Representative instances and γ-acyclic relational schemes

In this paper, we study under what conditions will a pairwise inconsistent relational database ≪R,r≫ have a universal/representative instance L. If R is γ-acyclic and r satisfies all existence constraints, then it is possible to construct a universal instance L, using unmarked nulls, whose total projections onto R yield exactly the relations in r. We show that L would actually be a representative instance under a set of functional dependencies if R satisfies the additional mild condition: for any functional dependency X → A where A is a single attribute, whenever XA is contained in two relation schemes R and R´ of R, it follows that R ∩R´ is a relation scheme of R, having X as one of its keys.