The Unified Modelling Language (UML) is intended to express complex ideas in an intuitive and easily understood way. It is important because it is widely used in software engineering and other disciplines. Although an official definition document exists, there is much debate over the precise meaning of UML models. ¶ In response, the academic community have put forward many different proposals for formalising UML, but it is not at all obvious how to decide between them. Indeed, given that UML practitioners are inclined to reject formalisms as non-intuitive, it is not even obvious that the definition should be “formal” at all. Rather than searching for yet another formalisation of UML, our main aim is to determine what would constitute a good definition of UML. ¶ The first chapter sets the UML definition problem in a broad context, relating it to work in logic and the philosophy of science. ...