# Re: A Rough Guide to Notation3

From: Sandro Hawke <sandro@w3.org>
Date: Sat, 24 Aug 2002 07:16:10 -0400
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

```

> > > > Yes.  I believe my approach of translating RDF to FOL means that a
> > > > proof of the satisfiability of my axioms is a proof of their
> > > > compatibility with RDF.  (I'll need to add some more axioms for RDFS
> > > > inference to be complete here.)
> > >
> > > You might want to look at some of the discussions on representing FOL
> > > sentences in n-triples while still retaining the RDF still retaining thei
> r
> > > RDF meaning.  [[Summary: you can't, at least not without some lossage.]]
> >
> > I've heard that conclusion (from you), but been unable to find the
> > evidence to support it.  Can you send me a pointer?
>
> It is easier to give the basics of the argument directly here.  Versions
> exist for DAML+OIL in the www-webont-wg mailing list.
>
>
> If you want to represent in RDF graphs a logic with composite
> non-conjunctive sentences, such as disjunctions, you have to represent
> the sentences, and their component sentences, as RDF resources
> somehow.  Following the RDF philosophy that any RDF graph,
> particularly non-tree graphs, should be allowable, non-tree versions
> of the logic's sentences should also be allowed.

I don't completely accept that last sentence.   DAML+OIL says the RDF
graph
_:x daml:differentIndividualFrom _:x.
is not allowed.  Each new vocabulary can do that.  The RDF philosophy
of "anyone can say anything about anything" does not extend to the

> An RDF graph, G, that asserts the truth of a logical sentence can only
> entail an RDF graph, H, for another sentence in an extension of RDF if
> the resource for the second sentence, and the resources for its
> component sentences, are in every interpretation for G, and are
> asserted to be true in G.  (Otherwise the extended interpretations of
> G wouldn't even be RDF interpretations of H.)  In most logics,
> including propositional logic, the only reasonable way to ensure this
> is if the representation of all sentences is in all interpretations.
> This means that every interpretation in the extension of RDF has to
> determine the truth of every allowable sentence.
>
> Unfortunately, some of the allowable sentences, such as the sentence
> that is its own negation, have problematic truth conditions.  Either
> the sentence is both true and false or no interpretation for the
> sentence is possible.  In both of these cases entailment in the
> extension breaks down.
>
> There are a number of solutions to this problem.  The most natural one
> to me is just to extend the syntax of RDF sentences, to give the
> composite sentences of the logic a meaning without having to represent
> them as RDF resources.  It is also possible to instead forbid certain
> kinds of RDF graphs, namely the ones that would correspond to non-tree
> sentences.

Can't we just just disallow RDF graphs which describe self-referencial
sentences (or at least self-negating) ones?

One possible way to restrict self-referencial sentences is to say
something like: for all X Y Z in U, the sentence (X Y Z) exists in
R(U) but not U.  R(U) is a superset of U and exists for all U.  (There
is some U0 which does not contain any sentences.  R(U0) constains
sentences, but not sentences about sentences.  R(R(U)) contains