Functional dependency implications, inducing horizontal decompositions

A new decomposition theory for the Relational Database Model is given. It uses a horizontal decomposition of a relation into two disjoint subrelations, of which the union is the given relation. This horizontal decomposition is based on a new constraint, the functional dependency implication (fdi), which is a partial implication between functional dependencies (fd's). This horizontal decomposition is especially useful for databases which cannot be decomposed vertically (in the classical way) because no (or too few) fd's hold.

The “goals”, conditional-functional dependencies (cfd's) and imposed-functional dependencies (ifd's), introduced in previous work, all are special kinds of fdi's, and so are functional dependencies.

The horizontal decomposition induces another new constraint: the anti-functional dependency (afd), of which the afunctional dependency (ad), introduced in previous work, is a special case. The membership problem is solved for mixed fdi's and afd's, and a complete set of inference rules is given. The inheritance problem, i.e. which dependencies hold in the subrelations (generated by the horizontal decomposition), is shown to be solvable in polynomial time.