By Brian Henderson-Sellers

Computing as a self-discipline is maturing quickly. even if, with adulthood frequently comes a plethora of subdisciplines, which, as time progresses, can turn into isolationist. The subdisciplines of modelling, metamodelling, ontologies and modelling languages inside software program engineering e.g. have, to a point, developed individually and with none underpinning formalisms.

Introducing set idea as a constant underlying formalism, Brian Henderson-Sellers exhibits how a coherent framework could be built that basically hyperlinks those 4, formerly separate, parts of software program engineering. specifically, he indicates how the incorporation of a foundational ontology will be useful in resolving a few debatable concerns in conceptual modelling, in particular in regards to the perceived adjustments among linguistic metamodelling and ontological metamodelling. An specific attention of domain-specific modelling languages is usually incorporated in his mathematical research of versions, metamodels, ontologies and modelling languages.

This encompassing and special presentation of the state of the art in modelling methods ordinarily goals at researchers in academia and undefined. they're going to locate the principled dialogue of a number of the subdisciplines tremendous worthy, they usually may perhaps make the most the unifying technique as a place to begin for destiny research.

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**Additional resources for On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages**

**Sample text**

E. a model within the M2 layer of Fig. 9. A portion of the UFO is shown in Fig. 6, clearly showing the high-level (metamodel) elements of Entity type, Sortal type and so on. Viewed as class diagrams, and remembering that an ontology is a (specialised) kind of model (Fig. 1), we can seek a relationship between a high-level ontology and a domain ontology. The ontological literature remains somewhat equivocal. For example, Kiryakov et al. (2001), while recognising ‘‘a significant real difference between the two types of ontologies’’ (viz.

49). In addition, a0 in Eq. 48 (the additional abstraction) is the identity function, which means that the mapping is one-to-one. A token model could be said to refer to ‘a model of a model’ and, as noted above, is transitive since a chain of token models is always valid. For type models, a0 is given as C which is the (nontransitive) classification function (Eq. 49), which Kühne (2006a) claims to be a homomorphism, although it seems to have a 1:m cardinality on the mapping. A type model could be said to refer to ‘a model of models’ (a commonly used definition of the term ‘metamodel’).

The corresponding expression for type models is given by qðS; MÞ ! S /t M ð3:4Þ where q is a classification abstraction (Eq. 49). In addition, a0 in Eq. 48 (the additional abstraction) is the identity function, which means that the mapping is one-to-one. A token model could be said to refer to ‘a model of a model’ and, as noted above, is transitive since a chain of token models is always valid. For type models, a0 is given as C which is the (nontransitive) classification function (Eq. 49), which Kühne (2006a) claims to be a homomorphism, although it seems to have a 1:m cardinality on the mapping.