Chris and Leo, (01)
It's extremely confusing to use technical terms from some system S
when talking about another system in which they are not defined. (02)
CM:
> The central trick here is that, in the semantics of Common Logic,
> classes *have* extensions but are not *identified* with their
> extensions in; this makes it easy to allow a class to be in its
> own extension without any need for non-well-founded set theory.
> Pat used the same idea when he developed the semantics of RDF. (03)
Section 6.2 of IS 24707 defines the CL semantics. That section
does not use the word 'class'. Using the word 'class' in discussing
CL semantics adds more confusion than it could ever clarify. (04)
The CL standard does use the word 'class' in a nontechnical sense
on page vi of the introduction: (05)
"Common Logic has some novel features, chief among them being
a syntax which is signature-free and permits 'higher-order'
constructions such as quantification over classes or relations
while preserving a firstorder model theory, and a semantics
which allows theories to describe intensional entities such
as classes or properties." (06)
The word 'property' is another technical-sounding word that
is not used in CL. (07)
I recommend that the introduction avoid using any technical or
technical-sounding words that are not used in CL itself. Such
terms may be used in an informative passage about using CL to
support other languages, but only when the CL terms and the
technical terms of the other languages are kept distinct. (08)
I suggest that the above sentence be shortened to (09)
"Common Logic has some novel features, chief among them being
a syntax which is signature-free and permits 'higher-order'
constructions such as quantification over relations while
preserving a first-order model theory." (010)
Leo:
> Are classes intensional objects (I guess, like types)? Could
> you point me to where in CL this is discussed? (011)
CM:
> The semantics allows for objects in the class role (more generally, the
> relation role) to be intensional, in the sense that there are CL models
> in which coextensional classes are not identical. (012)
Since CL semantics does not have classes, I suggest that this sentence
be restated: (013)
"CL semantics allows relations to be intensional, in the sense
that there are CL models in which coextensional relations are not
identical. In languages that use the terminology of classes,
a class could be represented by a CL relation. Such a class
could then have intensional identity criteria." (014)
For a discussion of the difference between intensional and extensional
criteria, I recommend Section 2 from Church's book on lambda calculus: (015)
http://www.jfsowa.com/logic/alonzo.htm (016)
John (017)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (018)
|