Revision over Partial Pre-orders: A Postulational Study

Abstract

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 properties, 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 partially pre-ordered information (representing inputs) while preserving AGM postulates? 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 examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

Efficient minimal preference change

“…There are some similarities between our work and the work of Ma et al [30], who study belief revision postulates for revision of a partial preorder by a partial preorder. Our preference sentences correspond to their units, and our revision by a set of preference sentences corresponds to their revision of a preorder by a preorder.…”