On Fri, January 21, 2011 12:18, Christopher Menzel said:
> On Jan 21, 2011, at 9:46 AM, doug foxvog wrote:
>> ...
>> A standard distinction between a set and a class, is that membership in
>> a [set] cannot change, while membership in a class can.
>
> I think it's useful to distinguish two claims when it comes to the
> identity conditions of classes:
>
> (1) Classes are not extensional (i.e., distinct classes can have the same
> members/instances)
>
> (2) Classes can change their membership.
>
> In the formal semantics of a number of KR languages, (1) is true but,
> strictly speaking at least, (2) is not. (01)
Ontology ALWAYS comes up against the problem that the same word is used
with different meanings. Meriam-Webster's 11th edition has 24 definitions
for "set" as a noun and 6 for "class" as a noun. (02)
I just said that this was A standard distinction, not that the word "class"
was not used in other ways. (03)
> Notably, classes in OWL are
> explicitly non-extensional: since a class is stipulated only to *have* an
> extension in OWL's formal semantics, nothing prevents distinct classes
> from having the same extension. The same is true of RDF. (04)
Agreed. (05)
> However, simply
> because there is no formal notion of change built into OWL's semantics,
> there is no possibility, within a given interpretation, that a class
> change its membership. (06)
The restriction here, "within a given interpretation", places the
restriction of unchangability on the class. A class can change its
membership from one interpretation to another merely with the addition
or removal of statements. (07)
> As noted in an earlier message in this thread,
> without augmenting the notion of an OWL interpretation somehow, change can
> only be represented formally in terms of something like a series of
> interpretations that are thought of as temporally ordered. (08)
Fine, for change that is thought of as temporal change. For change that
is spatial/jurisdictional, the different interpretations need not be
temporally ordered. Such change allows for membership in a class to
change, so I don't think that is an argument that membership in a class
can not change. (09)
> That said, (2)
> does seem to be a strong *intuitive* idea in the KR, AI, and database
> communities. (010)
This is the meaning i was referring to. (011)
The next comment deals with the meaning of "class" in a set theoretical
context. This is a different meaning of "class" than the ontological
context uses. (012)
> Finally, the idea that sets are extensional and classes are not is
> definitely not standard among logicians and mathematicians, who typically
> associate the notion of class with theories like VNBG, wherein both
> classes and sets are extensional. (013)
My understanding is that NBG's principle of class comprehension is
predicative. Since it is a set theory, the defining predicates of the
class are static, and thus an NBG class would have static membership. (014)
-- doug f (015)
> -chris (016)
=============================================================
doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (017)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
============================================================= (018)
_________________________________________________________________
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 (019)
|