# Re: WOWG: Report from WWW 2003 - OWL presentation/issues

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 05 Jun 2003 11:38:06 -0400 (EDT)
Message-Id: <20030605.113806.69311928.pfps@research.bell-labs.com>

From: Dan Connolly <connolly@w3.org>
Subject: Re: WOWG: Report from WWW 2003 - OWL presentation/issues
Date: 05 Jun 2003 10:27:02 -0500

>
> On Thu, 2003-06-05 at 09:58, Christopher Welty wrote:
> > Jeremy,
> >
> > I've argued this with Pat several times.  I'd like to see an
> > authoritative definition of what "first-order" means, otherwise we're
> > all using our own definitions.  In any dictionary of logic or
> > philosophy or mathematics that I've been able to find, "first-order"
> > is defined as "not higher order" and "higer order" is defined as
> > predication of predicates (or functions of functions).
> >
> > Until someone produces an authoritative definition of first-order that
> > says something else, I don't think it's ever "simply incorrect" to
> > call RDFS higher-order.   It is "simply" correct.  It may be incorrect
> > according to your (or Pat's) more complicated definition of what
> > first-order means, but that is by no means "simple"!
> >
> > I have claimed from the start that a useful distinction here is to say
> > that RDFS is syntactically higher-order and semantically first-order.
> > Pat has not agreed.
> >
> > More to the point, I believe it to be the case that RDFS is
> > undecidable (has this been proven?)
>
> on the contrary; that RDFS is decideable is so clear that
> nobody has bothered to prove it.
>
> The deductive closure of an RDFS KB is finite. You can
> work it out with a pencil.

[...]

The deductive closure of an RDFS KB is decidedly *not* finite!

For example, the RDF closure of the empty RDF graph includes

rdf:nil rdf:type _:a1 .
rdf:nil rdf:type _:a2 .
rdf:nil rdf:type _:a3 .
....

there are several other closure rules that result in infinite closures.

In fact, the RDFS closure rules have an infinite set of axioms, including

rdfs:_1 rdf:domain rdfs:Resource .
rdfs:_2 rdf:domain rdfs:Resource .
rdfs:_3 rdf:domain rdfs:Resource .
...

peter
Received on Thursday, 5 June 2003 11:38:44 GMT

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