variants of default logic: A modal approach

Recently some variants of Reiter’s default logic have been proposed. These variants have been defined by altering the definition of default extension and, sometimes, also the definition of default theory. Recently a uniform semantic framework has been introduced by Besnard and Schaub, in which the semantics of the various default logics is given in terms of Kripke structures. In this paper a uniform syntactic characterization for these different default logics is presented. First, a modal default logic, called K-default logic, is introduced. This logic is defined similarly to Reiter’s default logic but it is based on an underlying modal logic (instead of classical logic). We show how the different variants of default logic, like Schaub’s Constrained Default Logic, Brewka’s CDL and also Lukaszewicz’ variant, can be reconstructed within KDL: for each variant a different modal translation of default rules is proposed. In this way, the differences among the variants are made explicit on a syntactic ground.