Architecture, Analysis, and Design of Systems Using Extensions of Category Theory

Abstract

The engineering of systems has lacked the scientific and mathematical underpinnings enjoyed by traditional engineering disciplines. Earlier work of the authors formulated advanced mathematical methods for architecture definition and the use of model theory in engineering. In this article, an extension of the category of relations is defined by a semantically richer algebraic logic, denoted as CoR, suitable for analysis and design. This complements and extends the rigorous basis for our earlier work. CoR uses category theory coupled with the semantically richer logic as an architectural language for specifying structural views of concepts with concordant graphical and algebraic relational views for analysis and design. A radar case study is used to demonstrate methods for the application of these views to everyday engineering practice. CoR also addresses and can improve the expressiveness of modeling languages, such as SysMLv2. Schemata are defined to provide mathematical blueprints of the views. The intent is that CoR can be implemented in systems tools that are well-suited for engineering practitioners. This article offers a rigorous but practical platform for establishing a new generation of systems engineering methodologies, tools, and languages.