$G$-systems and 4E Cognitive Science

TL;DR

This paper introduces $G$-systems, a new class of dynamical systems with coupling, to formalize dependence and causality, aiming to establish mathematical foundations for 4E cognitive science.

Contribution

It defines $G$-systems with coupling, dependence, and causality concepts, and characterizes reducibility, advancing the mathematical framework for 4E cognitive science.

Findings

$G$-systems provide a formal structure for dependence and causality.

Characterization of reducibility in terms of dependence atoms.

Framework supports mathematical foundations for 4E cognitive science.

Abstract

We introduce a class dynamical systems called $G$-systems equipped with a coupling operation. We use $G$-systems to define the notions of dependence (borrowed from dependence logic) and causality (borrowed from Pearl) for dynamical systems. As a converse to coupling we define decomposition or ``reducibility''. We give a characterization of reducibility in terms of the dependence "atom". We do all this with the motivation of developing mathematical foundations for 4E cognitive science, see introductory sections.