Semantic Numeration Systems as Dynamical Systems

TL;DR

This paper models semantic numeration systems as dynamical systems, analyzing how semantic operators influence abstract entities within a mathematical framework, providing equations for different states and emphasizing the importance of the configuration matrix.

Contribution

It introduces a novel approach by representing semantic numeration systems as linear discrete dynamical systems with nonlinear control, highlighting the role of the configuration matrix.

Findings

CAO modeled as a linear discrete dynamical system

State equations derived for stationary and non-stationary cases

Configuration matrix crucial for system behavior

Abstract

The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal abstract object (CAO) formed by them in a certain connectivity topology is proposed to be considered as a linear discrete dynamical system with nonlinear control. Under the assumption of ideal observability, the CAO state equations are provided for both stationary and non-stationary cases. The fundamental role of the configuration matrix, which combines information about the types of cardinal semantic operators in the CAO, their parameters and topology of connectivity, is demonstrated.