Restructuring and dependencies in databases

Abstract

Let ϕ: ℜ→L be a mapping between databases over (different) schemes R and S. This paper considers the following question. What can we say about dependencies in ϕ(r) if we know dependencies in r ∈ ℜ. It is shown that under some conditions the existence of a sound and complete inference system for ℜ implies the existence of a sound and complete inference system for the triple (ℜ, ϕ, L). In the case of functional dependencies some necessary and sufficient conditions for the existence of a sound and complete inference system for the triple (ℜ, ϕ, L) is obtained. However, these conditions are rather strong. But these conditions could be eliminated if we extend the language for dependencies' description. The so called (untyped) mixed functional dependencies that generalize the functional ones are introduced. For these dependencies a sound and complete inference system D is constructed. Moreover, from the system D and the mapping ϕ a sound and complete inference system for the triple (ℜ, ϕ, L) is obtained.