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Re: Layering LX (or FOL) on RDF

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 27 Aug 2002 15:58:44 -0400 (EDT)
Message-Id: <20020827.155844.86419291.pfps@research.bell-labs.com>
To: seth@robustai.net
Cc: www-rdf-interest@w3.org

From: "Seth Russell" <seth@robustai.net>
Subject: Re: Layering LX (or FOL) on RDF 
Date: Tue, 27 Aug 2002 11:15:43 -0700

> From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
> 
> > From: "Seth Russell" <seth@robustai.net>
> >
> > > From: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
[...]

> > 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?
> 
> I don't understand your paragraph.   p is not a formula ... can never be a
> formula, in my view.  Doesn't "p" just identify a node or represent a
> resource?  {p negation ~p} is a formula.   

I don't understand how p cannot be a formula.  Primitive propositions are
formulae, and they seem to be naturally represented by resources.

What is { p negation ~p }?  Is it a set?


I would represent negation,
> conjunction, and disjuntion formula as per this mentograph:
> 
> http://robustai.net/mentography/negation_conjunction_disjunction.gif

What is the connection between this and RDF?  I don't see any, and the
point of this discussion is representing logic in RDF.

> What is the problem again with these kind of arrows ?

Well, lots, including the fact that the arrows are not RDF statements, as
they are more than triples.

> <snipping stuff who's complexity I do not understand>
> 
> > Truth and falsity are represented by inclusion in the classes pl:Truth and
> > pl:Falsity, respectively.
> 
> Ok, the pink resources (which are formula) can be of of rdf:type pl:Truth or
> pl:Falsity relative to some other graph.
> 
> > To forbid self-reference, you have to *forbid* RDF graphs that contain
> > things like
> > _:x pl:negation _:x .
> 
> I have no problem with calling that formula rdf:type pl:Falsity relative to
> any graph that purports to be binarilay logical.  But I dont' know if we
> must forbid it, I mean anybody can say anything about anything ... can't
> they?

Well the problem is that if you make this formula belong to pl:Falsity,
then the rules of logic say that it must belong to pl:Truth, and the rules
of logic also say that pl:Truth and pl:Falsity are disjoint.  Similarly, if
you make it belong to pl:Truth, then the rules of logic say that it must
belong to pl:Falsity.  So no matter what you do, you get into a bind.

> Seth Russell
> http://robustai.net/sailor/

peter
Received on Tuesday, 27 August 2002 15:59:06 GMT

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