A contribution to the scientific foundations of systems engineering: Solution spaces and requirements

Some researchers have suggested that scientific foundations expressed in a mathematical form are needed to thrust the success of systems engineering as a discipline on its own merit. In order to contribute the development of such systems science, this paper investigates from a foundational standpoint the relationships between stakeholder needs, system requirements, and sets of systems. Various theorems and corollaries are proposed and mathematically proven. The theoretical elements are presented as a foundation for the development of a science for requirements engineering. The proposed foundations are finally tested to mathematically describe, in a rigorous and precise manner, qualities of good requirements, which are otherwise traditionally defined using vague narrative. By showcasing practical examples of the theoretical aspects, the paper is intended to serve as a bridge between practitioners and theorists.