A Kripke-Stalnaker-Lewis semantics for AGM belief revision

We provide a new characterization of AGM belief revision in terms of a Kripke-Stalnaker-Lewis semantics. We consider pointed frames consisting of a set of states, a distinguished state interpreted as the actual state, a Kripke belief relation and a Stalnaker-Lewis selection function. Adding a valuation to a frame yields a model. Given a model, we identify the initial belief set K with the set of formulas that are believed at the actual state and the revised belief set K∗ϕ (prompted by the input represented by formula ϕ) as the set of formulas that are the consequent of conditionals that (1) are believed at the actual state and (2) have ϕ as antecedent. We show that this class of models characterizes the set of AGM belief revision functions, in the following sense: (1) each model gives rise to a (possibly partial) belief revision function that can be completed into a full AGM belief revision function, and (2) for every AGM belief revision function there is a model whose associated belief revision function coincides with it.