Re: rdfs:subClassOf and metaclasses

From: "pat hayes" <phayes@ai.uwf.edu>:

> By the way, the term 'metaclass' has no exact meaning of which I am
> aware, but I take it that by this term you mean to refer to a certain
> kind of class of classes, is that correct? Ie, a subclass of
> rdfs:Class ?

Yes, I defined that in a footnote.

> Why only pairs?

Well, because subClassOf is a binary relation.  But it doesn't matter
because...

> That is obviously invalid. For example, let www be the class of
> integers less than ten, xxx the class of all integers, yyy the class
> of all finite classes, and zzz the class of all infinite classes.

This is a very convincing counterexample that clearly disposes of my
complaint.  I yield.  :-)

> The
> basic point is that classes may have 'intrinsic' properties (such as
> finitude), which arise from their nature as a class rather than from
> the nature of their members.

Can you expand on this point, perhaps off-line?  (Since this doesn't concern
RDFS any more...)  While the metaclass restriction clearly doesn't apply to
every class, it does makes sense for some subset of them.  What is it that
makes those classes different?  How does UML get away with making the
constraint global?  I need to do some more thinking...

> This is already a consequence of the current closure rules.

(This == subClassOf being reflexive.)  As Arjohn said, I don't believe this
is the case unless the subclass graph already contains a cycle.  Given an
empty RDFS model, can you show how rdfs:Class ends up as a subclass of
itself?

        -- P.

--
  Piotr Kaminski <piotr@ideanest.com> http://www.ideanest.com
  It's the heart afraid of breaking that never learns to dance

Received on Thursday, 11 July 2002 20:32:59 UTC