The correspondence between the concepts in description logics for contexts and formal concept analysis  

作　　者：MA Yue SUI YueFei CAO CunGen 

机构地区：[1]Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing 100190,China [2]Graduate University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China(Information Sciences)》2012年第5期1106-1122,共17页中国科学（信息科学）（英文版）

基　　金：supported by National High-Tech Research & Development Program of China (Grant No. 2007AA-01Z325);National Natural Science Foundation of China (Grant Nos. 60496326,60573063,60573064,60773059)

摘　　要：Formal concept analysis （FCA） and description logic （DL） are meant to be formalizations of concepts.A formal concept in the former consists of its intent and extent,where the intent is the set of all the attributes shared by each object in the extent of the concept,and the extent is the set of all the objects sharing each property in the intent of the concept.A concept in the latter formalization is simply a concept name,the interpretation of which is a subset of a universe.To consider the correspondence between concepts in both formalizations,a multi-valued formal context must be represented both as a knowledge base and as a model of the DL for contexts,where concepts are decomposed into tuple concepts C,interpreted as a set of tuples and value concepts V,interpreted as a set of attribute-value pairs.We show that there is a difference between the interpretation of concepts R.V /R.C and the Galois connection between the extent/intent of formal concepts in FCA.According to the Galois connection,there should be concepts of the form ＋ R.V and ＋ R.C inter-preted in FCA,and hence the logical language L for DL is extended to be L ＋ together with ＋ as a constructor so that ＋ R.V and ＋ R.C are well-defined concepts.Conversely,according to the interpretation in DL there should be pseudo concepts in FCA so that the interpretation of concepts R.V /R.C is the extent/intent of pseudo concepts.The correspondence between formal concepts and concepts in L ＋,and between pseudo concepts and concepts in L are presented in this paper.Formal concept analysis （FCA） and description logic （DL） are meant to be formalizations of concepts.A formal concept in the former consists of its intent and extent,where the intent is the set of all the attributes shared by each object in the extent of the concept,and the extent is the set of all the objects sharing each property in the intent of the concept.A concept in the latter formalization is simply a concept name,the interpretation of which is a subset of a universe.To consider the correspondence between concepts in both formalizations,a multi-valued formal context must be represented both as a knowledge base and as a model of the DL for contexts,where concepts are decomposed into tuple concepts C,interpreted as a set of tuples and value concepts V,interpreted as a set of attribute-value pairs.We show that there is a difference between the interpretation of concepts R.V /R.C and the Galois connection between the extent/intent of formal concepts in FCA.According to the Galois connection,there should be concepts of the form ＋ R.V and ＋ R.C inter-preted in FCA,and hence the logical language L for DL is extended to be L ＋ together with ＋ as a constructor so that ＋ R.V and ＋ R.C are well-defined concepts.Conversely,according to the interpretation in DL there should be pseudo concepts in FCA so that the interpretation of concepts R.V /R.C is the extent/intent of pseudo concepts.The correspondence between formal concepts and concepts in L ＋,and between pseudo concepts and concepts in L are presented in this paper.

关 键 词：description logic formal concept analysis CONCEPT attribute/role 

分 类 号：TP311.5[自动化与计算机技术—计算机软件与理论] TP18[自动化与计算机技术—计算机科学与技术]