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Re: asymmetric VS non-symmetric

From: Antoine Zimmermann <antoine.zimmermann@deri.org>
Date: Fri, 31 Jul 2009 15:32:35 +0100
Message-ID: <4A730083.8070409@deri.org>
To: Christine Golbreich <cgolbrei@gmail.com>
CC: W3C OWL Working Group <public-owl-wg@w3.org>
Christine,

What I'm asking for is not a formula. The text is currently saying the 
same thing in a pretty clear way. I am just asking for a clarification, 
in case someone *do not* take a close look at the formal definition and 
wrongly assume that asymmetry is the negation of symmetry.

A sentence like:

"To say that a property is asymmetric is therefore stronger than saying 
the property is not symmetric."

would be enough.

I am raising this point because another person independently understood 
"asymmetric" in the same way I did, and he was puzzled by the formal 
definition which did not coincide with his notion of asymmetry. He was 
understanding this as an error of terminology.

In fact, for non-logicians or non-mathematicians, "asymmetric" is 
usually used as a synonym of "not symmetric". A lot of examples can be 
found in physics, biology, sociology and even in mathematics (asymmetric 
matrix, asymmetric geometric figure, etc).

Regards,
AZ.


Christine Golbreich wrote:
> Initially there were  the mathematical  fomula clarifying these
> features, as I thought it usefeul for users to prevent any
> misunderstanding but I was asked to cut it to shorten the doc
> 
> It's still there in the source code and if wanted I can easily restore it.
> 
>  <!-- An asymmetry axiom means --> - that is
> if the property expression OPE holds between the individuals <span
> class="name">x</span> and <span class="name">y</span>, then it cannot
> hold between <span class="name">y</span> and <span
> class="name">x</span>. <!--, or in mathematical notation, this is:
> 
> &forall;''x'' &forall;''y'' (''x'' OPE ''y'') &rArr; &not; (''y'' OPE ''x'') -->
> 
> cg
> 
> 2009/7/31 Antoine Zimmermann <antoine.zimmermann@deri.org>:
>> Dear all,
>>
>> Until today, I did not look at the semantics of AsymmetricProperty because
>> the word was familiar enough to me to intuitively understand it. I was
>> however wrongly assuming that the word was used to denote non-symmetric.
>> From a linguistic perspective, asymmetry is a lack or absence of symmetry.
>> Some mathematical texts use "asymmetric" to simply mean "not symmetric".
>>
>> I am aware that "asymmetric relation" is often used in mathematics to denote
>> "strongly asymmetric relation", i.e., no pairs of elements are related in a
>> bidirectional (symmetric) way. While it is perfectly ok that OWL2 defines
>> AsymmetricProperties the way it does, I am surprised not to find *any*
>> remark, neither in the formal specs, nor in the UFDs, nor in the mailing
>> list archives, about the fact that AsymmetricProperty is not the complement
>> of SymmetricProperty.
>>
>> I am sure that other people are understanding asymmetry in the same way as I
>> did, so I'd suggest adding a small sentence in the Primer (Sect.6.1 [1]) and
>> NF&R (Sect.2.2.3 [2]) stating that "asymmetric" is not the negation of
>> "symmetric". Since the UFDs are still in LC, this should be addressed
>> somehow.
>>
>> [1]
>> http://www.w3.org/TR/2009/WD-owl2-primer-20090421/#Property_Characteristics
>> [2]
>> http://www.w3.org/TR/2009/WD-owl2-new-features-20090421/#F6:_Reflexive.2C_Irreflexive.2C_and_Asymmetric_Object_Properties
>>
>> Regards,
>> --
>> Antoine Zimmermann
>> Post-doctoral researcher at:
>> Digital Enterprise Research Institute
>> National University of Ireland, Galway
>> IDA Business Park
>> Lower Dangan
>> Galway, Ireland
>> antoine.zimmermann@deri.org
>> http://vmgal34.deri.ie/~antzim/
>>
>>
> 
> 
> 


-- 
Antoine Zimmermann
Post-doctoral researcher at:
Digital Enterprise Research Institute
National University of Ireland, Galway
IDA Business Park
Lower Dangan
Galway, Ireland
antoine.zimmermann@deri.org
http://vmgal34.deri.ie/~antzim/
Received on Friday, 31 July 2009 14:33:16 GMT

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