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RE: Some basic questions about OWL-Full

From: Michael Schneider <schneid@fzi.de>
Date: Tue, 23 Oct 2007 23:42:55 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A04A8819@judith.fzi.de>
To: "Pat Hayes" <phayes@ihmc.us>
Cc: <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, <jjc@hpl.hp.com>

Pat Hayes wrote:

>>From: Pat Hayes <phayes@ihmc.us>
>>Subject: Re: Some basic questions about OWL-Full
>>Date: Tue, 23 Oct 2007 08:58:28 -0500
>>>  >Peter F. Patel-Schneider wrote:
>>>  >>
>>>  >>For homework:  Is EquivalentProperties(owl:sameAs 
>>>  >> 	 	       itself inconsisten?
>>>  >>
>>>  >
>>>  >I'm afraid I'm several years' late on my (easier) homework of:
>>>  >    Is (*empty*) itself inconsistent?
>>>  Yes, in RDF (and conventional FOL). This is the
>>>  only assumption of Tarskian semantic theory, that
>>>  there is something in the universe. One can build
>>>  a 'free' logic which allows an empty universe,
>>>  but then its proof theory can't have the usual
>>>  rules of instantiation and generalization, which
>>>  allow the inferences
>>>  (forall (x) (foo x))  |==   (foo A) for some
>>>  'new' name A |==  (exists (x)(foo x))
>>>  Pat
>>I think Jeremy meant an empty KB, i.e., whether OWL Full is trivial or
>Ah, I see. Sorry. Yes, that question amounts to 
>whether the OWL semantic conditions are 
>internally consistent when transcribed into 
>common logic (or FOL using the holds/app style). 
>Good question!

Hm, seems to me that I did not understand neither Jeremy, nor Peter, nor
you. :) What is meant by "whether OWL Full is trivial or not"? Is this the
question about whether empty OWL-Full ontologies are inconsistent or not?
I.e. whether an empty OWL-Full ontology entails contradictory statements? 

But if I have some arbitrary non-empty ontology O := {A1,...,An}, then O
contains the empty ontology as a sub-ontology. So I would assume that every
statement which is entailed by the empty OWL-Full ontology will also be
entailed by O itself. And if the empty OWL-Full ontology would entail
contradictory statements, then /every/ OWL-Full ontology would entail
contradictory statements, and then OWL-Full semantics would be totaly
broken! Is it this what you (Pat) mean by "whether the OWL semantic
conditions are internally consistent..."? 


Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Email: Michael.Schneider@fzi.de
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FZI Forschungszentrum Informatik an der Universität Karlsruhe
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Received on Tuesday, 23 October 2007 21:43:16 UTC

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