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"

翻译：我们提出了一种基于克里普克-刘易斯语义的信念更新与信念修正的新刻画方法。考虑由状态集合、克里普克信念关系与刘易斯选择函数构成的框架，通过为框架添加赋值函数即可得到模型。给定模型与状态后，我们将初始信念集K定义为该状态下所相信的公式集合，而将由公式A所表示的输入触发的更新后或修正后信念集，定义为在该状态下被相信且以A为前件条件句的后件所构成的公式集合。我们证明：这类模型以如下意义刻画了Katsuno-Mendelzon（KM）信念更新函数与AGM信念修正函数：（1）每个模型均可生成一个部分信念函数，该函数可被完备化为完整的KM/AGM更新/修正函数；（2）对任意KM/AGM更新/修正函数，均存在一个模型使其关联的信念函数与之完全一致。更新与修正之间的差异可归结为两种语义性质，这些性质在修正中相对于更新呈现更强形式，从而印证了Peppas等人（1996）的发现："对固定理论K而言，修正K与更新K几乎等同"。