  A vast and interesting family of natural semantics for belief revision is
defined. Suppose one is given a distance d between any two models. One may then
define the revision of a theory K by a formula a as the theory defined by the
set of all those models of a that are closest, by d, to the set of models of K.
This family is characterized by a set of rationality postulates that extends
the AGM postulates. The new postulates describe properties of iterated
revisions.
