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Re: A Rough Guide to Notation3

From: Sandro Hawke <sandro@w3.org>
Date: Sat, 24 Aug 2002 07:16:10 -0400
Message-Id: <200208241116.g7OBGAj21470@wadimousa.hawke.org>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
cc: seth@robustai.net, sean@mysterylights.com, www-rdf-interest@w3.org


> > > > 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
point of a receiver having to make sense of a contradiction.  

> 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
sentences about sentences, but not sentences about sentences about
sentences.)

Is there some reason we need any other kind of sentences to exist?

   -- sandro
Received on Saturday, 24 August 2002 07:16:32 GMT

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