Generalization of Typed Inclusion Dependencies with Null Values in Databases

A new type of dependency in databases, which is a generalization of inclusion dependencies, is considered. Traditionally, such dependencies are used in practice to ensure referential integrity. In this case, the constraint is established only between a pair of relations, the first of which is called the main relation, and the second one is the external relation. In practice, referential integrity often needs to be established for a larger number of relations, where several main relations and several external relations participate in the same constraint. This structure corresponds to an ultragraph. Generalized inclusion dependencies that take into account the presence of null values in external relations are justified. The system of axioms is obtained based on a study of the properties of typed dependencies. The consistency (soundness) and completeness of the system are proved.