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

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.