用量化信念逻辑重新定义信念修正，更贴合哲学直觉。
Study on Quantitative Dynamic Epistemic Logic for Belief Revision
- 引入带程度的信念逻辑 $P$，扩展传统AGM理论表达力。
- 构建动态信念修正逻辑 $P*$，证明其满足核心修正公理。
- 提出新修正函数 $*^0$，更符合信念更新的哲学直觉。
信念修正指个体从不信任某事转变为信任的过程。本文基于Gärdenfors（1998）与Hansson（1999）提出的修正公理，建立在AGM理论基础上。接着介绍van Ditmarsch（2005）提出的模态逻辑 $P$，该逻辑能刻画信念的“确信程度”，比AGM更具表达力。随后在 $P$ 上引入修正算子，形成动态认知逻辑 $P*$，以多种方式建模信念修正过程。本文进一步在 $P*$ 中形式化了AGM公理，并证明相关定理。最后分析 $P*$ 的修正行为是否符合哲学标准，发现van Ditmarsch（2005）提出的函数并不契合AGM的哲学本意；相反，本文提出的函数 $*^0$（受van Benthem, 2007 启发）更准确捕捉这一直觉，并提供了其实现方案。
原文摘要 · Abstract (English)
Belief revision is a process in which an agent begins to believe in something she previously did not. I begin the paper by presenting, based on (Gärdenfors, 1998; Hansson, 1999), postulates for belief revision that constitute the basis of the AGM theory. I will then briefly show the semantics of a modal logic introduced in (van Ditmarsch, 2005), which I call `$P$'. This logic formalizes static epistemic states and has greater expressive power than AGM in doing so because it captures the quantitative notion of "degrees of conviction". The third step is to introduce revision operators on $P$ and, mostly following (van Ditmarsch, 2005), obtain the Dynamic Epistemic Logic (DEL) I call `$P*$'. It models processes of belief revision in several ways. Original results are presented in the following two sections. The first one of these sections revolves around a formalization of AGM postulates within $P*$ by proving some theorems related to the satisfaction of those postulates by revisions defined in $P*$. The last section features an analysis of $P*$'s revisions that go beyond the mere satisfaction of postulates. I compare their formal behavior with respect to some philosophical criteria. At last, I conclude that the functions presented in (van Ditmarsch, 2005) are not good formalizations of the philosophical intuition behind AGM. Instead, it is captured by the function $*^0$ originally defined in this paper (but highly inspired by (van Benthem, 2007)). An implementation of this function is also provided.
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