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

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/ peterReceived on Tuesday, 27 August 2002 15:59:06 UTC

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