Abstract
In the study of the relational database model, the vertical decomposition of relations into projections of these relations was emphasized since the introduction in /CODD 72/. The use of vertical decompositions always requires some constraints to be satisfied, for instance a join dependency or a functional dependency, in order to be able to regain the original relation by taking the join of its projections. In /ARDE 80/, /THAL 84/ and AABM 80/ the idea of D. Smith and J. Smith /SMSM 77/, to decompose a relation horizontally into restrictions of these relations, using the union as composition operator, was formalized, using Codd-functional and multivalued dependencies. Such horizontal decompositions /DBPA 83/ are useful in the normalization of schemata in which hidden constraints are involved.
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