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.

缺乏系统工程的一些关键基础概念的形式化，其中最近承认的不足之一是系统工程实践对工程智能系统的不足。本文提出在智能系统的系统工程中可以使用封闭系统原则来完成所需的范式转变，然而为了实现这样的转变，需要对封闭系统原则的形式基础进行扩展。封闭性概念是封闭系统原则形式化的关键概念之一。我们提供了封闭性的形式、系统理论和信息理论定义，以识别和区分不同类型的封闭系统。接着，我们使用一个数学框架来评估这些系统的边界和约束的主观形成。最后，我们认为在多个层次的抽象系统上，通过适当的封闭和开放系统范例可以有助于工程化智能系统。总之，这个框架将为智能系统的系统工程提供必要的基础。