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A new normal form, namely, object-normal form (ONF), is introduced. It is shown that the existing definitions of the fifth normal form (5NF) are unsatisfactory. The correct definition is given for the first time. The importance of the 5NF is demonstrated. For improving data representation in a database with a 5NF schema, the notion of negating relation is introduced. It serves as a basis for the new normal form, namely, the sixth normal form. Combining requirements of the ONF and other normal forms, new normal forms are defined: the fourth object-normal form, the fifth object-normal form, and the sixth object-normal form. It is shown that the standard order of steps of the normalization procedure should be changed: first, the specific requirements of the fourth normal form should be satisfied, and only then the requirements of the second normal form, and so forth.

The issue of providing a formal justification for the use of fourth normal form (4NF) in relational database design is investigated. The motivation and formal definitions for three goals of database design are presented. These goals are the elimination of: redundancy, key-based update anomalies and fact-based replacement anomalies. It is then shown that, depending on the type of constraints permitted, either Boyce-Codd normal form (BCNF) or 4NF are the exact conditions needed to ensure most of the design goals. However, it is also shown that the conditions required to ensure the absence of a particular class of key-based update anomaly are new normal forms which have not previously been identified. In particular, for the case where the only constraints are functional dependencies (FDs), it is shown that the required normal form is a new normal form that is stronger than third normal form (3NF) yet weaker than BCNF. Similarly, in the more general case where both FD and multivalued dependencies (MVDs) are present, the required normal form is a new normal form that is weaker than 4NF.

In Ref. 8, we introduced a simplifying assumption about entity-relationship diagrams (ERDs), called regularity, and showed that regular ERDs have several desirable properties. One such property is that every relation schema in the ERD's canonical relational scheme can be put into Third Normal Form. We left open there the more basic question: under what conditions would the original relation schemas actually be in Boyce-Codd Normal Form (BCNF)? Since the visible semantics of ERDs determine naturally their associated functional dependencies (fd's), it is important to know when an ERD, as designed, already has this strongest normal form given purely in terms of fd's. We show here a sufficient diagrammatic condition (loop-free) under which a regular ERD will have databases enjoying the benefits of BCNF.