arXiv subjects

Alexander Chunikhin

Publications and source records attributed to Alexander Chunikhin.

5 recordsLinked to original sources

arXiv2026

Non-negative Rational Semantic Numeration Systems

A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The properties of positive rational Semantic Numeration Systems as dynamical systems are formulated and illustrated through analytical and numerical examples. A first attempt at defining partial integer Semantic Numeration Systems is proposed.

cs.LO↗

arXiv2024

Attractors of Parikh mapping iterations

Three types of the Parikh mapping are introduced, namely, alphabetic, alphabetic-basis and basis. Explicit expressions for attractors of the k-th order in bases n >= 8, including countable ones, are found. Properties for the alphabetic, alphabetic-basis and basis Parikh vectors are given at each step of the Parikh mapping. The maximum number of iterations leading to attractors of the k-th order in the basis n is determined.

cs.LO↗

arXiv2022

On Fuzzy Cardinal Semantic Transformations

The concept of fuzzy cardinal semantic transformation as a basis for creating fuzzy semantic numeration systems is introduced in this work. Both fuzziness of the initial data - cardinals of abstract entities - and fuzziness of the parameters of the cardinal semantic operators are considered. We also expressed cardinal semantic transformations for discrete fuzzy numbers and for continuous triangular fuzzy numbers. The principle of formation of the fuzzy common carry in the cardinal semantic operators with multiple inputs is formed.

cs.AI↗

arXiv2021

Fundamentals of Semantic Numeration Systems. Can the Context be Calculated?

This work is the first to propose the concept of a semantic numeration system (SNS) as a certain class of context-based numeration methods. The development of the SNS concept required the introduction of fundamentally new concepts such as a cardinal abstract entity, a cardinal semantic operator, a cardinal abstract object, a numeration space. The main attention is paid to the key elements of semantic numeration systems - cardinal semantic operators. A classification of semantic numeration systems is given.

cs.AI↗

arXiv2011

Polymultisets, Multisuccessors, and Multidimensional Peano Arithmetics

The goal of this paper is introduction of a concept of natural multidimensional numbers and to construct a generalized Peano arithmetic of these multidimensional numbers. For this purpose we define a polymultiset as a special set-like form of m-ary multirelation. In addition, multisuccessor and multipredecessor functions on polymultisets are determined. By introducing Peano-like axioms for natural multidimensional numbers, we build a commutative semiring of 2-numbers .

math.GM↗