  We present a framework for studying the concept of independence in a general
context covering database theory, algebra and model theory as special cases. We
show that well-known axioms and rules of independence for making inferences
concerning basic atomic independence statements are complete with respect to a
variety of semantics. Our results show that the uses of independence concepts
in as different areas as database theory, algebra and model theory, can be
completely characterized by the same axioms. We also consider concepts related
to independence, such as dependence.
