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The next paper introduced the concept of projection-join normal form (PJ/NF), also called 5NF. It can be
regarded as the definitive statement of what might be called “classical” normalization theory─i.e., the theory of
nonloss decomposition based on projection as the decomposition operator and natural join as the corresponding
recomposition operator, and the normal forms BCNF, 4NF, and 5NF.
Ronald Fagin: “Normal Forms and Relational Database Operators,” Proc. 1979 ACM SIGMOD
International Conference on Management of Data, Boston, Mass. (May/June 1979).
The next paper presents a sound and complete set of inference rules─in other words, an axiomatization─for
inclusion dependencies (INDs). Note: I'm not aware of any formal treatment anywhere of equality dependencies
(EQDs), which are an important, but in some ways rather trivial, special case.
Marco A. Casanova, Ronald Fagin, and Christos H. Papadimitriou: “Inclusion Dependencies and Their
Interaction with Functional Dependencies,” Proc. 1st ACM SIGACT-SIGMOD Symposium on Principles of
Database Systems, Los Angeles, Calif. (March 1982).
Domain-key normal form is defined in:
Ronald Fagin: “A Normal Form for Relational Databases That Is Based on Domains and Keys,” ACM TODS
6 , No. 3 (September 1981).
6NF is defined in:
C. J. Date, Hugh Darwen, and Nikos A. Lorentzos: Temporal Data and the Relational Model (Morgan
Kaufmann, 2003).
As for orthogonality, the concept was first discussed, though not by that name, in:
C. J. Date and David McGoveran: “A New Database Design Principle,” in C. J. Date, Relational Database
Writings 1991-1994 (Addison-Wesley, 1995); previously published in Database Programming & Design 7 ,
No. 7 (July 1994).
Note, however, that orthogonality as described in the present topic is significantly different from the version
discussed in the foregoing paper. (I accept full responsibility for this state of affairs; although the concept was
originally due to David McGoveran, I wrote the bulk of the referenced paper, and I realize now that I was rather
confused when I did so.)
Stop Press: “Our” redundancy free normal form (see Chapter 13 and Appendix B) has recently been
renamed essential tuple normal form (ETNF). It's described in:
Hugh Darwen, C. J. Date, and Ronald Fagin: “A Normal Form for Preventing Redundant Tuples in
Relational Databases,” Proc. 15th International Conference on Database Theory, Berlin, Germany (March
26th-29th, 2012).
All of the theorems, results, etc. discussed in Chapter 13 in connection with “our” RFNF (now ETNF) are
proved in this paper, but the terminology has been revised somewhat. Let me relate the terminology of the paper to
the terminology of Chapter 13. First of all, let R be a relvar, let r be a value of R , and let t be a tuple in r . Then t is
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