偏序集上的蕴涵  

The Implication on a Partial Ordered Set

作　　者：张昆龙[1] 孙一康[1] 蒋慎言[2] 

机构地区：[1]北京科技大学信息工程学院 [2]鞍钢集团公司,辽宁鞍山114000

出　　处：《内蒙古大学学报（自然科学版）》2004年第4期364-366,共3页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(批准号:10261003);内蒙古自然科学基金项目(批准号:200208020103)

摘　　要：首先引入偏序集上的基础蕴涵代数和蕴涵代数的概念,得到了偏序集上基础蕴涵代数和蕴涵代数的若干基本性质;给出了偏序集上基础蕴涵代数和蕴涵代数之偏序集的特征刻画,又从格论的角度出发;给出了偏序集上基础蕴涵代数和蕴涵代数之偏序集的一些格的性质以及蕴涵代数之偏序集成为格的一些条件.The concept of a basic implication algebra and an implication algebra on a partial ordered set are obtained by studying the conditions that the implicative operator in a logic system should be satisfied.The basic properties with different conditions and the characterizes of the implication algebra are given. The iff conditions for a basic implication algebra to be a implication algebra are discussed. The relations between the basic implication algebra and the implication algebra are gained. From the view of lattices, some lattice properties of the implication algebra and the conditions under which a implication algebra is a lattice are found.

关 键 词：偏序集 蕴涵 格 

分 类 号：O153.1[理学—数学]