Prioritizing Default Logic: Abridged Report

A number of prioritized variants of Reiter’s default logic have been described in the literature. In this paper, we introduce two natural principles for preference handling and show that all existing approaches fail to satisfy them. We develop a new approach which does not suffer from these shortcomings. We start with the simplest case, supernormal default theories, where preferences are handled in a straightforward manner. The generalization to prerequisite-free default theories is based on an additional fixed point condition for extensions. The full generalization to arbitrary default theories uses a reduction of default theories to prerequisite-free theories. The reduction can be viewed as dual to the Gelfond/Lifschitz reduction used in logic programming for the definition of answer sets. We finally show how preference information can be represented in the logical language.