Minimal lossless decompositions and some normal forms between 4NF and PJ/NF

Abstract

Two popular textbooks in relational database theory are shown to have the same ‘erroneous’ definition of the project-join normal form (PJ/NF) (‘erroneous’ in the sense that their definition is obviously not what the authors intend). A seemingly natural way to rephrase this definition is to introduce the concept minimal lossless decompositions. This concept is shown to yield a countable family of normal forms lying strictly between 4NF and Fagin's original PJ/NF. It also gives an upper bound on the complexity of join dependencies.