RE: >>>>> CORRECTION >> READ ME FIRST <<



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From: Mitch Kokar (kokar@coe.neu.edu)
Date: Mon 09 Sep 2002 - 23:26:05 BST


Joaquin,

>
> > >> 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.


I am not familiar with the 2U document, but it seems to me that in the above
sentence the concept of "semantic domain" does not look like the "semantic
domain" that I know of. In my understanding "semantic domain" is a
mathematical domain - like sets, elements, functions. What is the meaning of
"two elements in a set are equivalent"? In my understanding, equivalence is
a logical concept. So my reading is that what they call "semantic domain" is
actually a syntactic domain. But then again, I did not read the document.

Moreover, I saw Stuart's message. So it looks like this discussion is not
that relevant to 2U. But it is an interesting topic on its own. So thanks
for bringing this up.


==Mitch


>
> 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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