Geodesic
Order alteration in a cascade-ordered set
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 15 (2020) no. 2, pp. 96-115.

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The article examines the Partially and Cascade of Ordered Sets (POS and COS) in aspect of the development of algoritms in the Theory of Relational Databases (TRDB). COS expands the notion of POS by including himself a chain of Partial Orders (PO) wich nested into each other. An example of COS is the Sequence of the Derivation (SD) of the Functional Dependence (FD) from a given set of FDs which have two orders of following and of derivation of some FD from others. The need for restructuring arises in cases of repetitions of the FD in SD, which are transformed into their reuse or, in other words, replicas of any FD are replaced by the outgoing from him nesting. The received results can have an independent value in algebra. In the present paper, so-called logic schemes are used for proofs.
Keywords: syllogism, analysis, synthesis, database table, relation, attribute, scheme, key of table, functional dependence, graph, logical scheme, cortege, projection, nesting. 
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L. A. Pomortsev; V. I. Tsurkov. Order alteration in a cascade-ordered set. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 15 (2020) no. 2, pp. 96-115. http://geodesic.mathdoc.fr/item/FSSC_2020_15_2_a1/

[1] Gilbert D., Bernajs P., Foundations of mathematics. Logical calculus and formalization of arithmetic, Nauka Publ., Moscow, 1979 (in Russian)

[2] Gilbert D., Bernajs P., Foundations of mathematics. Proof theory, Nauka Publ., Moscow, 1982 (in Russian)

[3] Kurosh A. G., Lectures on general algebra, Fizmatlit Publ., Moscow, 1962 (in Russian)

[4] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lectures on Graph Theory, Nauka Publ., Moscow, 1990 (in Russian) | MR

[5] Mejer D., The theory of relational databases, Mir Publ., Moscow, 1987 (in Russian)

[6] Pomortsev L. A., “Calculation of moments of ordinal statistics of consecutive sums of symmetrically dependent random variables”, Proceedings of the Moscow Mathematical Society, 46 (1983), 201–242 (in Russian) | MR | Zbl

[7] Pomortsev L. A., “Combinatorial-symmetric analysis of multidimensional random walks”, Discrete mathematics, 3:1 (1991), 21–41 (in Russian) | MR | Zbl

[8] Pomortsev L. A., “Algebraic interpretation of the completeness of the axioms of inference”, Fundamental and Applied Mathematics, 8:1 (2002), 195–219 (in Russian) | MR | Zbl

[9] Pomortsev L. A., “Functional dependency algebras in relational database theory”, Proceedings of the Institute of System Analysis of the Russian Academy of Sciences. Dynamics of inhomogeneous systems, 29:1 (2007), 169–183 (in Russian)

[10] Pomortsev L. A., Tsurkov V. I., “Algebraization of inferring functional dependences in relational databases”, Journal of Computer and Systems Sciences International, 58:2 (2019), 212–228 | DOI | DOI | Zbl

[11] Pomortsev L. A., Tsurkov V. I., “SYNTHESIS AND ANALYSIS OF sequences of output of functional dependencies of tables”, Journal of Computer and Systems Sciences International, 6 (2020), 152–176

[12] Yablonskij S. V., Introduction to Discrete Mathematics, Nauka Publ., Moscow, 1986 (in Russian) | MR

[13] Szpilrajn E., “Sur l'extension de l'ordre partiel”, Fundamenta Mathematicae, 16 (1930), 386–389 | DOI | Zbl