Analysis of Typed Inclusion Dependences with Null Values

Abstract

Null values have become an urgent problem since the creation of the relational data model. The impact of uncertainty affects all types of dependences used in designing and operating a database. This fully applies to inclusion dependences, which are the theoretical basis for referential integrity on the data. Attempts to solve this problem contain inaccuracies in the statement of the problem and its solution. The errors in formulation of the problem can be associated with use in the definition of untyped inclusion dependences, which leads to permutations of the attributes, although, the attributes in database technology are identified by name and not by their place. In addition, linking with the use of inclusion dependences of heterogeneous attributes, even of the same type, is a sign of lost functional dependences and leads to interaction of inclusion dependences and non-trivial functional dependences. Inaccuracies in the solution of the problem are contained in the statements of axioms and proof of their properties, including completeness. In this paper we propose an original solution of this problem only for typed inclusion dependences in the presence of Null values: a new axiom system is proposed, its completeness and soundness are proven. On the basis of inference rules, we developed an algorithm for the construction of a nonredundant set of typed inclusion dependences. The correctness of the algorithm is proven.