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Title
Japanese: 
English:Dependence Structure - Dependence as a binary relation 
Author
Japanese: 飯島 淳一, 柴 直樹.  
English: Iijima Junichi, Shiba Naoki.  
Language English 
Journal/Book name
Japanese: 
English:International Journal of General Systems 
Volume, Number, Page Vol. 29    No. 5    pp. 655-670
Published date Oct. 2000 
Publisher
Japanese: 
English: 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL http://dx.doi.org/10.1080/03081070008960968
 
DOI https://doi.org/10.1080/03081070008960968
Abstract In systems theory, we often use the concept of dependence. There are several research to construct a unified framework for dependence. Mainly, the concept of dependence is defined with a dais of subsets, where the concept of algebraic closure systems is often used. In this paper, we define dependence as a binary relation, which we call dependence structure, and develop a similar argument as for the dependence with a class of subsets. And we will clarify a relationship between dependence structure and the usual concept of dependence. We also show what conditions assure the existence of a basis for a dependence structure. The concept of functional dependence in database theory can be represented as a dependence structure and we will show that a key for a relational scheme is a basis for the dependence structure.

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