A Generalization of the Inference Rules for Join Dependencies in Databases

Abstract

In this paper a generalisation of the inference rules of the join dependencies that are used in the design of database schemas that meets the requirements of the h normal form is considered. In the previous works devoted to this problem, a empts to construct systems of the axioms of such dependencies based on inference rules are made. However, while the justi cation for the consistency (soundness) of the obtained axioms does not cause di culties, the proof of completeness in general has not been satisfactorily resolved. First of all, this is due to the limitations of the inference rules themselves.is work focuses on two original axiom systems presented in the works of Sciore and Malvestuto. For the inclusion dependencies a system of rules that generalises existing systems and has fewer restrictions has been obtained. e paper presents a proof of the derivability of known systems of axioms from the presented inference rules. In addition, evidence of the consistency (soundness) of these rules is provided. e question of the completeness of the formal system based on the presented rules did not nd a positive solution. In conclusion, the theoretical and practical signi cance of the inference rules for the join dependencies is noted.