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Re: Reflexivity and antisymmetry uses cases?

From: Evren Sirin <evren@clarkparsia.com>
Date: Sun, 21 Jan 2007 12:05:25 -0500
Message-ID: <45B39D55.7080103@clarkparsia.com>
To: Michael Schneider <m_schnei@gmx.de>
CC: holger@topquadrant.com, public-owl-dev@w3.org

On 1/20/07 9:44 AM, Michael Schneider wrote:
> Holger Knublauch wrote on Wed, 17 Jan 2007:
>>  I don't remember a lot of requests for something
> > like owl:SelfRestriction on our mailing lists.
> And AFAICS, nobody here in this thread has given an example for 
> SelfRestrictions, yet. I thought about it yesterday evening for a 
> while, but could not come up with any serious example. Well, besides 
> this standard toy class of "SelfLovers", wherein property "loves" is 
> thought to behave transitively. ;-)
> It's easier for me to imagine that antisymmetry and ireflexivity could 
> become important, because, in combination with transitivity, I am able 
> to more precisely model all kinds of partial orderings between 
> instances, like e.g. ancestor relationships between people or events, 
> or inclusion relationships like "locatedIn"/"containedIn" between 
> geographical regions.
> But where is the "killer application" for owl11:SelfRestriction?
I'm not sure if you are only referring to SelfRestriction (local 
reflexivity) or ReflexiveProperty (global reflexivity) in general. I 
think it was mentioned earlier that reflexivity is used to describe 
part/whole relationships [1]. I don't know if this would be the "killer 
application" for reflexivity but it is certainly a widely used one. If 
you are asking about why we would want to use SelfRestriction instead of 
ReflexiveProperty then I can give a real-world example explaining this:

One might be inclined to define foaf:knows property to be a 
ReflexiveProperty (similar to your loves example) because you want to 
model that every foaf:Person knows himself/herself. However, adding this 
innocent looking statement to FOAF vocabulary would make concept such as 
foaf:Document, foaf:Organization, foaf:Project unsatisfiable and any 
FOAF description that describes instances of these concepts would end up 
to be inconsistent. The reason is simple: When you say a property is a 
ReflexiveProperty then every individual in the universe should have that 
property. This means if you have an instance of foaf:Document, say 
MyDocument, then we infer that MyDocument knows itself. But the 
domain/range restrictions on foaf:knows says only foaf:Person's can have 
foaf:knows property. Since foaf:Document is disjoint with foaf:Person 
this would be a contradiction. The right thing to do in this case would 
be to use SelfRestriction construct to define a local reflexivity axiom 
for foaf:Person.


[1] http://www.w3.org/2001/sw/BestPractices/OEP/SimplePartWhole/
> Michael
Received on Sunday, 21 January 2007 17:05:35 UTC

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