逻辑度量空间

取赋值格为［０，１］，用积分工具引入了公式的真度和相似度的概念，并从而在公式集Ｆ上建立了伪距离，为近似推理提供了一种可能的框架．  

A filled function method for finding a global minimizer of a function of several variables

The concept of a filled function is introduced. We construct a particular filled function and analyze its properties. An algorithm for global minimization is generated based on the concept and properties of the filled function. Some typical examples with 1 to 10 variables are tested and computational results show that in most cases this algorithm works better than the tunneling algorithm. The advantages and disadvantages are analyzed and further research directions are discussed.  

蕴涵格及其Fuzzy拓扑表现定理

以L－Lindenbaum代数为背景，引入了蕴涵格与正则蕴涵格的概念，讨论了其基本性质，引入了Fuzzy蕴涵空间的概念，为点集拓扑学中零维空间概念的推广．建立了正则蕴涵格的Fuzzy蕴涵空间表现定理，以此为基础可以给出著名的Stone表现定理的另一种证明．  

Theory of truth degrees of propositions in two-valued logic

By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.  

Boole代数上的度量结构及其在命题逻辑中的应用

设B是一个Boole代数, Ω是从B到Boole代数{0,1}的全体同态之集,μ是Ω上的概率测度.本文基于μ在B中引入了元素的尺寸概念以及元素对之间的相似度概念,并由此在B上建立了度量结构.作为应用,本文改进了新近提出的命题逻辑中的近似推理理论.  

平移空间的线性结构

本文证明了在平移空间上可利用距离在一定条件下构作出线性结构,引入了次范整线性空间的概念,还证明了平移空间是次范整线性空间当且仅当它的平移群是Abel群.泛函分析学中的有界线性算子定理,Hahn-Banach定理以及共鸣定理都可以移植于次范整线性空间之中.  

R_0-代数[0,1]的子代数与广义重言式

本文是对修正的Kleene系统中广义重言式理论的推广,讨论了R_0-代数[0,1]的各类无限子R_0-代数中的广义重言式,证明了在子R_0-代数E_2中,中存在着可数多个不同的广义重言式。  

关于Dirichlet L-函数的倒数的偶次幂的加权均值

本文利用特征和与三角和的一些恒等式及其估计式与解析方法讨论了Dirichlet L-函数的倒数的偶次幂的加权均值,得到一个均值分布的渐近公式。  

On ideals and congruences in bcc-algebras

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.