>>>>> CORRECTION >> READ ME FIRST <<



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From: Joaquin Miller (miller@joaquin.net)
Date: Mon 09 Sep 2002 - 15:37:24 BST


Well, if gross errors were embarrassing, that would be.

Of course, 'denotation' does not mean meaning.  Duh! I won't rewrite the 
message, but here is the short form of a message that does not make this 
gross error.  This short form is exactly the same as one part of the 
previous, wrong, message.  I just strike out the nonsense about denotation 
and meaning.

> >> A consequence of the semantic domain design principles is that the 
> semantic domain should not contain equivalences; i.e. all semantic 
> elements denote distinct concepts.

if the verb, 'denotes' connects a UML model element to an element in the 
semantic domain (which seems to be how you and i read it, Mitch), then i 
want to think that the same verb will connect an element in the semantic 
domain to something else further along, not back to something in the UML model.

i understand denotation to be an asymmetric relation.
[ asymmetric: x denotes y implies not (y denotes x) ]

which is why i asked where we could find the concepts that the semantic 
elements denote.




=======  previous, wrong, message ===================

Thanks for weighing in on this Mitch.  And welcome to the club.

I'm not in a position to have an opinion on what is correct usage.  Instead 
i'm in the position of a dictionary maker, trying to find what the usage is 
(the usage of specialists, in this case.)

>I think I can join the club - now I am confused. I am not sure whether my
>interpretation of what you said is correct, but here is what I think about
>denotations.
>
>An element of a semantic domain is a *denotation* of an element of the
>non-logical vocabulary. Conversely, an element of the non-logical vocabulary
>*denotes* an element of the semantic domain.

This fits with what i thought the usage was.  That's reassuring.

So, (i put this out for correction by the 2U authors) in 2U terms,
an element of UML (say class or attribute) denotes an element of the 
semantic domain (say object or slot).
and
an element of the semantic domain (say object or slot) is the denotation of 
an element of UML (say class or attribute),

In model theory terms, the word, if i have this right, would be 
'interpreation:'
an element of the model (semantic domain) is the interpretation of an 
element of the theory (UML).

>If this is what you meant, then we agree and there is no confusion. But 
>I'm not sure.

If this is what everyone means by 'to denote,' then there is no confusion 
about the meaning of that term.

But then i'm still confused about what the draft 2U text means:

> >> A consequence of the semantic domain design principles is that the 
> semantic domain should not contain equivalences; i.e. all semantic 
> elements denote distinct concepts.

if the verb, 'denotes' connects a UML model element to an element in the 
semantic domain (which seems to be how you and i read it, Mitch), then i 
want to think that the same verb will connect an element in the semantic 
domain to something else further along, not back to something in the UML model.

i understand denotation to be an asymmetric relation.
[ asymmetric: x denotes y implies not (y denotes x) ]

which is why i asked where we could find the concepts that the semantic 
elements denote.

======= end of reply =====================

[  Side comment: In a second meaning of 'to denote,' an element of UML 
denotes the meaning of that element.  This is the ordinary English and 
Cambridge Dictionary of Philosophy meaning of denotation.  And so, in this 
second meaning of 'denotation,' the denotation of an element of UML is the 
meaning of that element.  These meanings of 'to denote,' which i claim are 
two, may amount to the same thing in some cases, but in others there can be 
an important distinction between, on the one hand, image under the 
interpretation function in formal semantics and, on the other hand, meaning.
(The formal semantics can certainly serve as a ladder to meaning, but if we 
want to focus on meaning, the ladder is probably best thrown away after it 
has been climbed.)
(On the other hand, if we want to focus on trying to clean up the UML 
specification, (and cleaning it up will certainly help make it easier to 
figure out its meaning), then i expect we will find formal semantics 
extremely useful to keep around.  As long as it is cleanly distinguished 
from meaning.)
Of course, specialists tend to use 'meaning' as a synonym for 'denotation' 
(their specialist meaning of denotation), even when the denotation they 
have in mind is in some formal "universe."  That's fine (in specialist 
discussion), since these specialists know that they mean the specialist 
meaning of 'meaning.'  But perhaps misleading when addressing the laity (me).
But here i insist on beating my horse, and perhaps had better shut up on 
that, because of the danger of this side issue derailing the main 
discussion: where can we find the concepts that semantic elements denote. ]

