Mathematical definition of general systems based on semiotics and set theory

TL;DR

This paper develops a mathematical framework for general systems using semiotics and set theory, clarifying measurement concepts, properties, relations, and system structures.

Contribution

It introduces a novel mathematical definition of general systems grounded in semiotics and set theory, linking measurements, partitions, and system structures.

Findings

Established connections between measurements and partitions.

Defined properties and relations based on partitions and functions.

Presented a structure for general systems, including subsystems and isomorphisms.

Abstract

We clarified the connection between measurements and partitions, and discussed the meaning of semiotics for measurements based on functions. The terms of property and relation quantity were defined by our understanding of partitions and functions. Farther more, we discussed correspondences established between two quantities, and the theorems of complete set based on it. Finally, we presented the structure which can afford the obligation of general system, and also the definitions of subsystem and isomorphism.