研究如何让概率信念集在逻辑推理下保持封闭并最小化更新变化。
On Lockean beliefs that are deductively closed and minimal change
- 提出两种信念集逻辑封闭的刻画方式
- 设计最小化修改的概率更新方法
- 适用于需逻辑一致且稳定信念的智能系统
在洛克信念理论的形式框架中，个体信念集由置信度定义，并以概率形式描述。尽管该方法具有长期研究价值，但在信念变迁理论中存在局限性，例如洛克信念集通常不满足经典逻辑推理下的封闭性。本文旨在两方面推进：一方面给出两类信念集逻辑封闭性的刻画；另一方面提出一种概率更新方法，实现最小信念修改，即在容纳新信息的同时仅做最少的信念调整。特别地，展示了如何通过最小修改使信念集具备逻辑封闭性。
原文摘要 · Abstract (English)
Within the formal setting of the Lockean thesis, an agent belief set is defined in terms of degrees of confidence and these are described in probabilistic terms. This approach is of established interest, notwithstanding some limitations that make its use troublesome in some contexts, like, for instance, in belief change theory. Precisely, Lockean belief sets are not generally closed under (classical) logical deduction. The aim of the present paper is twofold: on one side we provide two characterizations of those belief sets that are closed under classical logic deduction, and on the other we propose an approach to probabilistic update that allows us for a minimal revision of those beliefs, i.e., a revision obtained by making the fewest possible changes to the existing belief set while still accommodating the new information. In particular, we show how we can deductively close a belief set via a minimal revision.
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