Re: Denotation, Meaning (and Humble Pie) (was Re: [])

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From: Andy Evans (
Date: Tue 10 Sep 2002 - 17:20:47 BST


> With regards to Joaquin's discussion over which things denote what
> in UML, I now think it is reasonable to say that:
> 2U UML models denote elements in the 2U semantic domain (in a proper
> *denotational* semantics approach);  the semantic elements are the
> denotations of UML model elements;

And the "denotation of" relationship is precisely what we aim to capture 
via the "of" associations from semantic domain elements to the abstract syntax 
elements in the submissions.

> I now understand from other contributors that the 2U semantic model 
> is itself described in terms of objects and slots, rather than on set
> theory.  If this model is totally describable in its own terms, then
> I guess there only need be three layers:  the real world, the UML
> models and the semantic domains.

Well, there is no fixed point, unless..

> However, in order to bootstrap the novel objects-and-slots semantic
> domain, it may also be appropriate to explain this in some even
> more primitive, but better-understood concrete set-theoretic model.

one bootstraps it in the way you say. Tony Clark has done some of this
work already by defining a 4th layer in terms of a very simple calculus.

> In which case Joaquin would be right in expecting the 2U semantic
> model to be further explained by a fourth level.

Absolutely, but one would probably not want to expose non-mathematicians
to this definition (although someone building a proof tool might well be interested).


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