RE: interpretation of instance and subclass

Hi Bill,

Perhaps the problem is your statement "members of M are *not* also members
of C". Shouldn't that simply be "membership in M does not transitively imply
membership in C"?

Cheers,
David

> -----Original Message-----
> From: www-rdf-interest-request@w3.org [mailto:www-rdf-interest-
> request@w3.org] On Behalf Of Burkett, Bill
> Sent: 13 May 2004 17:48
> To: Benja Fallenstein
> Cc: www-rdf-interest@w3.org
> Subject: RE: interpretation of instance and subclass
> 
> 
> Hello, Benja:
> 
> Thank you very much for the reply and explanation.  Your response helped
> in one respect in that you pointed out that C is also a subclass of C and
> peers of M and m.  A class is a subclass of itself - and I'd forgotten
> this, so you are right.
> 
> However, I still haven't found the clarity of understanding I would really
> like.  Perhaps this discussion has already taken place on different
> semantic web discussion threads and this is the reason I haven't received
> much feedback/input on this subject.  But I would like to press the matter
> a bit more because I still feel there's a fundamental paradox in
> considering a class as a member/instance of AND a subclass of a parent
> class.  And the paradox has to do with the transitivity.
> 
> "(-" = "member of"
> "<" = "subclass of"
> 
> Using my example again:
>   m (- M
>   M (- C
>   M  < C
> 
> The problem I have is an apparent contradiction in the latter two
> statements with respect to m.  As a member of C, members of M are *not*
> also members of C.  As a subclass of C, members of M *are* also members of
> C.  Is this where we find the Incompleteness of our rdf/rdfs
> representational langauge?  Is this an inherent paradox/contradiction that
> we just have to live with?
> 
> You've stressed the importance of a "metaclass", Benja.  Is there some
> aspect of this term that I'm failing to understand in my understanding of
> this situation?
> 
> Bill
> 
> 
> 
> -----Original Message-----
> From: Benja Fallenstein [mailto:b.fallenstein@gmx.de]
> Sent: Saturday, May 08, 2004 2:48 AM
> To: Burkett, Bill
> Cc: www-rdf-interest@w3.org
> Subject: Re: interpretation of instance and subclass
> 
> 
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> 
> I think the part from which all of this follows, and the one that you
> really have to wrap your mind around for the rest to become obvious, is
> that rdfs:Class is an instance of itself. (Of course, the whole thing is
> already obvious to me, so maybe my explanation won't help...)
> 
> Let's look at a normal rdf:type triple:
> 
> ~    prs:timbl   rdf:type   foaf:Person.
> 
> Obviously, we can infer from this triple that foaf:Person must be a class.
> 
> Or as a triple:
> 
> ~    foaf:Person   rdf:type   rdfs:Class.
> 
> But if we apply the same rule again (the object of rdf:type is a class),
> we find that:
> 
> ~    rdfs:Class   rdf:type   rdfs:Class.
> 
> Which makes sense if we see rdfs:Class as 'the kind of thing that can
> appear as the object of an rdf:type triple'...
> 
> So rdfs:Class is both an instance of itself, and a subclass of itself
> (since every class is a subclass of itself). We can call rdfs:Class a
> 'metaclass,' since it is a class of classes.
> 
> With that definition, *any* metaclass must be both--
> 
> - - an instance of rdfs:Class
> 
> ~  (because a 'class of classes' is by definition a class)
> 
> - - a subclass of rdfs:Class
> 
> ~  (because if all members of C are classes, then all its members
> ~  are instances of rdfs:Class, and therefore C is a subclass
> ~  of rdfs:Class)
> 
> The examples you cite are both instances and subclasses of
> rdfs:Class/owl:Class simply because they are metaclasses.
> 
> | Bill Burkett wrote:
> 
> |>A fundamental
> |>problem I'm having is understanding the transtivity of membership.  If
> m is an instance/member
> |>of class M, and M is both an instance/member of and a subclass of
> class C, then transitivity
> |>would state that m is also an instance/member of C (because M is a
> subclassOf C).
> 
> In other words, for the cases we have looked at:
> 
> ~    If M is a metaclass, and m is an instance of M, then m is a class
> ~    (instance of rdfs:Class/owl:Class).
> 
> Sounds sensible.
> 
> |>This would
> |>further imply that since M is also an instance of C, m and M are
> somehow peers as instances of
> |>C - which I find odd and hard to understand/reconcile.
> 
> More: In your examples, m, M, *and C* are peers as instances of C!
> 
> This is because all of m, M, and C are classes. M and C are a special
> kind of class, a metaclass, but they're still classes. So yes, in that
> sense they are 'peers.'
> 
> I find it all obvious ;) ;) ;)
> 
> Dunno if this helps,
> - - Benja
> 
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Received on Thursday, 13 May 2004 16:18:52 UTC