Process science is a highly interdisciplinary field of research. Despite numerous proposals, process science lacks an adequate understanding of the core concepts of the field, including notions such as process, event, and system. A more systematic framework to cope with process science is mandatory. We suggest such a framework using an example. The framework itself addresses three aspects: architecture, statics, and dynamics. Corresponding formal concepts, based on established scientific theories, together provide an integrated framework for understanding processes in the world. We argue that our foundations have positive implications not only for theoretical research, but also for empirical research, e.g., because hypothesized relationships can be explicitly tested. It is now time to start a discussion about the foundations of our field.