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[protege-owl] How to classify individuals with a reasoner (using axioms only at Class level) ?

Thomas Russ tar at ISI.EDU
Mon Aug 24 09:25:51 PDT 2009

On Aug 24, 2009, at 4:58 AM, Chabot Bernard wrote:

> Hello Ronald,
> OK for the OWA : It is true I have I've not stated anything about C1 !

I don't think you quite grasp all of the consequences of the OWA.

> (In fact I'm trying to avoid that - making statement at individuals  
> level - but I don't know if it is possible or not ?)
> In fact I wonder why the combination of those 3 axioms (as necessary  
> and sufficient conditions) doesn't match
> 	• Axiom 1 : "COMPONENT" equivalent to "Component_Linked or  
> Component_NotLinked"
> 	• Axiom 2 : "Component_Linked" equivalent to "COMPONENT and renders  
> some FUNCTION"
> 	• Axiom 3 : "Component_NotLinked" equivalent to "COMPONENT and not  
> Component_Linked"
> If C1 is a "COMPONENT" and it is not a "Component_Linked" ...
> ... it should be a "Component_NotLinked"
> (because "COMPONENT" is the union of the both)
> No ?

No.  Because of open world, it could still be a Component_Linked, but  
you haven't told the system about it yet.

OWA makes it difficult to perform any inferences that involve  
Complement(NOT), or exact or Max cardinalities.  The mere fact that an  
instance is NOT KNOWN to satisfy complement or exact/max cardinality  
restrictions doesn't mean that it DOES NOT satisfy them.  It could  
satisfy them using additional facts that the reasoner has not been told.

So, in order to conclude that something is in the complement of a  
class, it is necessary to prove that it CANNOT be a member of the  
class.  It is not enough that it IS NOT KNOWN to be a member of the  
class.  It must be provable that it is not a member.  Often this means  
that there must be an explicit assertion that it is not a member of  
the class.

> I suppose I"m wrong, but I don't really understand why it doesn't  
> works like that !
> Otherwise, is it possible to add a new axiom (at class level) to  
> have something working as I would expect ?

No.  You can't defeat the open world reasoning with any axioms.

> Or it is definitively impossible without stated something at C1  
> level ?

You have to provide enough additional assertions about the individual  
to enable a positive proof.

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