Distance based revision of preferential logics

Abstract

We first analyze AGM revision as conditions on choice functions for sets of models. This abstraction seems to us to capture the essentials of classical revision, it also immediately reveals the connection between revision and ranked preferential models, and gives further insight into the distance semantics for revision as developed by Lehmann, Magidor, and Schlechta. Our analysis shows how to apply the essential ideas of revision to other situations than classical theories and formulas, we exemplify this by examining preferential databases. We revise one preferential logic or database, |∼ with another one, |∼'. The basic idea is to describe such a logic as a partial order, either as the order of a preferential model which defines the logic, or as the order between formulas defined by the logic. A partial order can be seen as the set of total orders which extend it, and, given a distance on the set of total orders, we can define a revision as follows: |∼* |∼' will be the logic corresponding to the partial order generated by those total orders extending (the order of) |∼', which are closest to the set of total orders extending (the order of) |∼. We thus give a semantical approach to the problem. A representation result is proven.