Titlebook: On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages; Brian Henderson-Sellers Book 2012 The Author(s) 2012 m

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Ontologies,ed understanding nor does it model the whole of the domain (Fig.?.). It is widely stated that, while an ontology uses an open-world assumption, a model uses a closed-world assumption (e.g. A?mann et al. 2006; Atkinson et al. 2006) although some ontologies are based on a closed-world assumption (e.g. Wang et al. 2006).

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Linking Models, Metamodels, Ontologies and Modelling Languages, This is named, variously, meta-ontology, ontology specification language, foundational ontology or higher level ontology (see Fig.?. and previous discussion). Such a language provides reasoning support not possible in software modelling languages such as UML or ER, which many researchers are tempted to use and/or extend for this purpose.

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Mathematics for Modelling,pings (functions) between pairs of sets–whether such a mapping is one-to-one, onto or both can be critical in understanding many of the ‘problems’ identified in the software engineering modelling literature

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Metamodels,“a metamodel makes statements about what can be expressed in the valid models of a certain modelling language”. It should be stressed that the abstraction needed here is the F-abs kind of abstraction since it creates type rather than token models.

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