Philosophy-Guided Mathematical Formalism for Complex Systems Modelling

TL;DR

This paper introduces a formal mathematical framework for the allagmatic method, a system modeling approach inspired by philosophy and cybernetics, enabling rigorous analysis and comparison of complex systems like cellular automata and neural networks.

Contribution

It develops a new formalism that generalizes the allagmatic method, facilitating theoretical analysis and formal comparisons of complex system models.

Findings

Mathematical definitions for model creation

Proofs of equivalence between cellular automata and neural networks

Extension of the allagmatic method to a formal theoretical framework

Abstract

We recently presented the so-called allagmatic method, which includes a system metamodel providing a framework for describing, modelling, simulating, and interpreting complex systems. Its development and programming was guided by philosophy, especially by Gilbert Simondon's philosophy of individuation, Alfred North Whitehead's philosophy of organism, and concepts from cybernetics. Here, a mathematical formalism is presented to better describe and define the system metamodel of the allagmatic method, thereby further generalising it and extending its reach to a more formal treatment and allowing more theoretical studies. By using the formalism, an example for such a further study is provided with mathematical definitions and proofs for model creation and equivalence of cellular automata and artificial neural networks.