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

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