Basics of Intensionalized Data: Presets, Sets, and Nominats

• Main Authors: Mykola Nikitchenko, Alexey Chentsov
• Format: Article
• Language: English
• Published: Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova 2012-10-01
• Series: Computer Science Journal of Moldova
• Subjects: Set theory; alternative set theories; notion intension; intensionality; presets; nominats; computability; intensionalized computability
• Online Access: http://www.math.md/files/csjm/v20-n3/v20-n3-(pp334-365).pdf

In the paper we consider intensional aspects of the notion of data. We advocate an idea that traditional set-theoretic platform should be enhanced with new data structures having explicit intensional component. Among such data we distinguish the notions of preset and nominat. Intuitively, presets may be considered as collections of ``black boxes'', nominats may be considered as collections of ``grey boxes'' in which ``white boxes'' are names and ``black boxes'' are their values, while sets may be treated as collections of ``white boxes''. We describe intensions and properties of the introduced notions. We define operations over such data as functions computable in a special intensionalized sense.