A Framework for Cumulative Default Logics

We present a framework for default reasoning which has its roots in Reiter's Default Logic. Contrary to Reiter, however, we do not consider defaults as inference rules used to generate extensions of a classical set of facts. In our approach defaults are elements of the logical language, and we will deene inference rules on defaults. This has several advantages. First of all, we can reason about defaults, not just with defaults. This makes it easy to include diierent intuitions about the right behaviour of a default logic in an explicit form. Secondly, we can show how some of the problems of Reiter's logic and of some recent proposals to solve them can be handled adequately by exploiting the dependency information contained in derived defaults.