L-知识空间与L-蕴含空间的一一对应  

A One-to-one Correspondence between L-knowledge Spaces and L-implicational Spaces

作　　者：李文波 陈桂秀 李生刚[3] 黄秦安[3] 任芳[3] LI Wen-bo;CHEN Gui-xiu;LI Sheng-gang;HUANG Qin-an;REN Fang(College of Mathematics and Statistics,Huizhou University,Huizhou 516007,China;College of Mathematics and Statistics,Qinghai Normal University,Xi'ning 810008.China;College of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710062,China)

机构地区：[1]惠州学院数学与统计学院,广东惠州516007 [2]青海师范大学数学与统计学院,青海西宁810008 [3]陕西师范大学数学与统计学院,陕西西安710062

出　　处：《模糊系统与数学》2021年第5期53-57,共5页Fuzzy Systems and Mathematics

基　　金：青海省应用基础研究项目(2019-ZJ-7078);中央高校基本科研业务费专项资金项目(GK202105007)

摘　　要：用合情推理模式定义了L-知识空间与L-蕴含空间(其中L是具有逆合对应'的完备格),证明了(K(X,L),■)(即X上的L-知识系统的全体)和(I(X,L),■)(即X上的L-蕴含系统的全体)是彼此同构的完备格,并且具体地给出了它们之间的完备格同构。在此基础上,给出了从L-KSp(即L-知识空间及连续映射的范畴)到L-ISp(即L-蕴含空间及保蕴含映射的范畴)的同构函子。推广了已有的有关知识空间与蕴含空间的关系的结果。The notions of l-knowledge space and IL-implicational space are defined,by using thepattern of plausible inference,for L a complete lattice with an order-reversing involution'.It isproved that(K(X,L),■)(the set of all L-knowledge systems)and(I(X,L),■)(the set of all L-implicational systems)are complete lattices which are isomorphic to each other,and the completelattice isomorphism between them is also given.Based on this.an isormorphic functor from L-KSp(thecategory of L-knowledge spaces and continuous mappings)to L-ISp(the category of L-implicationalspaces and implication-preserving mappings)is given.The theorem obtained herein generalizes someresults on relationships between knowledge spaces and implicational spaces.

关 键 词：L-知识空间 L-蕴含空间 完备格同构 同构函子 合情推理 

分 类 号：O189[理学—数学]