Guaranteeing no interaction between functional dependencies and tree-like inclusion dependencies

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. A given set of FDs does not interact with a given set of INDs if logical implication of any FD can be determined solely by the given set of FDs, and logical implication of any IND can be determined solely by the given set of INDs. The set of tree-like INDs constitutes a useful subclass of INDs whose implication problem is polynomial time decidable. We exhibit a necessary and sufficient condition for a set of FDs and tree-like INDs not to interact; this condition can be tested in polynomial time.