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



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From: Tony Simons (A.Simons@dcs.shef.ac.uk)
Date: Mon 09 Sep 2002 - 16:51:11 BST


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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> 
> 
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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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