计量逻辑学中的线性逻辑公式  

Linear logic formulae in the theory of quantitative logic

作　　者：王庆平[1,2] 王国俊[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]聊城大学数学科学学院,山东聊城252059

出　　处：《陕西师范大学学报（自然科学版）》2012年第2期1-5,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10771129;61005046;11171200)

摘　　要：基于密码学中的线性布尔函数概念,在经典逻辑度量空间中提出了线性逻辑公式的概念,给出了n元线性逻辑公式的构造方法.研究了反射变换下线性逻辑公式的性质,证明了所有线性逻辑公式的真度等于1/2,并研究了一类代数次数等于k的布尔函数所对应的逻辑公式的性质,证明了该类公式的真度等于1/2k.Based on the concept of linear Boolean functions in cryptology, the concept of linearlogic formulae in classical logic metric space is proposed. And methods of construction of n-ray linear logic formulae are given. In classical logic metric space, the properties of linear logic formulae under reflexive transformation are studied. It is proved that the truth degrees of all linear logic formulae are equal to 1/2. And properties of some logic formulae induced by Boolean functions of degree equaling to k are studied and it is proved that the truth degrees of these logic formulae are equal to 1/2^k.

关 键 词：布尔函数 线性逻辑公式 真度 反射变换 不动点 

分 类 号：O142[理学—数学]