System-of-systems engineering and related models of engineering design require intertwining of structures, respectively, at least for components in products, engineering and business activities, and people involved in those activities as also specifically connected with production and its management. In this paper we describe the logical machinery of system-of-systems engineering and related models of engineering design in sufficient so as to enable to describe the algebraic foundation of the many-valued logic that is inherent in these systems and structures. We are thus essentially unravelling the hidden and underlying logic of these systems and their related information and process structures, focusing on interaction between elements of the system.