A Systems-Theoretical Formalization of Closed Systems

TL;DR

This paper develops a formal systems-theoretic framework for understanding closure in systems, aiming to enhance the formal foundations of systems engineering for intelligent systems.

Contribution

It introduces formal, information-theoretic definitions of closure and a mathematical framework for boundary formation in closed systems, advancing systems engineering theory.

Findings

Defines formal concepts of closure using information theory

Provides a framework for boundary and constraint evaluation

Supports engineering of intelligent systems with closed and open paradigms

Abstract

There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous works, we proposed that closed systems precepts could be used to accomplish a required paradigm shift for the systems engineering of intelligent systems. However, to enable such a shift, formal foundations for closed systems precepts that expand the theory of systems engineering are needed. The concept of closure is a critical concept in the formalism underlying closed systems precepts. In this paper, we provide formal, systems- and information-theoretic definitions of closure to identify and distinguish different types of closed systems. Then, we assert a mathematical framework to evaluate the subjective formation of the boundaries and constraints of such systems. Finally, we argue that engineering an intelligent system can benefit from appropriate closed and open systems paradigms on multiple levels of abstraction of the system. In the main, this framework will provide the necessary fundamentals to aid in systems engineering of intelligent systems.