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>

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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