Alchourrón, Gärdenfors and Makinson have developed and investigated a
set of rationality postulates which appear to capture much of what is
required of any rational system of theory revision. This set of postulates
describes a class of revision functions, however it does not provide a
constructive way of defining such a function. There are two principal
constructions of revision functions, namely an epistemic entrenchment and
a system of spheres. We refer to their approach as the AGM paradigm. We
provide a new constructive modeling for a revision function based on a
nice preorder on models, and furthermore we give explicit conditions
under which a nice preorder on models, an epistemic entrenchment, and a
system of spheres yield the same revision function. Moreover, we
provide an identity which captures the relationship between revision
functions and update operators (as defined by Katsuno and Mendelzon).