Re: Layering LX (or FOL) on RDF

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>

> > 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.

Ok, sorry, I was thinking about 'not' in the sense that the world is divided
into penutbutter and not penutbutter.   Here is a graph that is more what we
are talking about:

http://robustai.net/mentography/negation_paradox.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.

I can write all of those graphs in RDF.  For example Figure C is

<http://robustai.net/sailor/paradox.rdf>

<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:ex="http://example.org/examples#">
    <rdf:Description rdf:about="">
        <ex:negates rdf:resource=""/>
    </rdf:Description>
</rdf:RDF>

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

Within one document, all the arrows are triples.  To express multiple
formula, we need to use multiple RDF documents.

> 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.

Yes, I agree.  <http://robustai.net/sailor/paradox.rdf> is a paradox and
should excluded from all graphs that purports to be binarialy logical.

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