- From: Henry Story <henry.story@bblfish.net>
- Date: Mon, 7 Feb 2005 14:57:21 +0100
- To: semantic-web@w3.org
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 Monday, 7 February 2005 13:57:46 UTC