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 fifth normal form is considered. In the previous works devoted to this problem, attempts to construct systems of the axioms of such dependencies based on inference rules are made. However, while the justification for the consistency (soundness) of the obtained axioms does not cause difficulties, 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. This 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. The 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. The question of the completeness of the formal system based on the presented rules did not find a positive solution. In conclusion, the theoretical and practical significance of the inference rules for the join dependencies is noted.
Highlights
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
While the justi cation for the consistency of the obtained axioms does not cause di culties, the proof of completeness in general has not been satisfactorily resolved. 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
Summary
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. 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. В работе рассматривается обобщение правил вывода зависимостей соединения, которые используются при проектировании схемы базы данных, удовлетворяющей требованиям пятой нормальной формы. Для зависимостей включения получена система правил, которая обобщает существующие системы и при этом имеет меньше ограничений. В работе представлено доказательство выводимости известных систем аксиом из представленных правил вывода. В заключение отмечена теоретическая и практическая значимость правил вывода для зависимостей соединения. Если предположить наличие зависимости соединения ( 1 2, 2 3, 1 3), то в результате декомпозиции отношения [ 1, 2, 3] будет получено три отношения:. Аналогичные зависимости возникают везде, где требуется сопоставить объекты с ограниченным множеством событий в системе
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