均匀逻辑公式的基本性质及其真度的分布

基于密码学中布尔函数的等重性在二值命题逻辑中引入了均匀公式的概念。证明了每个均匀公式的真度都小于或等于1／2, 全体均匀逻辑公式的真度之集在逻辑度量空间中有惟一的聚点0。 研究了均匀逻辑公式的基本性质, 给出了含有同样原子公式的二均匀逻辑公式的析取式真度以及二者之间的相似度的简单计算方法。

Basic properties of uniform logic formulas and distribution of their truth degrees

The equal weight property of Boolean functions in cryptology is introduced in two valued propositional logic and the corresponding definition of uniform logic formulas is proposed. It is proved that truth degrees of uniform logic formulas are less or equal to 1／2. The set consisting of truth degrees of all uniform logic formulas has exactly one limit point zero. Also, basic properties of uniform logic formulas are investigated, and a simple method for computing the truth degree of the disjunction of two uniform logic formulas with the same atoms, as well as the similarity degree of them are obtained。