A context - for default its

We present a new context-based approach to default logic, called contextual default logic. The approach”extends the notion of a default rule and supplies each extension with a context. Contextual default logic allows for embedding all existing variants of default logic along with more traditional approaches like the closed world assumption. A key advantage of contextual default logic is that it provides a syntactical instrument for comparing existing default logics in a unified setting. In particular, it reveals that existing default logics mainly differ in the way they deal with an explicit or implicit underlying context. Thus, the primary purpose of this work is to integrate the different variants of default logic in a more general but uniform system, which combines the expressiveness of the various default logics. The basic idea is twofold. First, we supply each default extension (ie. a set of default conclusions) with an underlying context. Second, we extend the notion of a default rule in order to allow for a variety of different application conditions which arise naturally from the distinction between the initial set of facts, the default extension at hand, and its context.