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Re: [ontolog-forum] Ontology of Rough Sets

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "doug foxvog" <doug@xxxxxxxxxx>
Date: Fri, 21 Jan 2011 23:22:17 -0500 (EST)
Message-id: <49826.>
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)

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