Revision over partial pre-orders: a postulational study

Abstract. Belief revision is the process that incorporates, in a consistent way, a new piece of information, called input, into a belief base. When both belief bases and inputs are propositional formulas, a set of natural and rational proper-ties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue: How to revise a partially pre-ordered information (representing initial beliefs) with a new par-tially pre-ordered information (representing inputs) while preserving AGM pos-tulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some exam-ples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revi-sion for both cases where the input is either a single propositional formula or a total pre-order.