From: Henry Story <henry.story@bblfish.net>

Date: Mon, 7 Feb 2005 09:02:06 +0100

Message-Id: <e52f0598a254be02e176b916e9f22a81@bblfish.net>

To: semantic-web@w3.org

Date: Mon, 7 Feb 2005 09:02:06 +0100

Message-Id: <e52f0598a254be02e176b916e9f22a81@bblfish.net>

To: semantic-web@w3.org

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_relationReceived on Monday, 7 February 2005 08:02:33 UTC

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