Partial dependencies in relational databases and their realization

Weakening the functional dependencies introduced by Armstrong the authors get the notion of the partial dependencies defined on the relational databases. They show that the partial dependencies can be characterized by the closure operations of the poset formed by the partial functions on the attributes of the databases. On the other hand, the authors give necessary and sufficient conditions so that for such a closure operation one can find on the given set of attributes a database whose partial dependencies generate the given closure operation. They also investigate some questions about how to realize certain structures related to databases by a database of minimal number of rows, columns or elements.