From: Yuzhong Qu <yzqu@seu.edu.cn>

Date: Fri, 11 Feb 2005 18:24:26 +0800

Message-ID: <011101c51023$de0de700$fd0b77ca@xobjects>

To: "Henry Story" <henry.story@bblfish.net>

Cc: "SWIG" <semantic-web@w3.org>

Date: Fri, 11 Feb 2005 18:24:26 +0800

Message-ID: <011101c51023$de0de700$fd0b77ca@xobjects>

To: "Henry Story" <henry.story@bblfish.net>

Cc: "SWIG" <semantic-web@w3.org>

The definition of the quotientOf(p) [denoted as q] as follows: x q y iff there exists z such that x p z and y p z. (suppose p is functional) You can Google it for a more formal definition. Yuzhong Qu ----- Original Message ----- From: "Henry Story" <henry.story@bblfish.net> To: "Yuzhong Qu" <yzqu@seu.edu.cn> Sent: Friday, February 11, 2005 6:05 PM Subject: Re: equivalence relation (quotient relation) > Do you have a link to a good definition of the quotient relation you > are thinking of? > > I was not myself so much interested in the role of the > 'owner' relation in the graph. I had just added it to make > it clearer that there was a simplification that had taken place, > and that relations that had previously applied to _blank, also applied > to <http://bblfish.net/>. This is clearly true if "relation" is just > the identity property, since two identical things have > all the same properties. > > Henry > > > On 11 Feb 2005, at 10:28, Yuzhong Qu wrote: > > > 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 10:24:17 UTC

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