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Re: Help needed. Isn't this OWL document inconsistent?

From: Aditya Kalyanpur <swap_adityak@yahoo.com>
Date: Mon, 26 Sep 2005 10:11:39 -0700 (PDT)
Message-ID: <20050926171139.31588.qmail@web52708.mail.yahoo.com>
To: Mekan Ikzain <mekanikzain@gmail.com>, www-rdf-logic@w3.org

--- Mekan Ikzain <mekanikzain@gmail.com> wrote:

> Thanks for the comment!
> Here're what I have learned so far.
> 
> 1) Unsatisfiable concepts in an OWL document do not
> make the document
> inconsistent.
> 2) If an instance of any unsatisfiable concept is
> introduced into the
> document, the document becomes inconsistent.
> 
> Well, any error in the statements? 

That's right. However, it's not the complete picture, 
it's a little trickier :) 

A better way to look at it is: an unsatisfiable
concept cannot have any individuals (in general, a
class is a set of individuals, and an unsatisfiable
class is an empty set). Like in your first MadCow
example, all the axioms in the ontology cause the
class MadCow to *not* possibly have any individuals
because of the contradictory definition of the class
MadCow. However, note that the axioms in the ontology
still hold, i.e., each of them can be made
individually true.

However, an ontology is inconsistent when the axioms
in the ontology itself cannot hold. For example,
suppose I incorrectly define a class Person as:
--
Person
  owl:equivalentTo
    [owl:complementOf Person]
--
and suppose the axiom above is the only axiom in my
ontology, then not only is the Person class
unsatisfiable because it cannot have any instances,
but the ontology itself is inconsistent because the
axiom above cannot be made true in any context. Since,
irrespective of what individuals the class Person
contains, the complementOf Person certainly cannot
contain those individuals, and so the equivalence
relation can never hold. 

Thus, as you can see in the example above, you don't
need an individual to get an inconsistent ontology.
(though now you can probably see why adding an axiom
which asserts that an individual belongs to an
unsatisfiable class, makes the ontology inconsistent.)

Hope this helps,
Aditya

>Quite natural now
> it seems. ;-)

 
> So, the following document contains one
> unsatisfiable concept, a:MadCow.
> 
> @prefix rdfs:
> <http://www.w3.org/2000/01/rdf-schema#>.
> @prefix rdf:
> <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
> @prefix owl: <http://www.w3.org/2002/07/owl#>.
> @prefix a: <http://www.ex.org/2005/ex#>.
> 
> a:Vegetarian
> owl:intersectionOf
> (a:Animal
> [a owl:Restriction;
> owl:onProperty a:eats;
> owl:allValuesFrom a:Plant
> ]
> ).
> a:Plant owl:complementOf a:Animal.
> a:Sheep rdfs:subClassOf a:Vegetarian.
> a:Cow rdfs:subClassOf a:Vegetarian.
> a:MadCow
> owl:intersectionOf
> (a:Cow
> [a owl:Restriction;
> owl:onProperty a:eats;
> owl:someValuesFrom a:Sheep
> ]
> ).
> 
> And, the following document, which contains an
> instance a:MadDolly of
> a:MadCow class, is inconsistent.
> 
> @prefix rdfs:
> <http://www.w3.org/2000/01/rdf-schema#>.
> @prefix rdf:
> <http://www.w3.org/1999/02/22-rdf-syntax-ns#>.
> @prefix owl: <http://www.w3.org/2002/07/owl#>.
> @prefix a: <http://www.ex.org/2005/ex#>.
> 
> a:Vegetarian
> owl:intersectionOf
> (a:Animal
> [a owl:Restriction;
> owl:onProperty a:eats;
> owl:allValuesFrom a:Plant
> ]
> ).
> a:Plant owl:complementOf a:Animal.
> a:Sheep rdfs:subClassOf a:Vegetarian.
> a:Cow rdfs:subClassOf a:Vegetarian.
> a:MadCow
> owl:intersectionOf
> (a:Cow
> [a owl:Restriction;
> owl:onProperty a:eats;
> owl:someValuesFrom a:Sheep
> ]
> ).
> a:MadDolly a a:MadCow.
> 
> Well, hope this helps any novice in OWL. ;-)
> 
> Regards,
> Mekan Ikzain
> 
> On 9/26/05, Peter F. Patel-Schneider
> <pfps@research.bell-labs.com> wrote:
> >
> > One modelling problem in your example is that
> vegetarians are only
> > required to
> > eat at least one thing that is a plant. You
> probably want that everything
> > that
> > vegetarians eat is derived from plants, although
> there is a different
> > problem
> > here for you to spot.
> >
> > The mad cow example has received a lot of
> attention. You might want to
> > look at
> > http://www.mindswap.org/2005/debugging/ for more
> information. There is as
> > well
> > a mad cow ontology from Manchester.
> >
> > Peter F. Patel-Schneider
> > Bell Labs Research
> >
> >
> > From: Mekan Ikzain <mekanikzain@gmail.com>
> > Subject: Help needed. Isn't this OWL document
> inconsistent?
> > Date: Sun, 25 Sep 2005 23:17:25 +0900
> >
> > > Hi all,
> > >
> > > I think the following OWL document is
> inconsistent,
> > > but Pellet says that it's consistent.
> > > Please shed some light on my ignorant brain.
> > >
> > > @prefix rdfs: <
> http://www.w3.org/2000/01/rdf-schema#
> > > <http://www.w3.org/2000/01/rdf-schema#> >.
> > > @prefix rdf: <
> http://www.w3.org/1999/02/22-rdf-syntax-ns#
> > > <http://www.w3.org/1999/02/22-rdf-syntax-ns#> >.
> > > @prefix owl: < http://www.w3.org/2002/07/owl#
> > > <http://www.w3.org/2002/07/owl#> >.
> > > @prefix a: < http://www.ex.org/2005/ex#
> <http://www.ex.org/2005/ex#> >.
> > >
> > > a:Vegetarian
> > > owl:intersectionOf
> > > (a:Animal
> > > [a owl:Restriction;
> > > owl:onProperty a:eats;
> > > owl:someValuesFrom a:Plant
> > > ]
> > > ).
> > > a:Plant owl:complementOf a:Animal.
> > > a:Sheep rdfs:subClassOf a:Vegetarian.
> > > a:Cow rdfs:subClassOf a:Vegetarian.
> > > a:MadCow
> > > owl:intersectionOf
> > > (a:Cow
> > > [a owl:Restriction;
> > > owl:onProperty a:eats;
> > > owl:someValuesFrom a:Sheep
> > > ]
> > > ).
> > >
> > > Thanks in advance!
> > > Mekan Ikzain
> > >
> >
> 





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Received on Monday, 26 September 2005 17:12:34 GMT

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