Multidimensional Numbers and Semantic Numeration Systems:Theoretical Foundation and Application

Abstract

In this article, we present a new class of numeration systems, namely Semantic Numeration Systems. The methodological background and theoretical foundations of such systems are considered. The concepts of abstract entity, entanglement and valence of abstract entities, and the topology of the numeration system are introduced. The proposed classification of semantic numeration systems allows to choose the numeration system depending on the problem being solved. Examples of the use of a two-dimensional number system for image compression problems and computation of a two-dimensional convolution are given.