N-Tuple Algebra as a Unifying System to Process Data and Knowledge

N-Tuple Algebra as a Unifying System to Process Data and Knowledge

Boris Alexandrovich Kulik, Alexander Yakovlevich Fridman
Copyright: © 2019 |Pages: 14
DOI: 10.4018/978-1-5225-7598-6.ch044
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Abstract

Information technologies for analysis and processing heterogeneous data often face the necessity to unify representation of such data. To solve this problem, it seems reasonable to search for a universal structure that would allow for reducing different formats of data and knowledge to a single mathematical model with unitized manipulation methods. The concept of relation looks very prospective in this sense. So, with a view to developing a general theory of relations, the authors propose n-tuple algebra (NTA) developed as a theoretical generalization of structures and methods applicable in intelligence systems. NTA allows for formalizing a wide set of logical problems (deductive, abductive and modified reasoning, modeling uncertainties, and so on).
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N-Tuple Algebra: Basics And Features

N-tuple algebra is a mathematical system to deal with arbitrary n-ary relations. In NTA, such relations can be expressed as four types of structures called NTA objects. Every NTA object is immersed into a certain space of attributes. Names of NTA objects contain an identifier followed by a sequence of attributes names in square brackets; these attributes determine the relation diagram in which the NTA object is defined. For example, R[XYZ] denotes an NTA object defined within the space of attributes

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