A Systems-Theoretical Formalization of Closed Systems

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 article, 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 present a high-level overview of the engineering implications stemming from this formalism, with a specific focus on its application in engineering intelligent systems. In the main, this framework lays the groundwork for understanding and applying closed systems precepts in the engineering of complex systems, especially those characterized by high levels of intelligence.