By Brian Henderson-Sellers
Computing as a self-discipline is maturing quickly. despite the fact that, with adulthood frequently comes a plethora of subdisciplines, which, as time progresses, can develop into isolationist. The subdisciplines of modelling, metamodelling, ontologies and modelling languages inside of software program engineering e.g. have, to some extent, advanced individually and with none underpinning formalisms.
Introducing set thought as a constant underlying formalism, Brian Henderson-Sellers exhibits how a coherent framework should be built that basically hyperlinks those 4, formerly separate, parts of software program engineering. particularly, he exhibits how the incorporation of a foundational ontology may be precious in resolving a few arguable matters in conceptual modelling, specially in regards to the perceived modifications among linguistic metamodelling and ontological metamodelling. An particular attention of domain-specific modelling languages can also be integrated in his mathematical research of types, metamodels, ontologies and modelling languages.
This encompassing and unique presentation of the cutting-edge in modelling ways usually goals at researchers in academia and undefined. they are going to locate the principled dialogue of a number of the subdisciplines super important, they usually may perhaps make the most the unifying strategy as a kick off point for destiny research.
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Extra info for On the Mathematics of Modelling, Metamodelling, Ontologies and Modelling Languages
Example text
Classification is expressed as an F-abs abstraction (Eq. 36) whereas generalization is an R-abs abstraction (Eq. 35). Classification refers to the allocation of individuals into a set defined by a set of predicates. Eq. 32 links the extensional and intensional definitions of a set that thus permits an answer to the question whether a specific instance, e, does or does not belong to the set; in other words whether e is classified by concept C. From an extensional viewpoint, we have: e C C , e 2 eðCÞ ð2:49Þ where e(C) is given intensionally by Eq.
Symbol, word) to a sentence that allocates semantics to the syntax (abstract and concrete). e. one word may have multiple meanings. g. Ludewig 2003) stress the importance of abstraction (for example, classification, generalization, aggregation) as important for the creation of models (as shown in Fig. 3). Roughly speaking (Giunchiglia and Walsh 1992), the technique allows one to focus on relevant attributes of the problem whilst discarding those that are ‘irrelevant details’2 (see also, for example, Keet 2007).
However, this differentiation must be identified within the constraints of a specific context—Kühne (2006a, p. 374) notes that a model may play the role of a token model or a type model, perhaps both under two different sets of circumstances. Token models are probably the more common understanding for the concept of ‘model’ (Kühne 2005) although the assertion by Gaševic´ et al. (2007) that RepresentationOf is nontransitive strongly suggests that they assume all models to be type models. For a token model, Kühne (2006a) modifies the model-of notation (Eq.