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Re: equivalence relation

From: Danny Ayers <danny.ayers@gmail.com>
Date: Fri, 11 Feb 2005 11:57:52 +0100
Message-ID: <1f2ed5cd05021102577ac14004@mail.gmail.com>
To: Henry Story <henry.story@bblfish.net>
Cc: semantic-web@w3.org, yzqu@seu.edu.cn

On Fri, 11 Feb 2005 10:59:49 +0100, Henry Story <henry.story@bblfish.net> wrote:

> I don't understand. Why would it have to be that for
> 
> _blank ---relationR--> <http://bblfish.net/>
>    |------owner-------> "Henry Story"
> 
> to entail [1] the graph
> 
> <http://bblfish.net> ----owner----> "Henry Story"
> 
> _blank and <http://bblfish.net/> only need to be in the
> same classes? Is that because you are assuming that elements
> of the same class share all the properties of the class? 

I could be wrong, but the way I read it is that for this specific
case, all that is necessary is for _blank to be in a class X for
which:

forall
[individual in X] ----owner----> "Henry Story"

Generalising from there, if you want _blank to have all the properties
of <http://bblfish.net/> then you'd have _blank being in all the same
classes as <http://bblfish.net/> (possibly an infinite number). This
certainly holds for resources that are the owl:sameAs
<http://bblfish.net/>, but I don't believe it necessary follows from
being in all the same classes that there's an identity relationship
between the individuals. (Although this could be an axiom somewhere in
the small print ;-)

I suspect this falls outside what is covered by RDF/OWL, I think
Yuzhong Qu may have found the right relation with quotient (I found
the ref [1] which sounds about right). I'd guess that the rule that 'X
is member of all same classes as Y' => 'X is Y' would make hard work
for decidability - you'd have to be able to enumerate all the classes.

In practice I would think it would be reasonable to use the identity
to go the other way:

<atom:entry>
    <atom:id rdf:resource="http://bblfish.net/" />
</atom:entry>

<atom:id rdf:type="http://www.w3.org/2002/07/owl#ObjectProperty>
    <owl:equivalentProperty rdf:resource="http://www.w3.org/2002/07/owl#sameAs">
</atom:id>

But I'm sure whether this would still be in OWL DL.

Cheers,
Danny.

[1] http://mathworld.wolfram.com/QuotientSpace.html 

-- 

http://dannyayers.com
Received on Friday, 11 February 2005 10:57:54 UTC

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