Philosophy-Guided Mathematical Formalism for Complex Systems Modelling
This work offers a formal framework for theoretical studies in complex systems modelling, though it appears incremental as it builds on a previously introduced method.
The authors developed a mathematical formalism for the allagmatic method's system metamodel, which describes and models complex systems, and demonstrated its application by providing mathematical definitions and proofs for creating and equating cellular automata and artificial neural networks.
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.