循环描述逻辑系统FL0最大不动点模型的有穷基  

Finite Basis of Implicational System Associated with Finite Models of Description Logic FL0 Under the Greatest Fixed Point Semantics

作　　者：郑添健 侯金宏 张维 王驹[4] ZHENG Tian-jian;HOU Jin-hong;ZHANG Wei;WANG Ju(School of Computer and Information,Qiannan Normal University for Nationalities,Duyun,Guizhou 558000,China;The NO.1 High Middle School of Shanglin Coutry,Nanning 530500,China;School of Mathematics and Statistics,Qiannan Normal University for Nationalities,Duyun,Guizhou 558000,China;School of Computer Science and Information Engineering,Guangxi Normal University,Guilin,Guangxi 541004,China)

机构地区：[1]黔南民族师范学院计算机与信息学院,贵州都匀558000 [2]南宁上林县第一中学,南宁530500 [3]黔南民族师范学院数学与统计学院,贵州都匀558000 [4]广西师范大学计算机科学与信息工程学院,广西桂林541004

出　　处：《计算机科学》2020年第S02期92-96,共5页Computer Science

基　　金：贵州省教育厅自然科学基金项目(黔教科20090047);贵州省科学技术基金资助项目(黔科合J字[2012]2310);黔南民族师范学院一般项目(qnsy2018023)。

摘　　要：描述逻辑和形式概念格都是以概念为基础的形式系统,它们都有各自的优缺点,近年来人们开始将两者结合起来,取长补短。文中将形式概念分析的方法引入描述逻辑,研究了循环描述逻辑系统FL0在最大不动点语义下有限模型的有穷基。在形式概念分析中,属性有限的形式背景都存在Duguenne-Guigues基,文章将循环FL0的最大不动点模型作为描述背景,将FL0概念作为属性,定义了描述背景下的属性蕴含,证明了循环描述逻辑系统FL0的最大不动点模型也存在有穷基底。Description logic and formal concept analysis are two different formalisms based on concept,each has its own advantages and disadvantages.Researchers begin to combine them together recently.In this paper,methods of formal concept analysis are introduced into research in description logic to analyze the finite basis of finite models of FL0 under greatest fixed point semantics.In formal concept analysis,there always exists the Duguenne-Guigues basis as long as the attribute set is finite.The finite model of cyclic FL0 terminology under greatest fixed point semantics is taken as description context,FL0 concept as attribute and implications are defined in this context.It is proved that there exists a finite basis of the finite model,which is also sound and completed.

关 键 词：描述逻辑 形式概念分析 属性探测 有穷基 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]