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Re: status of rdfs:Class

From: Graham Klyne <GK@ninebynine.org>
Date: Thu, 19 Jun 2003 11:32:59 +0100
Message-Id: <5.1.0.14.2.20030619111426.031ae4a8@127.0.0.1>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, www-rdf-comments@w3.org

At 15:21 18/06/03 -0400, Peter F. Patel-Schneider wrote:

>I had always thought that
>         x rdf:type y .
>rdfs-entailed
>         y rdf:type rdfs:Class .
>but I am having problems getting this entailment to go through.
>
>So, is this supposed to be an entailment?

I believe so.  Noting that you said "entailment", and working from the 
model theory elements of a printed copy of Pat's draft of about 2 days ago:

rdf:type rdfs:range rdfs:Class is axiomatic.

then <I(rdf:type),I(rdfs:Class)> is in IEXT(I(rdfs:range)), from definition 
of RDF interpretation. (1)

<I(x),I(y)> in IEXT(I(rdf:type)), from given and definition of RDF 
interpretation  (2)

then I(y) in ICEXT(I(rdfs:Class)), from (1), (2) and conditions on RDFS 
interpretation concerning rdfs:range.  (3)

then <I(y),I(rdf:Class)> in IEXT(I(rdf:type)), from (3) and RDFS 
interpretation conditions. (4)

then I(y rdf:type rdfs:Class .) is True from (4) and definition of RDF 
interpretation.  QED.

#g


-------------------
Graham Klyne
<GK@NineByNine.org>
PGP: 0FAA 69FF C083 000B A2E9  A131 01B9 1C7A DBCA CB5E
Received on Thursday, 19 June 2003 07:58:42 GMT

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