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[protege-owl] Complement Classes

Thomas Russ tar at ISI.EDU
Fri Jan 8 09:06:54 PST 2010

On Jan 7, 2010, at 4:02 PM, Adonis Damian wrote:

> Hi All,
> I trying to figure out how complements and open world reasoning work.
> Here is a simple example:
> I have a
> CalssA
>    ClassAWithName – which should be the individuals of ClassA which  
> have a property “name”
>    ClassAWithoutName – which should be the complement of  
> ClassAWithName – the individuals that don’t have a property “name”
> How should I model ClassAWithName and ClassAWithoutName so  
> individuals with property name will be inferred under  
> ClassAWithName and individuals without property “name” will be  
> inferred under ClassAWithoutName?
> The problem that I see is that if for an individual i_1, the “name"  
> property is not asserted then doesn’t mean the it doesn’t have the  
> “name” property. Meaning that the inference engine doesn’t see that  
> i_1 doesn’t has property name as provable false but only  
> satisfiable false.

You have grasped the situation correctly.

Open world reasoning will always have difficulty with negation (the  
absence of something) and also similarly with maximum cardinality and  
allValuesFrom restrictions.  This is precisely because there could  
always be some other property value that is not known that make it  
impossible to prove the complement (maximum, allValuesFrom).

So the reasoning you will get is generally asymmetric.

   Inference of ClassAWithName will succeed easily.

   Inference of ClassAWithoutName will not happen because of open  
world.  There aren't a lot of solutions, but what you essentially  
have to do is explicitly tell the system that the individual doesn't  
have a name.  Yes, that sort of defeats part of the purpose of  
inference, but you don't really have much of an option with open  
world semantics.  It must be possible to prove that the individual  
CANNOT have a name for it to be inferred as belonging to the  
complement class.

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