A Theory of Default Reasoning

We propose a theory of default reasoning satisfying a list of natural postulates. These postulates imply that knowledge bases containing defaults should be understood not as sets of formulas (rules and facts) but as collections of partially ordered theories. As a result of this shift of perspective we obtain a rather natural theory of default reasoning in which priorities in interpretation of predicates are the source of nonmonotonicity in reasoning. We also prove that our theory shares a number of desirable properties (completeness, soundness etc.) with the theory of normal defaults of R. Reiter. We limit our discussion to logical properties of the proposed system and prove some theorems about it. Modal operators or second order formulas do not appear in our formalization. Instead, we augment the usual, two-part logical structures consisting of a metalevel and an object level, with a third level- a referential level. The rderential level is a partially ordered collection of defaults; it contains a more permanent part of a knowledge base. Current situations are described on the object level. The metalevel is a place for rules that can eliminate some of the models permitted by the object level and the referential level.