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Converting text into algebra

Search engines *Semantics *Algorithms *Natural Language Processing *
Translation

Algebra and language (writing) are two different learning tools. When they are combined, we can expect new methods of machine understanding to emerge. To determine the meaning (to understand) is to calculate how the part relates to the whole. Modern search algorithms already perform the task of meaning recognition, and Google’s tensor processors perform matrix multiplications (convolutions) necessary in an algebraic approach. At the same time, semantic analysis mainly uses statistical methods. Using statistics in algebra, for instance, when looking for signs of numbers divisibility, would simply be strange. Algebraic apparatus is also useful for interpreting the calculations results when recognizing the meaning of a text.

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Context category

Search engines *Semantics *Algorithms *Natural Language Processing *
Translation

The mathematical model of signed sequences with repetitions (texts) is a multiset. The multiset was defined by D. Knuth in 1969 and later studied in detail by A. B. Petrovsky [1]. The universal property of a multiset is the existence of identical elements. The limiting case of a multiset with unit multiplicities of elements is a set. A set with unit multiplicities corresponding to a multiset is called its generating set or domain. A set with zero multiplicity is an empty set.

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Concordance of sense

Search engines *Semantics *Algorithms *Natural Language Processing *
Translation

In [1,2,3] texts (sign sequences with repetitions) were transformed (coordinated) into algebraic systems using matrix units as word images. Coordinatization is a necessary condition of algebraization of any subject area. Function (arrow) (7) in [1]) is a matrix coordinatization of text. One can perform algebraic operations with words and fragments of matrix texts as with integers, but taking into account the noncommutativity of multiplication of words as matrices. Structurization of texts is reduced to the calculation of ideals and categories of texts in matrix form.

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