Abstract: Rough set theory is a mathematical tool to deal with inexactness or uncertainties. As an important branch of rough set theory, rough logic has attracted more and more attention from scholars in this community. The present paper aims to introduce the quantitative approach to the study of rough logic for the first time. The concept of rough truth degree is proposed within the context of a representative rough logic [LR]. Based upon the fundamental notion, the concepts of rough similarity degree and rough distance between any two formulae are also proposed. Correspondingly, the desired rough logic metric space is therefore obtained. Moreover, two kinds of rough reasoning modes within the context of rough logic metric space are proposed. The results obtained in this paper helps to syncretize quantitative logic and rough set theory, which are regarded as two different theories concerning with approximations. It may bring enlightenment to the study of approximate reasoning based on rough set theory.

Key words: rough logic, rough truth degree, rough similarity degree, rough pseudo distance, rough metric space

摘要： 将计量化方法引入到粗糙逻辑的研究当中，在一种典型的粗糙逻辑[LR]中引入了公式的粗糙真度概念。在此基础上，提出了公式之间的粗糙相似度、粗糙伪距离等概念，得到了粗糙逻辑度量空间。在粗糙度量空间中提出了两种不同的粗糙近似推理模式。这一结果实现了粗糙集与计量逻辑学这两种不同的处理近似问题理论的融合，同时对进一步丰富基于粗糙集的近似推理有一定启示。

关键词: 粗糙逻辑, 粗糙真度, 粗糙相似度, 粗糙伪距离, 粗糙度量空间