Abstract: The concepts of modal truth degree of logic formulae（i.e.，[Δ]truth degree and ΢ truth degree） in modal logic are proposed in this paper.The concept of modal truth degree in a given Kripke model is initially given，then based on this，the concept of （n） modal truth degree is proposed as well.Finally，the modal similarity degree between any two formulae is introduced，and the modal pseudo-metric between any two formulae is therefore derived.Compared with [9]，the results obtained in the present paper embodies the idea of modal connectives[Δ]and ΢，and it provides a kind of approximate reasoning mechanism in modal logic from another standpoint.

Key words: modal logic, （n） modal truth degree, （n） modal similarity degree, （n）modal pseudo-metric, （n）-modal pseudo-metric logic space

摘要： 在模态逻辑中提出了公式的模态真度理论，即Δ真度与΢真度。先给出在一个给定Kripke模型之下的模态真度理论，此后利用均匀概率思想，提出了更为合理的(n)模态真度理论，定义了两公式之间的(n)模态相似度，并由此导出了(n)模态伪距离，得到了相应的模态度量空间。结果同文[9]相比更能体现模态词的思想特点，从而为在模态逻辑中展开近似推理提供一个可能的框架。

关键词: 模态逻辑, (n)模态真度, (n)模态相似度, (n)模态伪距离, (n)模态度量空间