Justification for inclusion dependency normal form

Functional dependencies (FDs) and inclusion dependencies (INDs) are the mos t fundamental integrity constraints that arise in practice in relational da tabases. In this paper, we address the issue of normalization in the presen ce of FDs and INDs and, in particular, the semantic justification for inclu sion Dependency Normal Form (IDNF), a normal form which combines Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. W e show that, as for FDs, in the presence of INDs being free of redundancy i s equivalent to being free of update anomalies. Then, for each of these pro perties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and th e restriction that an FD not be embedded in the righthand side of an IND is common to three of the conditions. However, we also show that, for these t hree goals of database design to be satisfied simultaneously, IDNF is both a necessary and sufficient condition.