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RE: [OWLWG-COMMENT] Re: Cardinality Restrictions and Punning

From: Michael Schneider <schneid@fzi.de>
Date: Thu, 3 Jan 2008 19:39:44 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A05A60E3@judith.fzi.de>
To: "Pat Hayes" <phayes@ihmc.us>
Cc: "Owl Dev" <public-owl-dev@w3.org>

Hi, Pat!
 
Pat Hayes wrote:

>>>And I am
>>>talking about real examples, not "research examples". Such as being
>>>able to infer, from the fact that a taxonomy represented as a class
>>>of classes contains only three members and that a thing is not in any
>>>of them, that it is not classified by the taxonomy.
>>
>>I don't see how to express this example in OWL-DL.
>
>I think you will be able to in 1.1, using 
>punning: but you will not be able to draw the 
>right conclusions. So I would prefer to say, that 
>you will SEEM to be able to represent it in 1.1, 
>but this is in fact an illusion.

While I did not succeed to build from your idea a working
1.1-DL-consistent/Full-inconsistent example, I instead found this pretty
simple one:

  (A1) <C> a owl:Thing
  (A2) <D> a owl:Thing
  (A3) <p> a owl:ObjectProperty
  (A4) <p> rdfs:range [ oneOf (C) ]
  (A5) <x> a owl:Thing
  (A6) <x> <p> <D>
  (A7) <C> a owl:Class
  (A8) <D> a owl:Class
  (A9) <C> owl:ComplementOf <D>

Because of (A4), this ontology will entail from (A6):

  (E1) <C> owl:sameAs <D>

both in DL[Punning] and in Full.

Now, Full, but *not* DL[Punning], will further entail from (E1), (A7) and
(A8):

  (E2) <C> owl:equivalentClass <D>

(E2) directly contradicts (A9). Thus, the ontology is *inconsistent* in
Full.

This ontology is *consistent* in DL[Punning]: To see this easily, just
"un-pun" the ontology by substituting all occurrences of the *instance*
names 'C' and 'D' with 'c' and 'd', respectively, in the axioms (A1), (A2),
(A4) and (A6). It is then obvious that this is a satisfiable ontology.

So, after Jeremy's data/object punning example, we now have an example where
through *instance/class* punning an ontology gets DL-consistent, but
Full-inconsistent.

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

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Received on Thursday, 3 January 2008 18:39:54 GMT

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