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 K⋄ϕ or 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 that state and (2) have ϕ as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the Alchourrón, Gärdenfors and Makinson (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) [30] that, “for a fixed theory K, revising K is much the same as updating K”. It is argued that the proposed semantic characterization brings into question the common interpretation of belief revision and update as change in beliefs in response to new information.

中文翻译：

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用于信念更新和信念修正的 Kripke-Lewis 语义


我们根据 Kripke-Lewis 语义提供了信念更新和信念修正的新特征。我们考虑由一组状态、Kripke 信念关系和 Lewis 选择函数组成的框架。将估价添加到框架中将生成一个模型。给定一个模型和一个状态，我们将初始信念集 K 与在该状态下相信的一组公式确定为初始信念集 K⋄φ 或修正后的信念集 K⁎φ（由公式 φ 表示的输入提示）作为公式集，这些公式是 （1） 在该状态下被相信并且 （2） φ为前提的条件语句的结果。我们表明，这类模型在以下意义上表征了 Katsuno-Mendelzon （KM） 信念更新函数和 Alchourrón、Gärdenfors 和 Makinson （AGM） 信念修正函数：（1） 每个模型都产生了一个部分信念函数，该函数可以完成为完整的 KM/AGM 更新/修订函数，以及 （2） 对于每个 KM/AGM 更新/修订函数，都有一个模型，其关联的信念函数与之一致。更新和修订之间的区别可以简化为两个语义属性，它们在修订中相对于更新以更强的形式出现，从而证实了 Peppas 等人（1996）[30] 的发现，即“对于固定理论 K，修订 K 与更新 K 大致相同”。有人认为，所提出的语义表征对信念修正和更新作为对新信息的反应信念变化的常见解释提出了质疑。