Abstract: The concepts of [ξ-]conditional truth degree of formulas and [ξ-]conditional opening degree of a theory are introduced in [n-]valued Lukasiewicz propositional logical system. Some basic properties of [ξ-]conditional truth degree are studied. It is proved that the set of atomic formulas is not totally [ξ-]conditional opening. It is totally [ξ-]conditional opening or not is decided by the randomized probability distribution.

Key words: randomized truth degree, ξ-conditional truth degree, ξ-conditional opening degree

摘要： 在[n]值Lukasiewicz命题逻辑系统中引入公式的[ξ-]条件真度的概念，引入理论的[ξ-]条件开放度的概念，得到了[ξ-]条件真度的一些基本性质，证明了全体原子公式之集[S={q1,q2,?}]不是[ξ-]条件全开放的，其是否条件全开放取决于给定的随机概率分布。

关键词: 随机真度, &xi, -条件真度, &xi, -条件开放度