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Set-theoretic analysis of nominative data. (English) Zbl 1390.68196

Summary: 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.

MSC:

68P01 General topics in the theory of data
03E20 Other classical set theory (including functions, relations, and set algebra)
06A06 Partial orders, general
06A12 Semilattices
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)

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