Towards a fundamental theory of modeling discrete systems

Abstract

Modeling is a central concern in both science and engineering. However, we need a new fundamental theory to address the challenges of the digital age. In this paper, we first explain why modeling is fundamental and which challenges must be addressed in the digital world. As a main contribution, we introduce the Heraklit modeling framework as a new approach to modeling. We conclude with some general remarks. Future work will involve the correctness of modeling, the notion of information, and the description of invariance in modeling.

arXiv comment6 pages, 2 figures, author prepared version of final manuscript accepted at the 44th International Conference on Conceptual Modeling, 20-23 October 2025, Poitiers / Futuroscope, France, Workshop on Fundamentals of Conceptual Modeling (FCM)