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Re: equivalence relation (quotient relation)

From: Yuzhong Qu <yzqu@seu.edu.cn>
Date: Fri, 11 Feb 2005 17:28:00 +0800
Message-ID: <00d601c5101b$fb4658a0$fd0b77ca@xobjects>
To: "Henry Story" <henry.story@bblfish.net>
Cc: "SWIG" <semantic-web@w3.org>
 From your Example:
----------------------------------

 _blank ---relation---> <http://bblfish.net/>
   |------owner-------> "Henry Story"

      deduce the graph

   <http://bblfish.net> ----owner----> "Henry Story"

------------------------------------

I think that a "quotient relation" of a property (e.g. "owner") might be what you needed.

Just use the following triple:

:yourRelation rdfs:subPropertyOf  quotientOf(owner)


Note that quotientOf is a mathematical construct, and not yet been supported by OWL DL.

BTW, is there any Description Logic supporting "quotient relation" ?


Yuzhong Qu
Dept.Computer Science & Engineering
Southeast University
Nanjing, China, 210096




----- Original Message ----- 
From: "Henry Story" <henry.story@bblfish.net>
To: <semantic-web@w3.org>
Sent: Monday, February 07, 2005 9:57 PM
Subject: Re: equivalence relation


> 
> I just realized that not everyone may know (including me btw.)
> what I mean by an equivalence relation .
> 
> I think this is the concept I am getting at:
> 
> <http://en.wikipedia.org/wiki/Equivalence_relation>
> 
> Henry Story
> 
> 
> On 7 Feb 2005, at 09:02, Henry Story wrote:
> 
> >
> > I am looking for a way to state that a relation is an equivalence 
> > relation [1]. I want to know this so that I can starting from a graph 
> > such as
> >
> > _blank ---relation---> <http://bblfish.net/>
> >   |------owner-------> "Henry Story"
> >
> > deduce the graph
> >
> > <http://bblfish.net> ----owner----> "Henry Story"
> >
> >
> > My thought was that a relation that is functional, symmetric and 
> > transitive
> >  is just such a relation. Here is how I come to this conclusion.
> >
> > 1) Functional and symmetric
> >
> >  If a relation is functional and symmetric, then it is also
> >  inverse functional. It is a 1 to 1 mapping.
> >
> > 2) If it is functional, inverse functional and symmetric
> >
> >    then for all aRb we also have bRa
> >
> >    this still allows a and b to be different
> >
> > 3) if it is transitive then for any a, b and c, where
> >
> >    [1] aRb
> >    [2] bRc
> >
> >    then
> >
> >    [3] aRc
> >
> >    but since R is symmetric
> >
> >    from [2] bRc we deduce that
> >
> >    [4] cRb
> >
> >     and since R is inverse functional
> >
> >    from  [1] aRb and [4] cRb we deduce that a==c
> >
> >    similarly from [3] aRb, [1] aRc and the functional nature of R
> >    we deduce that c == b.
> >
> >    So a == c and c == b and so a == b.
> >
> > Is this reasoning ok?
> > I was hoping it would be, cause then I can just specify in OWL that 
> > properties
> > are functional, symmetric and transitive if I want them to be 
> > equivalence relations (or is there a shorthand for this)
> >
> > Henry Story
> >
> > [1] http://en.wikipedia.org/wiki/Equivalence_relation

> >
> 
> 
> 
> 
Received on Friday, 11 February 2005 09:27:44 UTC

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