Dependence structure - Dependence as a binary relation

In systems theory, we often use the concept of dependence. There are severa l research to construct a unified framework for dependence. Mainly, the con cept of dependence is defined with a class of subsets, where the concept of algebraic closure systems is often used. In this paper, we define dependence as a binary relation, which we carl dep endence structure, and develop a similar argument as for the dependence wit h 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 dependen ce 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 sche me is a basis for the dependence structure.