Knowledge Measures (KMs) aim at quantifying the amount of knowledge/information that a knowledge base carries. On the other hand, Belief Change (BC) is the process of changing beliefs (in our case, in terms of contraction, expansion and revision) taking into account a new piece of knowledge, which possibly may be in contradiction with the current belief. We propose a new quantitative BC framework that is based on KMs by defining belief change operators that try to minimise, from an information-theoretic point of view, the surprise that the changed belief carries. To this end, we introduce the principle of minimal surprise. In particular, our contributions are (i) a general information-theoretic approach to KMs for which [1] is a special case; (ii) KM-based BC operators that satisfy the so-called AGM postulates; and (iii) a characterisation of any BC operator that satisfies the AGM postulates as a KM-based BC operator, i.e., any BC operator satisfying the AGM postulates can be encoded within our quantitative BC framework. We also introduce quantitative measures that account for the information loss of contraction, information gain of expansion and information change of revision. We also give a succinct look into the problem of iterated revision, which deals with the application of a sequence of revision operations in our framework, and also illustrate how one may build from our KM-based contraction operator also one not satisfying the (in)famous recovery postulate, by focusing on the so-called severe withdrawal model as an illustrative example.

翻译：知识测度旨在量化知识库所承载的知识/信息量。另一方面，信念变化是指考虑新知识（可能当前信念相矛盾）时对信念进行修正的过程（本文中具体表现为收缩、扩展与修正操作）。我们提出一种基于知识测度的新型定量信念变化框架，通过定义信息论视角下最小化变化后信念所蕴含"意外性"的信念变化算子。为此，我们引入最小意外性原则。具体贡献包括：（1）提出知识测度的一般信息论方法，其中文献[1]为其特例；（2）构建基于知识测度且满足AGM公设的信念变化算子；（3）证明所有满足AGM公设的信念变化算子均可表征为基于知识测度的信念变化算子，即任何满足AGM公设的信念变化算子均可在我们的定量信念变化框架中编码实现。我们还提出用于量化收缩信息损失、扩展信息增益及修正信息变化的定量测度。本文简要探讨迭代修正问题（该问题研究序列修正操作在本框架中的应用），并以严重撤回模型为例，说明如何基于我们的知识测度收缩算子构建不满足（声名狼藉的）恢复公设的替代算子。