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Re: Logic and Using The Semantic Web Toolbox

From: Drew McDermott <drew.mcdermott@yale.edu>
Date: Thu, 30 Nov 2000 18:05:59 -0500 (EST)
Message-Id: <200011302305.SAA09513@mr3.its.yale.edu>
To: www-rdf-logic@w3.org
CC: drew.mcdermott@yale.edu

   Graham Klyne wrote:

   I think the short answer is:  "we don't".  As TimBL also points out in the 
   notes you cite [1]:

   "(No comment needs to be made about the huge number of languages which 
   allow logical expression. In the classification of languages, normally 
   logic is introduced before the ability to make statements about statements 
   -- or rather, it was until Goedel. Here, the "first order" question is 
   taken backwards, in that RDF statements already break the "first order" 
   assumptions before basic logic has been introduced. Not extends the toolbox 
   to propositional logic.)."

   Thus, to make logical assertions, something needs to be added to RDF.

I have watched the discussion about reified this and that with growing
perplexity.  Pat Hayes did a good job of summarizing a lot of the
problems with the reification scheme.  What I'd like to ask is, Why
bother?  Is it supposed to be a bug or a feature that we have to
define "not" in terms of reification?

This is not a rhetorical question.  Can anyone explain to me what the
motivation is for (e.g.) forbidding nesting of expressions?
Intuitively, a statement like 

(if (wins Bush election2000) (not (recounted election2000)))

contains the subexpressions (wins Bush election2000) and (recounted
election2000) without asserting them.  Since we can't do this in RDF
(apparently), we have to say, as it were, Suppose there was an
assertion about Bush winning the election, etc.  I believe Pat pointed
out that if I speak in this roundabout way I don't really solve the
problem.  If I describe a formula in complete detail, specifying its
predicate and arguments, have I somehow referred to it while
preventing it from existing?  How is that possible?  Once I've
completely described a formula, what else is there *to* a formula?
Suppose I tell you that I'm thinking of a certain fraction.  Its
numerator is 3 and its denominator is 0.  Whew!  That was close; I
almost wrote down a meaningless expression.  But it's okay, because I
only described it.  Huh?  Sorry for the sarcastic tone, but this
really sounds like a theory of names devised by medieval philosophers
to avoid summoning S-A-T-A-N by not actually saying his name out loud.

In any case, this nonsolution is addressed to a nonproblem.  If I
simply allow expressions to contain expressions that are not asserted,
the problem goes away.  That's the traditional solution; what's wrong
with it?

                                             -- Drew McDermott
Received on Thursday, 30 November 2000 18:06:07 UTC

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