Characterizability in Belief Revision

A formal framework is given for the postulate characterizability of a class of belief revision operators, obtained from a class of partial preorders using minimization. It is shown that for classes of posets characterizability is equivalent to a special kind of definability in monadic second-order logic, which turns out to be incomparable to first-order definability. Several examples are given of characterizable and non-characterizable classes. For example, it is shown that the class of revision operators obtained from posets which are not total is not characterizable.