Evidence-based lean logic profiles for conceptual data modelling languages

Abstract: Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies simultaneously for all three modelling language families as unifying mechanism. This hampers interchangeability, interoperability, and tooling support. In addition, due to the lack of a systematic design process of the logic used for the formalisation, hidden choices permeate the formalisations that have rendered them incompatible. We aim to address these problems, first, by structuring the logic design process in a methodological way. We generalise and extend the DSL design process to apply to logic language design more generally and, in particular, by incorporating an ontological analysis of language features in the process. Second, we specify minimal logic profiles availing of this extended process, including the ontological commitments embedded in the languages, of evidence gathered of language feature usage, and of computational complexity insights from Description Logics (DL). The profiles characterise the essential logic structure needed to handle the semantics of conceptual models, therewith enabling the development of interoperability tools. There is no known DL language that matches exactly the features of those profiles and the common core is small (in the tractable DL $\mathcal{ALNI}$). Although hardly any inconsistencies can be derived with the profiles, it is promising for scalable runtime use of conceptual data models.