We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more diversity, and (total) independence with the presence of maximum diversity. We show that our theory of dependence and independence covers a variety of dependence concepts, for example the seemingly unrelated concepts of linear dependence in algebra and dependence of variables in logic.

翻译：我们在一个非常笼统的框架内引入依赖和独立的概念,我们使用等级概念来研究依赖和独立。我们用等级概念来研究依赖和独立。我们通过等级来识别(完全)依赖而没有能力创造更多的多样性,和(完全)独立而存在最大的多样性。我们表明,我们的依赖和独立理论包含各种依赖概念,例如代数中的线性依赖概念似乎不相干,逻辑中变量的依赖性概念似乎不相干。