Skeptical Rational Extensions

In this paper we propose a version of default logic with the following two properties: (1) defaults with mutually inconsistent justi-cations are never used together in constructing a set of default consequences of a theory; (2) the reasoning formalized by our logic is related to the traditional skeptical mode of default reasoning. Our logic is based on the concept of a skeptical rational extension. We give characterization results for skeptical rational extensions and an algorithm to compute them. We present some complexity results. Our main goal is to characterize cases when the class of skeptical rational extensions is closed under intersection. In the case of normal default theories our logic coincides with the standard skeptical reasoning with extensions. In the case of seminormal default theories our formalism provides a description of the standard skeptical reasoning with rational extensions.