RE: [discussion@2uworks.org] RE: [wg@2uworks.org] 3C + 2U = xP?



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From: Mitch Kokar (kokar@coe.neu.edu)
Date: Tue 10 Sep 2002 - 11:58:40 BST


Tony,

I agree, it's really difficult to figure out in what meaning people use
particular words. Even in your example below, I'm not sure whether "denotes"
is used as a meta-concept or not. But I don't think this is so important. I
think it's more important to just settle the issue of how many kinds of
entities are involved in the explanation of "meaning". I think this was
Joaquin's initial question. And this has been settled. There are three
kinds: symbols (syntactic domain), sets/functions (semantic domain) and the
system itself. The system itself should be "indistinguishable" from the
model (i.e., from the semantic domain). Then the modeller is happy.

==Mitch


> -----Original Message-----
> From: Tony Simons [mailto:A.Simons@dcs.shef.ac.uk]
> Sent: Monday, September 09, 2002 11:51 AM
> To: kokar@coe.neu.edu
> Cc: puml-list@cs.york.ac.uk
> Subject: RE: [discussion@2uworks.org] RE: [wg@2uworks.org] 3C + 2U = xP?
>
>
> Hi Mitch,
>
> > An element of a semantic domain is a *denotation* of an element of the
> > non-logical vocabulary.
>
> -- is a true statement in my vocabulary;
>
> > Conversely, an element of the non-logical vocabulary
> > *denotes* an element of the semantic domain.
>
> -- is a false statement in my vocabulary;  I say that the semantic
>    element "denotes" the non-logical element; or that the non-logical
>    element "is denoted by" the semantic element.
>
> This comes from usage in denotational semantics, where they say
> things like:
>
>   "let [[p]] denote the meaning of program p".
>
> Elsewhere, expressions like [[p]] are deemed equivalent to
> semantic elements from some domain, in the style:
>
>   [[p]] == s
>
> so I infer from this that the semantic elements denote the non-
> logical ones.  But in all fairness, some authors use "denote" in
> different senses, which is quite confusing.
>
> Best,
>
> --Tony
>
>
> >
> >
> >
> > > -----Original Message-----
> > > From: puml-list-request@cs.york.ac.uk
> > > [mailto:puml-list-request@cs.york.ac.uk]On Behalf Of Joaquin Miller
> > > Sent: Saturday, September 07, 2002 4:19 PM
> > > To: Tony Simons
> > > Cc: puml-list@cs.york.ac.uk; wg@2uworks.org; discussion@2uworks.org
> > > Subject: RE: [discussion@2uworks.org] RE: [wg@2uworks.org] 3C
> + 2U = xP?
> > >
> > >
> > > 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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> ==========================================================================
>
> 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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