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Re: more on a same-syntax extension from RDF(S) to OWL

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Sun, 3 Mar 2002 01:22:59 +0100
To: pfps@research.bell-labs.com
Cc: "www-webont-wg" <www-webont-wg@w3.org>
Message-ID: <OF98ECCBBB.AB3F14AF-ON41256B70.00839B9A@agfa.be>

[...]

> Now from the looping rule on r, rdfs:Literal; c; and l there is a
> restriction r', class c', and list l' such that
>    <r',bowl:Restriction> in EXT(rdf:type)
>    <r',rdf:type> in EXT(bowl:onProperty)
>    <r',0> in EXT(bowl:maxCardinalityQ)
>    <r',c'> in EXT(bowl:hasClassQ)
>    <c',rdfs:Class> in EXT(rdf:type)
>    <c',l'> in EXT(bowl:oneOf)
>    <l',bowl:List> in EXT(rdf:type)
>    <l',r'> in EXT(bowl:first)
>    <l',bowl:nil> in EXT(bowl:rest)
>
> The restriction r' exhibits the paradox.  It is a restriction whose
> instances do not have an rdf:type property that belongs to the class
whose
> sole member is the restriction itself.
>
> If <r,r'> in EXT(rdf:type) then r does not meet the requirements of r'
and
> thus <r,r'> must not be in EXT(rdf:type).
> If <r,r'> is not in EXT(rdf:type) then r does meet the requirements of r'
> and thus <r,r'> must be in EXT(rdf:type).

asserting
  c' owl:oneOf ( r' ) .
log:entails
  r' a c' .
and asserting
  r' a owl:Restriction .
  r' owl:onProperty rdf:type .
  r' hasClassQ c' .
  r' maxCardinalityQ "0" .
log:notEntails
  r' a c' .
which is just a contradiction (p and not(p))

--
Jos De Roo
Received on Saturday, 2 March 2002 19:23:38 GMT

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