A New Approach to Preferential Structures

Abstract

This paper deals with some fundamental concepts and questions of preferential structures. Traditionally, a model for preferential reasoning is a strict partial order on the set of classical models of the language; in this article it will be a total order on the classical models. Instead of representing non-monotonic inference relations by individual partial orders, we represent them by sets of total orders. We thus stay close to the way completeness proofs are done in classical logic. Our new approach will also justify multiple copies (or labelling functions) present in most work on preferential structures. A representation result for the finite case is proven; for the infinite case it remains an open question.