A New Category of Relations: Combinationally Constrained Relations.

The normalization theory in relational database design is a classical subject investigated in di erent papers. the results of these research works are the stronger normal forms such as 5nf, dknf and 6nf. in these normal forms, there are less anomalies and redundancies, but it does not mean that these stronger normal forms are free of anomalies and redundancies. each normal form discussion is based on a particular constraint. in this paper, we introduce relations which contain a new kind of constraint called combinational constraint. we distinguish two important kinds of this constraints, namely strong and weak. also we classify the combinationally constrained relations as single and multiple. we introduce all kinds of such relations and specify them using their quantitative properties, formally. it can be shown that these relations are in 5nf or 6nf and still they contain redundancies and have some anomalies.