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SM ISO690:2012 SKOBELEV, Volodymyr, IVANOV, Ievgen, NIKITCHENKO, Mykola. Analysis of Nominative Data Sets Structure. In: Workshop on Foundations of Informatics, 24-29 august 2015, Chisinau. Chișinău, Republica Moldova: "VALINEX" SRL, 2015, I, pp. 65-76. ISBN 978-9975-4237-3-1. |
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Workshop on Foundations of Informatics I, 2015 |
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Conferința "Workshop on Foundations of Informatics" Chisinau, Moldova, 24-29 august 2015 | ||||||
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Pag. 65-76 | ||||||
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The paper deals with several mathematical problems associated with a mathematical model of data in computing systems (nominative sets) used in the composition-nominative approach to software system formalization. In this paper the structure of the partially-ordered set of nominative sets is investigated in terms of set theory, lattice theory and algebraic systems theory. To achieve this aim the correct transferring of basic set-theoretic operations to nominative sets is investigated in detail. A basic partially ordered algebraic system intended to provide correct analogues of basic set-theoretic operations for nominative sets is elaborated and its structure is investigated. It is established that this structure is a lower semilattice. Properties of lower and upper cones of subsets of the poset of nominative sets are investigated in detail. Subsets for which upper cones are non-empty are characterized. Closed intervals of nominative sets are examined. Boolean algebra is determined on any such interval. A criterion for isomorphism of two closed intervals is obtained. Maximal closed intervals are investigated. It is established that the poset of nominative sets is a union of isomorphic overlapping maximal closed intervals. |
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Cuvinte-cheie nominative set, nominative data, Set theory, lattice theory, lower semilattice, lower and upper cones, closed intervals, Algebraic system |
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