Set Theory as a Semantic Framework for Object-Oriented Modeling

The author has modeled complex systems in a variety of business contexts, from healthcare to telecoms, using a variant of Z. The notation, like Z itself, is a syntactically sugared form of ZF set theory but it permits the use of weak postconditions -- a small, but crucially important, semantic device. The style of construction is very similar to that employed in Object-Oriented modeling, but it illuminates many dark corners of that paradigm, especially as concerns: composition, (multiple) inheritance, concurrency, invariance, inconsistency, emergence, modalities of interpretation, and the clinical aspects of enterprise modeling. This paper describes some of the author's work-in-progress in these areas, and provides references to several models that have been published.