Philosophy-Guided Mathematical Formalism for Complex Systems Modelling

Mathematical modelling heavily employs differential equations to describe the macroscopic or global behaviour of systems. The dynamics of complex systems is in contrast more efficiently described by local rules and thus in an algorithmic and local or microscopic manner. The theory of such an approach has to be established still. 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, and concepts from cybernetics. Here, a mathematical formalism is presented to more precisely describe and define the system metamodel of the allagmatic method, further generalising it and extending its reach to a more formal treatment and allowing more theoretical studies. Using the formalism, an example for such a further study is finally provided with mathematical definitions and proofs for model creation and equivalence of cellular automata and artificial neural networks.