IMI/Publicaţii/CSJM/Ediţii/CSJM v.23, n.3 (69), 2015/

Set-theoretic Analysis of Nominative Data

Authors: Volodymyr G. Skobelev, Ievgen Ivanov, Mykola Nikitchenko
Keywords: nominative set, nominative data, set theory, lattice theory, algebraic system, lower semilattice, lower and upper cones, closed intervals.


In the paper we investigate the notion of nominative data that can be considered as a general mathematical model of data used in computing systems. The main attention is paid to flat nominative data called nominative sets. 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 proposed. We investigate a lower semilattice of nominative sets in terms of lower and upper cones, closed and maximal closed intervals of nominative sets. The obtained results can be used in formal software development.

Volodymyr G. Skobelev
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
40 Glushkova ave., Kyiv, Ukraine, 03187
Phone: +38 063 431 86 05

Ievgen Ivanov, Mykola Nikitchenko
Taras Shevchenko National University of Kyiv
01601, Kyiv, Volodymyrska st, 60
Phone: +38044 2590519
E-mail: ,

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