 > -----Original Message-----
> >
> > That does help, Tony, very much so.  Thanks.
> >
> > I had not realized that 'to denote' was also used to mean 'to be the
> > interpretation of.'  I suppose that's because of my distinction
> > between
> > the range of the interpretation function of formal semantics
> > and
> > the system that the model represents;
> > and because i took 'to denote' in its ordinary dictionary meaning
> > (e.g. Cambridge Dictionary of Philosophy).  As a result
> > of that distinction and that meaning, i would expect 'to denote'
> > to be used
> > with respect to the relation of a model element to what that element
> > represents, not the relation of that element to something in an
> > interpretation (model) of that model (theory).  So i had it all backwards.
> >
> > Probably best to avoid the jargon of the formal semantics trade in the 2U
> > documents.  That's not your problem, or puml's.  I'll suggest it to 2U.
> >
> > It is reassuring to see we share the idea that there are three things,
> > model (theory), system, and interpretation (model).  And at least two
> > essential relations, representation and interpretation (or, as
> > used in the
> > text, denotation).
> >
> > Here is where we part company:
> >
> > >-- well, the meaning of the concepts-as-UML-elements is given in the
> > >semantic domain;  the meaning of the real world/system is more tricky!
> >
> > i would say the meaning of the model elements is found in the system.
> > and that the system has no meaning.
> > (Sure, some things do have meaning.  If statues of the leader are erected
> > in the squares, the statues have a meaning.)
> >
> > that's because i feel the distinction between meaning and formal
> > semantics
> > is central to keeping everything straight.  (and, since experts
> > tend to use
> > 'semantics' to mean formal semantics: i feel the distinction between
> > meaning and semantics is central to keeping everything straight.)
> >
> > the (set-theoretic) semantics of a model element might be some
> > set, but the
> > model element does not mean some set, it means a certain item in
> > the system.
> >
> > or, if we don't want to use 'to mean' in that way, then the appearance of
> > an element in a model does not mean there is a certain set, it
> > means there
> > is to be a certain item in the system.
> >
> > but that is just to explain my frequent confusion.  i don't mean
> > to suggest
> > changes to the technical language used by experts.  i know that 'x means'
> > is often used by experts to mean the image of x under the
> > interpretation is.
> >
> > Again, thanks for the careful elucidation.
> >
> >
> > At 10:17 AM 9/7/2002, Tony Simons wrote:
> > >Hi again,
> > >
> > >Joaquin Miller wrote:
> > >
> > >=====
> > > > > >A consequence of the semantic domain design principles is that the
> > > > > >semantic domain should not contain equivalences; i.e. all semantic
> > > > > >elements denote distinct concepts.
> > >
> > >One possible reading:
> > >    semantic elements are the items in the semantic domain
> > >    the items in the semantic domain denote concepts
> > >=====
> > >
> > >Well I can't really comment on the wording of the 2U document, but I
> > >I read this as meaning that each element in the semantic domain is
> > >unique (not equivalent to any other in the domain) and therefore a
> > >denotation of a distinct element from the UML model.  I don't think
> > >that there's meant to be another level of concepts below the semantic
> > >domain, which somehow explains that domain.  Granted, the wording does
> > >seem a bit fluffy.
> > >
> > >It would have been easier to say:  "Because of the way the semantic
> > >domain is constructed, elements in the domain are unique.  No element
> > >is equivalent to any other."
> > >
> > >This would have avoided introducing "concepts" which seems to be the
> > >source of the confusion.  I haven't seen the full context of the above
> > >statement, but the "concepts" may refer to UML model elements, in which
> > >case I would read this as meaning: "if two model elements are denoted
> > >by different semantic elements, then they are distinct".
> > >
> > >My preferred answers to your questions are therefore:
> > >
> > > >  Which are the concepts that the items in the semantic domain (the
> > > > "semantic elements") denote?
> > >
> > >-- elements from the semantic domain are the denotations (interpretation)
> > >    of UML model elements;  it is reasonable to say that they "denote the
> > >    concepts" (from the model layer above)
> > >
> > > >  Where are those concepts found?
> > >
> > >-- these "concepts" are just ordinary elements of UML models, whose
> > >    meaning is given by the mapping to elements in the semantic domain
> > >
> > > >  What do those concepts denote?
> > >
> > >-- probably not a well-formed question; they model some aspect of the
> > >    software system under consideration, but "denoting" may be the
> > >    wrong term, since the relationship is one of abstraction rather
> > >    than precise characterisation.
> > >
> > > >  Where do we find the meaning of those concepts?
> > >
> > >-- well, the meaning of the concepts-as-UML-elements is given in the
> > >    semantic domain;  the meaning of the real world/system is more
> > >    tricky!
> > >
> > >I hope this helps,
> > >
> > >--Tony
> > >
> > >=================================================================
> > =========
> > >
> > >Dr Anthony J H Simons                   a.simons@dcs.shef.ac.uk
> > >Senior Lecturer in Computer Science     http://www.dcs.shef.ac.uk/~ajhs
> > >Director of Teaching
> > >
> > >Department of Computer Science          tel:  (+44) 114 22 21838
> > >University of Sheffield                 dept: (+44) 114 22 21800
> > >Regent Court, 211 Portobello Street     fax:  (+44) 114 22 21810
> > >SHEFFIELD, S1 4DP                       univ: (+44) 114 22 22000
> > >United Kingdom
> > >
> > >=================================================================
> > =========
> >
> >
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> >
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