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Re: TEST: 6 of 7: empty universe example,

From: Mehrdad Omidvari <Mehrdad.Omidvari@networkinference.com>
Date: Thu, 24 Jul 2003 10:46:27 +0100
Message-ID: <3BE4D3F0FB726240966DEF40418472B55FE8@ni-lon-server1.ad.networkinference.com>
To: <www-webont-wg@w3.org>

"owl:Thing owl:equivalentClass owl:Nothing" is *inconsistent* in OWL-DL.

In OWL-DL (as in FOL), the universe of the interpretation is always
required to be a non-empty set. If there is no non-empty interpretations
of an ontology, then the ontology is unsatisfiable (and hence
inconsistent in proof-theoretic terms).
As owl:Nothing is the complement of owl:Thing, you can reformulate the
above axiom as:
owl:Thing owl:equivalentClass complementOf(owl:Thing) which is obviously
inconsistent in DL and FOL, being an example of "A <=> not A".

Mehrdad Omidvari
Received on Thursday, 24 July 2003 05:46:47 UTC

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