  We provide a new characterization of both belief update and belief revision
in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of
states, a Kripke belief relation and a Lewis selection function. Adding a
valuation to a frame yields a model. Given a model and a state, we identify the
initial belief set K with the set of formulas that are believed at that state
and we identify either the updated belief set or the revised belief set,
prompted by the input represented by formula A, as the set of formulas that are
the consequent of conditionals that (1) are believed at that state and (2) have
A as antecedent. We show that this class of models characterizes both the
Katsuno-Mendelzon (KM) belief update functions and the AGM belief revision
functions, in the following sense: (1) each model gives rise to a partial
belief function that can be completed into a full KM/AGM update/revision
function, and (2) for every KM/AGM update/revision function there is a model
whose associated belief function coincides with it. The difference between
update and revision can be reduced to two semantic properties that appear in a
stronger form in revision relative to update, thus confirming the finding by
Peppas et al. (1996) that, "for a fixed theory K, revising K is much the same
as updating K"
