Towards Simplifying and Formalizing UML Class Diagram Generalization/Specialization Relationship with Mathematical Set Theory

Abstract

The Unified Modeling Language (UML) is considered the de facto standard for object-oriented software model development. This makes it appropriate to be used in academia courses at both the graduate and undergraduate levels of education. Some challenges to using the UML is academia are its large number of model concepts and the imprecise semantic of some of these concepts. These challenges are daunting for students who are being introduced to the UML. One approach that can be taken in teaching UML towards addressing these concerns is to limit the number of UML concepts taught and recognize that students may not be able to develop correct UML system models. This approach leads to research work that develop a limited set of UML model concepts that are fewer in number and have more precise semantics. In this paper, we present a new approach to resolve an aspect of this problem by simplifying the generalization/specialization semantics of the class diagram through the application of mathematical formality to usage of these class diagram concepts. This research work derives a core set of concepts suitable for graduate and undergraduate comprehension of UML modeling and defines more precise semantics for those modeling concepts. The applicable mathematical principles applied in this work are from the domains of set theory and predicate logic. This approach is particularly relevant for the pedagogy of software engineering and the development of software systems that require a high level of reliability.