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RE: some x has only y

From: Swanson, Tim <tim.swanson@semanticarts.com>
Date: Wed, 12 Mar 2008 10:52:15 -0600
Message-ID: <51F1B258494D5A4488C95F40E55F35D53E6C10@exchsrvr.semanticarts.local>
To: "Matthew Pocock" <matthew.pocock@ncl.ac.uk>
Cc: <public-owl-dev@w3.org>


> -----Original Message-----
> From: Matthew Pocock [mailto:matthew.pocock@ncl.ac.uk]
> Sent: Wednesday, March 12, 2008 10:33 AM
> 
> > you would not be creating an inconsistency. Instead, you would be
> implying
> > that :BeerDrinkingThatLeadsToKaraoke is an empty class (i.e.
> equivalent to
> > owl:Nothing). At this point, we haven't actually REQUIRED that the
> members
> > of the class exist.
> 
> Hi,
> 
> The model-theoretic structure within which OWL and other DLs are framed
> makes 'consistent' eqivalent to being disjoint from Nothing. So, every
> class
> is either inconsistent, or is capable of having instances. Of course,
> in a
> particular situation, you may not know anything about those existances
> other
> than that it is possible for them to exist. That is, you may have no
> assertions naming any of these individuals in your knowledge-base.
> 

Maybe what I'm trying to get at isn't that same thing that you're talking about. I'm wondering if it's possible to distinguish between a class that may have members and a class that does have members. In your original post, you postulated the following:

>  b1 causes k1 ; b1 instanceof beer ; k1 instanceof karaoke

In this case, the class "beer and causes some karaoke" is known to be non-empty, because the individual b1 belongs to this class. This seems to be an additional step beyond satisfiable, because if an assertion were added to this ontology to make the class unsatisfiable the ontology would be inconsistent.



Consider the following class assertions:

  # Class A is unsatisfiable. It has no members.
  # Class A is PROVABLY equivalent to owl:Nothing
  OWLClass(:ClassA)
  OWLClass(:TestClass)
  EquivalentClasses(:ClassA 
                    ObjectIntersectionOf(:TestClass ObjectComplementOf(:TestClass)))
  
  # Class B is satisfiable. It may have members.
  # Class B is SATISFIABLY equivalent to owl:Nothing
  OWLClass(:ClassB)
  
  # Class C is satisfiable. It does have members.
  # Class C is PROVABLY NOT equivalent to owl:Nothing
  OWLClass(:ClassC)
  Individual(:x)
  ClassAssertion(:x :ClassC)


There is a difference here between class C and class B. If axioms were to be added to the ontology to make class B unsatisfiable, we would still have a consistent ontology. If axioms were to be added to make class C unsatisfiable, then we would have an inconsistent ontology.

What I'm wondering is if it is possible to express this distinction in the absence of an ABox. In my post, I wondered if it could be done like this:

  # Class D is satisfiable. It does have members
  # Class D is PROVABLY NOT equivalent to owl:Nothing
  OWLClass(:ClassD)
  DisjointClasses(:ClassD owl:Nothing)


> The point I was trying to make in my post was that classes like "Beer
> drinking
> that leads to karaoke" probably capture the logic needed,

I don't think they do, because creating the class description does not require that such classes have at least one member. In any case, it is not as strong as your ABox method, which asserts that the class of beer drinking experiences that cause karaoke does indeed have at least one member.



Thanks,

Tim Swanson
Semantic Arts, Inc.
Fort Collins, Colorado
Received on Wednesday, 12 March 2008 16:53:01 GMT

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