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

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Fri, 06 Jun 2003 13:44:21 -0400 (EDT)
Message-Id: <20030606.134421.30686384.pfps@research.bell-labs.com>
To: jjc@hplb.hpl.hp.com
Cc: welty@us.ibm.com, www-webont-wg@w3.org

From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
Subject: Re: WOWG: Report from WWW 2003 - OWL presentation/issues
Date: Fri, 06 Jun 2003 18:20:58 +0100

> Sorry for not replying sooner ...
> 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.  
> I see what you're getting at.
> The normal discussion about triples is to call the middle term a predicate, 
> and then RDF permits predicates to apply to predicates.
> However, a different understanding of RDF; for examle that seen in the 
> DAML+OIL axciomatic semantics use essential one 3 place predicate for 
> expressing a true triple.
> So - in terms of underlying complexity and difficulty a first order theory 
> is one that can be mapped into first order logic; and RDFS trivially can 
> be. 

Hmm.  I do not believe that the mapping from RDFS to first-order logic is
particularly trivial.  Pat Hayes's mapping from RDFS to Lbase is certainly
not trivial.  

It hasn't even yet been completely shown to be possible.  For example,
there might be some weird part of the XML or XML Schema datatypes
specifications that cannot be encoded in first-order logic.  (I don't
believe that this is so, but it has not yet been rigorously shown not to be
the case.)

> Truely higher order statements like Grelling's paradox[1] cannot be 
> expressed in RDF.

Perhaps there is some strange aspect of IRIs that causes the definition of,
for example, the XML Schema string datatype to break down, perhaps because
the definition of IRIs depends on the XML Schema string datatype, which, of
course, depends on IRIs.  I don't think that there is, but has this been
shown to not be the case?  Or perhaps there is some aspect of the integers
that affects RDF and that cannot be captured in first-order logic.  Again,
I don't think that there is, but I don't think that it has been shown to
not be the case.

> Jeremy
> [1]
> [[
> If an adjective truly describes itself, call it "autological", otherwise 
> call it "heterological". For example, "polysyllabic" and "English" are 
> autological, while "monosyllabic" and "pulchritudinous" are heterological. 
> Is "heterological" heterological? If it is, then it isn't; if it isn't, 
> then it is. Grelling's paradox cannot be expressed in first-order predicate 
> logic, and is difficult to prevent in higher-order predicate logics.
> ]]
> http://www.earlham.edu/~peters/courses/logsys/glossary.htm#g

Received on Friday, 6 June 2003 13:44:38 UTC

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