Normal Forms And Syntactic Completeness Proofs For Functional Independencies

We prove normal form theorems of a complete axiom system for the inference of functional dependencies and independencies in relational databases. We also show that all proofs in our system have a normal form where the application of independency rules is limited to three levels. Our normal form results in a faster proof search engine in deriving consequences of functional independencies. As a result, we get a new construction of an Armstrong relation for a given set of functional dependencies. It is also shown that an Armstrong relation for a set of functional dependencies and independencies do not exist in general, and this generalizes the same result valid under the closed world assumption.