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Re: A Rough Guide to Notation3

From: Sandro Hawke <sandro@w3.org>
Date: Sat, 24 Aug 2002 13:14:04 -0400
Message-Id: <200208241714.g7OHE4p23255@wadimousa.hawke.org>
To: "Seth Russell" <seth@robustai.net>
cc: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, sean@mysterylights.com, www-rdf-interest@w3.org


> > One possible way to restrict self-referencial sentences is to say
> > something like: for all X Y Z in U, the sentence (X Y Z) exists in
> > R(U) but not U.  R(U) is a superset of U and exists for all U.  (There
> > is some U0 which does not contain any sentences.  R(U0) constains
> > sentences, but not sentences about sentences.  R(R(U)) contains
> > sentences about sentences, but not sentences about sentences about
> > sentences.)
> >
> > Is there some reason we need any other kind of sentences to exist?
> 
> I don't see why we cant just make any sentence that has itself as it's own
> subject be a syntax error at parse time.  This probably doesnt have much to
> do with RDF, since RDF does not provide an identity for triples; but an
> application (such as sailor agents) could generate a serial number for every
> RDF triple and allow for a language to use that serial number to make
> statements about statements.  When we parse such a language into a graph and
> find that the serial number of {S1 p o} is S1, we raise a syntax error.

It can't just be a syntax error because (in the systems I imagine) we
could infer "{S1 p o} is S1",  from various inputs, like
  "{S2 p o} is S3" and "S2 = S1" and "S3 = S1".  
Each of those has fine syntax; it's the combined semantics that are in
error. 

Another problem is larger loops:
     S1 says S2 is true
     S2 says S3 is true
     S3 says S4 is true
     S4 says S1 is false
Each of these statements is fine; it's only the combination that's in
error. 

There may be a simpler way than R(...R(U0)...) to avoid such loops,
but probably not much simpler.    With this approach, the conjunction
of the above four sentences is contradictory (a semantic error).

> Is there some reason we need a sentence to be it's own subject?

I don't think so.  My proposal forbids that kind of sentence as well
as the bigger loops.  We could try to only rule out paradoxical loops
(I remember some formulation of wtr that's supposed to do this) if
someone comes up with a good reason to allow benign loops.

   -- sandro
Received on Saturday, 24 August 2002 13:14:29 GMT

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