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 (Institute of Problems in Mechanical Engineering RAS, Russia) and Alexander Yakovlevich Fridman (Institute for Informatics and Mathematical Modelling, Kola Science Centre of RAS, Russia)
DOI: 10.4018/978-1-5225-7598-6.ch044

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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