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Generalization of Derivation Rules for Join Dependencies in Database

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Abstract

In this paper, we consider a generalization of the derivation rules for join dependencies, which are used in designing a database scheme that satisfies the requirements of the fifth normal form. Attempts to construct systems of axioms of such dependencies based on derivation rules were made in previous works devoted to this problem. However, while the substantiation of the consistency (soundness) of the obtained axioms does not cause difficulties, then a satisfactory solution to prove the completeness in the general case was not obtained. First of all, this is due to the limitations of the derivation rules themselves. Here, we focus on two original axiom systems presented in the Sciore and Malvestuto works. For join dependencies, a system of rules that generalizes existing systems and at the same time has fewer restrictions is obtained. A proof of the derivability of known systems of axioms from the presented derivation rules is present. Besides, evidence of the consistency (soundness) of these rules is provided. A positive solution to the issue of the completeness of the formal system based on the presented rules was not found. In conclusion, the theoretical and practical importance of derivation rules for join dependencies is noted.

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Funding

The research was funded in accordance with the state task of the the Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, project no. FWNF-2022-0016.

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  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. V. Zykin

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  1. S. V. Zykin
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Correspondence to S. V. Zykin.

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Translated by A. Ivanov

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Zykin, S.V. Generalization of Derivation Rules for Join Dependencies in Database. Aut. Control Comp. Sci. 55, 731–737 (2021). https://doi.org/10.3103/S0146411621070191

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