Taking the representation relation seriously

Structural vs. Usage definitions

There  are different ways to define a model or a DSL. One is the structural definition and the other one is the usage definition. We may draw these two orthogonal dimensions with the conformance relation between a model and its metamodel and by the representation relation between a model and the system it represents.

Structural vs. Usage definition

The conformance relation between a program and its grammar has been studied in Grammarware for half a century.  The conformance relation between a model and its metamodel is of similar nature and is starting to be understood.

But the problem we have is that the representation relation has practically never been studied seriously as of today. As B. Cantwell Smith puts it:

“What about the [relationship between model and real-world]? The answer, and one of the main points I hope you will take away from this discussion, is that, at this point in intellectual history, we have no theory of this [...] relationship”.

The structural definition answer the question of how a model is organized, of what it is composed, etc. These are important questions, but of course not as important as the usage definition adressing the questions of how a model is or should be used, when it should be used (in which situations), how it should be used, etc.

In order to stress the importance of the usage definition vs. the structural definition, we could do this for any tool that we are using, for example a hammer:

Usage and structural definition of a hammer

Every metamodel is a treaty

There are very narrow relations between DSLs, Metamodels and Ontologies. Many lessons from ontology engineering are of relevance to model-driven engineering. This is why it may be interesting to read a recent paper by Tom Gruber, one of the most influential researcher in ontology engineering. As a matter of fact, Tom Gruber may be considered as one of the founders of modern ontology. He gave the first definition of an ontology that has been quoted since then times and times: “An ontology is a shared formal specification of an abstraction“. As we know, this could as well be taken as a concise defintion for a metamodel.
So, after a long time working in the field, Tom Gruber recently delivered again a new strong message: “Every ontology is a treaty“.

http://www.aiai.ed.ac.uk/~jessicac/psfiles/SIG-SEMIS/issue3-tom-gruber.pdf

In the sometimes hot debates on the the future (or no future) of UML, and particularly UML 2.0, I found this to be an interesting reading.