On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages
The subdisciplines of modelling, metamodelling, ontologies and modelling languages within software engineering have, to some degree, evolved separately and without any underpinning formalisms. Introducing set theory as a consistent underlying formalism, we show how a coherent framework can be developed that clearly links these four, previously separate, areas of software engineering. In particular, we show how the incorporation of a foundational ontology can be bene?cial in resolving a number of controversial issues in conceptual modelling, especially with regard to the perceived differences between linguistic metamodelling and ontological metamodelling. We also suggest the focus on the modelmetamodel `instantiation linkage can be replaced by a model-modelling language linkage. Consideration of domain-speci?c modelling languages is also included in this mathematical analysis of models, metamodels, ontologies and modelling languages.
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