Semantics *

S.B. Pshenichnikov

The article outlines a new mathematical apparatus for verbal calculations in NLP (natural language processing). Words are embedded not in a real vector space, but in an algebra of extremely sparse matrix units. Calculations become evidence-based and transparent. The example shows forks in calculations that go unnoticed when using traditional approaches, and the result may be unexpected.

The use of IT in Natural Language Processing (NLP) requires standardization of texts, for example, tokenization or lemmatization.

After this, you can try to use mathematics, since it is the highest form of standardization and turns the objects under study into ideal ones, for example, data tables into matrices of elements. Only in the language of matrices can one search for general patterns in data (numbers and texts).

If text is turned into numbers, then in NLP these are first natural numbers for numbering words, which are then embedded into real vectors is irreversible ed in a real vector space.

Perhaps we should not rush to do this but come up with a new type of numbers that is more suitable for NLP than numbers for studying physical phenomena. These are matrix hyperbinary numbers. Hyperbinary numbers are one of the types of hypercomplex numbers.

Hyperbinary numbers have their  own  arithmetic,  and  if  you get used to  it,  it  will  seem  more  familiar  and  simpler  than  Pythagorean arithmetic.

In Decision Support Systems (DSS), the texts are value judgments and a numbered verbal rating scale. Next (as in NLP), the numbers are turned into vectors of real numbers and used as sets of weighted arithmetic average coefficients.

The article is an abstract of my book [1] based on previously presented publications [2], [3], [4], [5]

The published material is in the Appendix of my book [1]

Modern civilization finds itself at a crossroads in which to choose the meaning of life. Because of the development of technology, the majority of the world's population may be "superfluous" - not in demand in the production of values. There is another option, where each person is a supreme value, an absolute individual and can be indispensably useful in the technology of the collective mind.

In the eighties of the last century, the task of creating a scientific field of "collective intelligence" was set. Collective intelligence is defined as the ability of the collective to find solutions to problems more effectively than each participant individually. The right collective mind must be...

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.

We present a guide to name entities in code based on putting naming in perspectives of semantic space, design, and readability. 

The main idea is that naming should not be considered as creation of tags, but as a fundamental part of design process, which implies integral and consistent vocabulary to be used. We discuss naming process and naming formalism from these perspectives and we provide guidelines for practical use.

The work is based on 15 years of experience in engineering work, coding and development management in high-tech industries.

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.

The previous work from ref [1] describes the method of transforming a sign sequence into algebra through an example of a linguistic text. Two other examples of algebraic structuring of texts of a different nature are given to illustrate the method.

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.