Re: Layering LX (or FOL) on RDF

From: "Seth Russell" <seth@robustai.net>
Subject: Re: Layering LX (or FOL) on RDF 
Date: Tue, 27 Aug 2002 09:18:11 -0700

> From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
> 
> > Well, how does one forbid self-referencing sentences.  To do so, one would
> > have to say something like
> >
> > _:s rdf:type rdf:Statement .
> > _:s rdf:subject _:s .
> >
> > is not an RDF graph.
> 
> It seems to me that  "_:s rdf:subject _:s"  is not a self referencing
> triple.  In fact I dont's see how you could even write a self referencing
> triple in RDF at all, since RDF does not even provide for triples to have an
> identity.  In the example above "_:s" is the identity of the thing of type
> Statement, not the identity of the triple.
> 
> Help, I'm confused  ?
> 
> Seth Russell

Hmm.  You have a point here.  You would not have to use RDF reification at all.

However, suppose you have a way of representing formulae in RDF.  This will
have to use resources and statements.  When you represention ~p, you will
have to have an RDF graph with a resource for the formula p and another resource
for the formula ~p.  How can you allow this, and forbid the RDF graph that
is your RDF graph for ~p except that it replaces the resource for p with
the resource for ~p?

For example, suppose you represent 
1/ atomic propositions by resources,
2/ negations as
	_:x pl:negation y .
   where y is the resource that represents the negand
3/ conjunctions and disjunctions as 
	_:x pl:conjunction (or pl:disjunction) _:l .
	_:l rdf:first c1 .
	_:l rdf:rest _:ll .
	_:ll rdf:first c2 .
	_:ll rdf:rest rdf: nil .
  where c1 and c2 are the components of the conjunction or disjunction.

Truth and falsity are represented by inclusion in the classes pl:Truth and
pl:Falsity, respectively.

To forbid self-reference, you have to *forbid* RDF graphs that contain
things like
	_:x pl:negation _:x .

peter