  Conceptual modeling is a strongly interdisciplinary field of research.
Although numerous proposals for axiomatic foundations of the main ideas of the
field exist, there is still a lack of understanding main concepts such as
system, process, event, data, and many more. Against the background of the
tremendously gaining importance of digital phenomena, we argue that axiomatic
foundations are needed for our discipline. Besides the general call, we provide
a particular case study using HERAKLIT. This modeling infrastructure
encompasses the architecture, statics, and dynamics of computer-integrated
systems. The case study illustrates how axiomatically well-founded conceptual
models may look like in practice. We argue that axiomatic foundations do not
only have positive effects for theoretical research, but also for empirical
research, because, for instance, assumed axioms can explicitly be tested. It is
now time to spark the discussion on axiomatic foundations of our field.
