可换逻辑的代数语义综述  

A survey of algebraic semantic systems

作　　者：杨小飞 辛小龙 Yang Xiaofei;Xin Xiaolong(College of Business,Xi’an International University,Xi'an 710077,China;School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西安外事学院商学院,陕西西安710077 [2]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2022年第1期59-71,共13页Pure and Applied Mathematics

基　　金：国家自然科学基金(11971384).

摘　　要：主要介绍九种可换逻辑的语义系统,它们是布尔代数,MV-代数,BL-代数,MTL-代数,剩余格,Hoops,半Hoops,EQ-代数和相等代数,并给出相应的例子.进而结合作者的工作介绍了这些代数系统在概率、格序群和拓扑中的研究进展,同时给出如下看法:布尔代数是经典逻辑;从代数角度讨论了经典逻辑与模糊逻辑的区别.最后给出值得进一步研究的公开问题.Algebraic semantic systems from commutative logics are introduced comprehensively and systematically.They mainly include Boolean algebras,MV-algebras,BL-algebras,MTL-algebras,residuated lattices,hoops,semihoops,EQ-algebras and equality algebras,and the corresponding examples are presented.Combined with our work,the study researches on these algebras are introduced in probabilities,lattice ordered groups and topologies,and some viewpoints are as following:Boolean algebras are classic logics;the differences between classic logics and fuzzy logics are discussed from the algebraic view.Finally some valuable questions are put forward for readers.

关 键 词：逻辑 语义系统 剩余结构 拓扑 格序群 

分 类 号：O153.1[理学—数学]