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Layering LX (or FOL) on RDF (was Re: A Rough Guide to Notation3)

From: Sandro Hawke <sandro@w3.org>
Date: Mon, 26 Aug 2002 17:12:19 -0400
Message-Id: <200208262112.g7QLCJ811834@wadimousa.hawke.org>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
cc: seth@robustai.net, sean@mysterylights.com, www-rdf-interest@w3.org


> > > The problem is not their (potential) existence.  It is their existence
> > > everywhere.  The problem is that if you allow self-referential
> > > sentences and also need to have sentences exists everywhere, removing just
> > > the problematic ones is problematic. 
> > 
> > I don't quite follow that, sorry.
> 
> The problem with some self-referential sentences, such as the self negating
> one, is that they have no models, not even models that assign them a truth
> value of false.  

I'm proposing that the logical formula

    % there exists a triple whose subject is itself
    exists t subjTerm predTerm objTerm pred obj (
      rdf(t, lx_subjectTerm, subjTerm) &
      rdf(subjTerm, lx_denotation, t) &
      rdf(t, lx_predicateTerm, predTerm) &
      rdf(predTerm, lx_denotation, pred) &
      rdf(t, lx_objectTerm, objTerm) &
      rdf(objTerm, lx_denotation, obj)       
    )

has the same meaning as any other formula which contradicts the
layering axioms or contradicts itself, such as

     % there exists some triple which is both true and false
     exist a b c (
       rdf(a,b,c) & -rdf(a,b,c)
     )

You sound concerned that the triple (self,x,y) doesn't have a truth
value, but in my proposal the triples one would have to use to
construct such a triple essentially contradict each other, so one
can't even phrase the problematic triple to notice that you have no
truth value for it.  This seems very like FOL, which disallows
self-referencial terms, although it manages such a restriction in a
purely-syntactic manner.

> This is not a problem for a DAML+OIL.  Entailment defined on top of
> DAML+OIL would be very weak, because not all DAML+OIL classes need exist in
> all DAML+OIL interpretations.  Mentioning the analogue of a self-negating
> sentence in DAML+OIL is like stating a contradiction.
> 
> However, if DAML+OIL is to be given a reasonable notion of entailment, so
> that, for example, John in Student and John in Employee entails John in the
> intersection of Student and Employee, then all DAML+OIL classes must
> exist in all DAML+OIL interpretations.  However, this then includes the
> problematic ones, which ends up with all DAML+OIL knowledge bases having no
> interpretations.
> 
> Trying to forbid just the problematic classes requires something like ``A
> class is acceptable syntactially if it is acceptable semantically'' which
> is itself problematic.

I'd rather not get into DAML+OIL issues.

> >    -- sandro
> 
> Again, there are lots of ways around this problem, just none that fit into
> the strong version of the RDF philosophy.
> 
> peter

My question is a fairly narrow technical one, not a political one.
Can one precisely define a way to reach out from the RDF sublanguage
of FOL to full FOL by means of a pre-arranged vocabulary and
associated semantics?  

If you think the answer is "No", then please point out the weak link
in my demonstration [1].  (If it's in the handling of self-reference
in the axioms, then please say so (no need to try to find a flaw in
the axioms), and let me polish that area first.  It'll be tricky, and
I'd like to avoid the work if it's not necessary.)

I seriously appreciate your time in this.

   -- sandro

[1] http://www.w3.org/2002/08/LX/RDF/layering
Received on Monday, 26 August 2002 17:13:07 GMT

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