The Logical Operations on Relations, Scales and Concept Lattices
Object-attribute-value-relationships, which are a frequently used data structure to code real-world problems, are formalized via many-valued contexts in Formal Concept Analysis (FCA). The aim of FCA is to explore (formal) concepts from empirical data contexts. A concept of a context consists of two parts: the extent (objects the concept covers) and the intent (attributes describing the concept). From the logical point of view, the intent of each concept is a conjunction of some attributes. Similar to conjunction, negation and disjunction are also important logical operations of attributes or attributevalue pairs, which are common in human language. However, the classical FCA as a mathematical theory of concepts lacks a theory of negation and disjunction. In this paper, we take negation and disjunction into consideration in the process of constructing concepts, and hence obtain the following extended concepts: negative concepts of a context (i.e., a binary relation), negative concepts of a relation with some scales, V-concepts of a relation, V-concepts of a relation with some scales, logical concepts of a relation, and logical concepts of a relation with some scales. Compared with concepts in the classical FCA, the extended concepts mentioned above are more pertinent and more meaningful.
relational databases concept lattices logical operations negation disjunction conjunction
Yuxia Lei Yuefei Sui Cungen Cao
Key Laboratory of Intelligent Information Processing Institute of Computing Technology, Chinese Acad Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Acade
国际会议
Fifth International Conference on Semantics,Knowledge and Grid(第五届语义、知识与网格国际会议 SKG 2009)
珠海
英文
160-167
2009-10-12（万方平台首次上网日期，不代表论文的发表时间）