# Functional dependency implications, inducing horizontal decompositions

## Abstract

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.

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