Redundancy Elimination and a New Normal Form for Relational Database Design

The relationship between redundancy elimination and normal forms in relational database design is investigated for the case where the constraints contain functional dependencies (FDs) and arbitrary join dependencies (JDs). Extending previous work on the relationship between fourth normal form (4NF) and redundancy elimination, a general definition of redundancy is proposed which is applicable to any type of relational dependency including arbitrary JDs. It is then shown that redundancy is eliminated if and only if the set of dependencies satisfies a new condition called key-complete normal form (KCNF). KCNF requires that the left-hand side of every FD is a superkey and that for every JD, every attribute in the relation scheme is contained in the union of the components of the JD which are superkeys. It is also shown that KCNF is a strictly weaker condition than projection-join normal form (PJ/NF), the original normal form proposed for JDs.