Re: equivalence relation

Note that a functional property cannot be specified as being transitive [in OWL DL], it's related to the decidability issue of reasoning in OWL.

The OWL S&AS says:
 
To preserve decidability of reasoning in OWL Lite (and DL), not all properties can have cardinality restrictions placed on them or be specified as functional or inverse-functional. An individual-valued property is complex if 
1/ it is specified as being functional or inverse-functional, 
2/ there is some cardinality restriction that uses it, 
3/ it has an inverse that is complex, or 
4/ it has a super-property that is complex. 
Complex properties cannot be specified as being transitive. 



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 4:02 PM
Subject: equivalence relation


> 
> 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 08:22:09 UTC