By Brian Henderson-Sellers

Computing as a self-discipline is maturing swiftly. notwithstanding, 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 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 indicates how a coherent framework should be constructed that in actual fact hyperlinks those 4, formerly separate, parts of software program engineering. particularly, he exhibits how the incorporation of a foundational ontology may be priceless in resolving a few debatable concerns in conceptual modelling, in particular in regards to the perceived changes among linguistic metamodelling and ontological metamodelling. An specific attention of domain-specific modelling languages can be incorporated in his mathematical research of types, metamodels, ontologies and modelling languages.

This encompassing and distinctive presentation of the cutting-edge in modelling techniques customarily goals at researchers in academia and undefined. they are going to locate the principled dialogue of some of the subdisciplines tremendous precious, and so they could make the most the unifying strategy as a kick off point for destiny research.

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

**Example text**

G. Kühne 2009) since they both lose information/detail. 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.

A set of sets is effectively a powerset, or more likely a family of sets that can be described by Eqs. 14 and Book becomes a clabject (Fig. 4). Chapter 5 Ontologies Aßmann et al. (2006, p. 253), quoting Gruber (1993), state that an ontology is a formal specification of a shared conceptualisation. g. Nirenburg 2004; Guizzardi 2005, p. 6; Aßmann et al. 2006, p. 256) but one that is descriptive, domain-relevant and static as opposed to a system-focussed model, which does not require any shared understanding nor does it model the whole of the domain (Fig.

Since Book is now a class, it can be instantiated and create a number of objects, book1, book2, etc. of type Book. e. consider Class not as a set but as a ‘set of sets’, those members (like Book in Fig. 4a) being both instances of Class and also types for their own instances (like book1). A set of sets is effectively a powerset, or more likely a family of sets that can be described by Eqs. 14 and Book becomes a clabject (Fig. 4). Chapter 5 Ontologies Aßmann et al. (2006, p. 253), quoting Gruber (1993), state that an ontology is a formal specification of a shared conceptualisation.