The Implication Problem for Functional and Inclusion Dependencies

Abstract

There are two implication problems for functional dependencies and inclusion dependencies: general implication and finite implication. Given a set of dependencies ∑∪{σ}, the problems are to determine whether σ holds in all databases satisfying ∑ or all finite databases satisfying ∑. Contrary to the possibility suggested in [5], there is a natural, complete axiom system for general implication. However, a simple observation shows that both implication problems are recursively unsolvable. It follows that there is no recursively enumerable set of axioms for finite implication.