The hierarchy of normal forms for schema design by decomposition using only projection and join was completed by Fagin in 1979 with his description of projection-join normal form (PJ/NF, also called 5NF) [1]. More than a decade later, many practitioners and database textbooks continue to focus on third normal form (3NF) and Boyce-Codd normal form (BCNF), paying only scant attention to the “higher” fourth normal form (4NF) and PJ/NF. The authors attribute this situation to the fact that 4NF and PJ/NF are defined in terms of multivalued dependencies and join dependencies, relationships that are harder to understand than functional dependencies. The purpose of this work is to give simple conditions, expressed solely in terms of functional dependencies, that are sufficient to guarantee higher normal forms. Their primary results show that (a) if a schema is in 3NF and every key consists of a single attribute, then the schema is also in PJ/NF, and (b) if a schema is in BCNF and any key consists of a single attribute, then the schema is also in 4NF (but not necessarily in PJ/NF).

Although these results will not radically change the way we go about designing databases via decomposition, this paper is a must-read for both database designers and individuals interested in theoretical issues of database design. The results are important to the practitioner because they give a simple, practical way to assure that a BCNF schema is already in 4NF. The results will be equally useful to instructors discussing higher normal forms and to researchers working in the database design field. Lastly, the style of exposition is an excellent example of how a paper can be written to benefit practitioners and theoreticians alike.

Since this paper was intended to have a practical appeal, a review of the relative complexity of two problems of determining whether or not any single attribute in a schema is a key and the more difficult problem of determining whether every key for a schema is composed of a single attribute would have been useful. Otherwise, the paper is self-contained and accessible to anyone familiar with relational database design issues.