On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages

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2012, First
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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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