一种基于闭包空间和Scott型信息系统的连续domain的表示方法  

A New Characterization of Continuous Domains Based on Closure Spaces and Scott-type Information Systems

作　　者：贾振华 郭兰坤 甘艳萍 JIA Zhen-hua;GUO Lan-kun;GAN Yan-ping(College of Mathematics and Statistics Hunan Normal University,Changsha 410012,China;Key Laboratory of Computing and Stochastic Mathematics(Hunan Normal University),Ministry of Education,Changsha 410012,China)

机构地区：[1]湖南师范大学数学与统计学院,湖南长沙410012 [2]计算与随机数学教育部重点实验室(湖南师范大学),湖南长沙410012

出　　处：《模糊系统与数学》2020年第6期76-84,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61976089);湖南省自然科学基金优秀青年科学基金资助项目(2019JJ30016);湖湘青年英才支持计划项目(2017RS3030);湖南省教育厅优秀青年项目(16B153)。

摘　　要：概念层次结构的序性质是形式概念分析的研究重点。本文基于对关系相容F-扩张形式背景的研究,提出一种基于闭包空间的Scott型信息系统,为连续domains提供一种新的表示方法。首先,我们基于对关系相容F-扩张形式背景诱导的信息系统的研究,公理化地提出基于闭包的信息系统的概念。然后,利用信息态这一概念,我们证明:任意一个基于闭包的信息系统都可诱导一个连续domain.而且,我们提出F-态射作为基于闭包的信息系统之间的态射,并研究了它的性质。最后,我们建立了基于闭包的信息系统范畴和连续domains范畴之间的等价性。The order-theoretic properties of hierarchical structure of concepts is an important topic in formal concept analysis.In this paper,we provide a new representation of continuous domains by developing a notion of closure-based Scott-type information systems based on the study of relationally consistent F-augmented contexts.Firstly,we investigate the information systems induced by relationally consistent F-augmented contexts and axiomatically introduce the notion of closure-based information systems.Then,by means of the notion of states,we show that every closure-based information system can generate a continuous domain.We also introduce the notion of F-morphisms which serves as the morphisms between closure-based information systems and investigate its properties.Finally,we establish the equivalence between the category of closure-based information systems and that of continuous domains.

关 键 词：形式概念分析 闭包空间 信息系统 连续DOMAIN 范畴等价 

分 类 号：O141[理学—数学]