An Extension of "Representative Instances and γ-Acyclic Relational Schemes"

Let R be a γ-acyclic relational scheme, and let F be the set of functional dependencies (FD´s) embodied in R. Given an existence constrained database r over R, it was shown in [1] that it is possible to connect tuples from different relations in r and construct a universal instance L, possibly containing null values δ, such that the total projection of L onto R yields exactly the set r. Moreover, conditions were given which guarantee that this L would satisfy the functional dependency with nulls (NFD) counterparts of FD´s, in F. The purpose of this note is to generalize the latter result and show that under the same conditions, L actually satisfies NFD counterparts of FD´s in the closure F+ of F.