Geodesic
Generalization of typed include dependencies with null values in databases
Modelirovanie i analiz informacionnyh sistem, Tome 30 (2023) no. 3, pp. 192-201

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The paper discusses a new type of dependency in databases, which is a generalization of inclusion dependencies. Traditionally, such dependencies are used in practice to ensure referential integrity. In this case, the restriction is established only between a pair of relations, the first of which is called the main, the second is external. In practice, referential integrity often needs to be established for a larger number of relations, where several main and several external relations participate in the same constraint. Such a structure corresponds to an ultragraph. The paper provides a rationale for generalized inclusion dependencies that take into account the presence of null values in external relations. Based on the study of the properties of typed dependencies, a system of axioms is obtained, for which consistency (soundness) and completeness are proved.
Keywords: database, inclusion dependencies, axiomatics, null values. 
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     author = {S. V. Zykin},
     title = {Generalization of typed include dependencies with null values in databases},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {192--201},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2023_30_3_a0/}
}
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S. V. Zykin. Generalization of typed include dependencies with null values in databases. Modelirovanie i analiz informacionnyh sistem, Tome 30 (2023) no. 3, pp. 192-201. http://geodesic.mathdoc.fr/item/MAIS_2023_30_3_a0/