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Re: equivalence relation

From: Henry Story <henry.story@bblfish.net>
Date: Tue, 8 Feb 2005 19:17:16 +0100
Message-Id: <33601f74c63a24875b492b7a4b2ef740@bblfish.net>
Cc: <semantic-web@w3.org>
To: "Yuzhong Qu" <yzqu@seu.edu.cn>

I suppose the simple solution would be to just write

:relation rdfs:sameAs rdfs:sameAs .

but I just found the place in the spec that mentions this

<http://www.w3.org/TR/owl-ref/#equivalentProperty-def>

I should just say

:relation owl:equivalentProperty rdfs:sameAs .

Thanks for pointing out those interesting quirks concerning
complex properties.

Henry Story


On 7 Feb 2005, at 09:22, Yuzhong Qu wrote:
> 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 Tuesday, 8 February 2005 18:17:33 UTC

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