Set-theoretic Analysis of Nominative Data
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vladimir Andrunachievici Institute of Mathematics and Computer Science
2015-11-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | http://www.math.md/files/csjm/v23-n3/v23-n3-(pp270-288).pdf |
| _version_ | 1798040535895638016 |
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| author | Volodymyr G. Skobelev Ievgen Ivanov Mykola Nikitchenko |
| author_facet | Volodymyr G. Skobelev Ievgen Ivanov Mykola Nikitchenko |
| author_sort | Volodymyr G. Skobelev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T22:08:58Z |
| format | Article |
| id | doaj.art-a1ab8ae10c8340c1812f3a76a6bfe283 |
| institution | Directory Open Access Journal |
| issn | 1561-4042 |
| language | English |
| last_indexed | 2024-04-11T22:08:58Z |
| publishDate | 2015-11-01 |
| publisher | Vladimir Andrunachievici Institute of Mathematics and Computer Science |
| record_format | Article |
| series | Computer Science Journal of Moldova |
| spelling | doaj.art-a1ab8ae10c8340c1812f3a76a6bfe2832022-12-22T04:00:36ZengVladimir Andrunachievici Institute of Mathematics and Computer ScienceComputer Science Journal of Moldova1561-40422015-11-01233(69)270288Set-theoretic Analysis of Nominative DataVolodymyr G. Skobelev0Ievgen Ivanov1Mykola Nikitchenko2V.M. Glushkov Institute of Cybernetics of NAS of Ukraine, 40 Glushkova ave., Kyiv, Ukraine, 03187Taras Shevchenko National University of Kyiv, 01601, Kyiv, Volodymyrska st, 60Taras Shevchenko National University of Kyiv, 01601, Kyiv, Volodymyrska st, 60In 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.http://www.math.md/files/csjm/v23-n3/v23-n3-(pp270-288).pdfnominative setnominative dataset theorylattice theoryalgebraic systemlower semilatticelower and upper conesclosed intervals |
| spellingShingle | Volodymyr G. Skobelev Ievgen Ivanov Mykola Nikitchenko Set-theoretic Analysis of Nominative Data Computer Science Journal of Moldova nominative set nominative data set theory lattice theory algebraic system lower semilattice lower and upper cones closed intervals |
| title | Set-theoretic Analysis of Nominative Data |
| title_full | Set-theoretic Analysis of Nominative Data |
| title_fullStr | Set-theoretic Analysis of Nominative Data |
| title_full_unstemmed | Set-theoretic Analysis of Nominative Data |
| title_short | Set-theoretic Analysis of Nominative Data |
| title_sort | set theoretic analysis of nominative data |
| topic | nominative set nominative data set theory lattice theory algebraic system lower semilattice lower and upper cones closed intervals |
| url | http://www.math.md/files/csjm/v23-n3/v23-n3-(pp270-288).pdf |
| work_keys_str_mv | AT volodymyrgskobelev settheoreticanalysisofnominativedata AT ievgenivanov settheoreticanalysisofnominativedata AT mykolanikitchenko settheoreticanalysisofnominativedata |