In Pursuit of Unification of Conceptual Models: Sets as Machines

Abstract: Conceptual models as representations of real-world systems are based on diverse techniques in various disciplines but lack a framework that provides multidisciplinary ontological understanding of real-world phenomena. Concurrently, systems complexity has intensified, leading to a rise in developing models using different formalisms and diverse representations even within a single domain. Conceptual models have become larger; languages tend to acquire more features, and it is not unusual to use different modeling languages for different components. This diversity has caused problems with consistency between models and incompatibly with designed systems. Two main solutions have been adopted over the last few years: (1) A currently dominant technology-based solution tries to harmonize or unify models, e.g., unifies EER and UML. This solution would solidify modeling achievements, reaping benefits from huge investments over the last thirty years. (2) A less prevalent solution is to pursuit deeper roots that reveal unifying modeling principles and apparatuses. An example of the second method is a category theory-based approach that utilizes the strengths of the graph and set theory, along with other topological tools. This manuscript is a sequel in a research venture that belongs to the second approach and uses a model called thinging machines (TMs) founded on Stoic ontology and Lupascian logic. TM modeling contests the thesis that there is no universal approach that covers all aspects of an application, and the paper demonstrates that pursuing such universality is anything but a dead-end method. This paper continues in this direction, with emphasis on TM foundation (e.g., existence and subsistence of things) and exemplifies this pursuit by proposing an alternative representation of set theory.