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

From: Michael Schneider <schneid@fzi.de>
Date: Fri, 4 Jan 2008 13:42:26 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A05A60FD@judith.fzi.de>
To: "Pat Hayes" <phayes@ihmc.us>
Cc: "Owl Dev" <public-owl-dev@w3.org>

Pat Hayes wrote:

>Perhaps Im not following your notation, but I 
>fail to see how this works. 

Please see below!

>However, I see how 
>the general idea works and what your point is. 
>And again, I do not see this as a problem to be 
>resolved: on the contrary, I see it as inevitable 
>that this kind of thing will happen. IMO, 
>examples like this show that DL is too weak to 
>detect (a) certain (class of) obvious 
>inconsistencies, not that Full is broken.

I did not intend to make the latter claim, at least not in general. I rather
was about saying that from DL-consistent/Full-inconsistent examples one can
see that something in the *interplay* between OWL-DL and OWL-Full might be
broken. But I still have to think a little more about your statements in
your previous and this mail, so I'm only going to clarify the question
regarding my example here.

>>   (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>
>
>Thats the part I don't follow. Perhaps I don't 
>understand what A4 is saying exactly. Could you 
>write this out in RDF, which is much easier to 
>follow? Ignore the 'typing' information, which is 
>irrelevant.

This just says (in RDF/Turtle syntax) that the range of the ObjectProperty p
is the singleton class {C}. And since "M := range(p)" generally means that
from a triple "s p o" one can conclude "o rdf:type M", this means in the
case of "M = {C}" that from (A6) follows "<D> = <C>", which is entailment
(E1).

>>both in DL[Punning] and in Full.
>>
>>Now, Full, but *not* DL[Punning], will further entail from 
>(E1), (A7) and
>>(A8):
>
>Doesn't A7 follow from the use of oneOf in A4?

No, since from (A4) only follows that <C> is an instance of some
(enumeration) class.

But I now see that I can get the same effect even much easier:

   (A1') <C> a owl:Thing
   (A2') <D> a owl:Thing
   (A3') <C> owl:sameAs <D>
   (A4') <C> a owl:Class
   (A5') <D> a owl:Class
   (A6') <C> owl:ComplementOf <D>

Now, in Full follows from (A3')

   (E1') <C> owl:equivalentClass <D>

Thus, by (E1') and (A6'), the new ontology is Full-*inconsistent*. But
because (E1') doesn't follow in DL+Pun (punning is too weak for this), this
ontology is DL+Pun-*consistent*. 

Oh dear, this ontology is so simple! One could even savely remove all the
typing axioms, leaving just the two triples (A3') and (A6'). I really should
have found this example immediately, how embarrassing! :)

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

FZI Forschungszentrum Informatik an der Universität Karlsruhe
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Received on Friday, 4 January 2008 12:42:46 GMT

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