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Comment about reflexive properties

From: Evren Sirin <evren@cs.umd.edu>
Date: Sun, 02 Oct 2005 00:55:18 -0400
Message-ID: <433F6836.5090404@cs.umd.edu>
To: public-swbp-wg@w3.org

In the "Simple part-whole relations in OWL Ontologies" document there is 
a section named "Representation Pattern 5: Reflexive parts" that has a 
discussion about reflexive properties:

> Logically these classes do not give us reflexivity at all, a reflexive 
> property is one that holds between an object and itself, not between 
> an object and something in the same class (which is, technically, what 
> the |CarPart_reflexive| definition says). It is not possible in OWL to 
> state such a restriction or inference...


I don't quite agree with this last sentence because you can use some 
tricks to make a property reflexive. Assuming that we want the property 
to be reflexive over the whole universe then the following axioms would 
do the job:

ObjectProperty( partOf_reflexive Symmetric Transitive )
SubPropertyOf( partOf_reflexive partOf )
SubClassOf( owl:Thing restriction( partOf_reflexive minCardinality(1) )

These axioms use an anonymous individual to get the partOf relation 
inferred for the individual itself effectively making the property 
reflexive. One might want to define the property reflexive only over the 
instances of a certain class, e.g. the domain of the property. As in 
your example, if we are only interested in car parts then we can change 
the above subclass axiom to define reflexivity only over the instances 
of Car class:

SubClassOf( Car restriction( partOf_reflexive minCardinality(1) )

Of course the property 'partOf_reflexive' should not be used in any 
other axiom or assertion, it is just there to get the semantics right. 
The good thing is that these axioms do not have other side effects for 
the original property 'partOf' and will not make it symmetric or 
transitive if it wasn't explicitly defined so.

I'm not sure if such tricks would be considered as "best practice" but 
seems like an option with the given expressivity. I personally believe 
extending OWL to define reflexive properties would be much more useful, 
such extensions and more are already presented in [1].

Regards,
Evren

[1] Ian Horrocks, Oliver Kutz and Ulrike Sattler. The Irresistible SRIQ. 
In OWL: Experiences and Directions Workshop, 2005, To Appear.

---
Evren Sirin evren@cs.umd.edu
Graduate Research Assistant
Computer Science Department
Univ of Maryland, College Park, MD 20742
Phone: (301) 405-7027, Fax: (301) 405-6707
Received on Sunday, 2 October 2005 04:55:52 UTC

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