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

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Sun, 03 Mar 2002 03:14:48 -0500
To: jos.deroo.jd@belgium.agfa.com
Cc: www-webont-wg@w3.org
Message-Id: <20020303031448A.pfps@research.bell-labs.com>
From: "Jos De_Roo" <jos.deroo.jd@belgium.agfa.com>
Subject: Re: more on a same-syntax extension from RDF(S) to OWL
Date: Sun, 3 Mar 2002 01:22:59 +0100

> 
> [...]
> 
> > 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

But the whole point is that, using your terminology,

  
log:entails
   c' owl:oneOf ( r' ) .
   r' a owl:Restriction .
   r' owl:onProperty rdf:type .
   r' hasClassQ c' .
   r' maxCardinalityQ "0" .

so an empty hypothesis entails a contradiction, which is a paradox.


Peter F. Patel-Schneider
Received on Sunday, 3 March 2002 03:15:53 GMT

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