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Re: A Rough Guide to Notation3

From: Jos De_Roo <jos.deroo.jd@belgium.agfa.com>
Date: Sat, 24 Aug 2002 14:17:30 +0200
To: Sandro Hawke <sandro@w3.org>
Cc: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, sean@mysterylights.com, seth@robustai.net, www-rdf-interest@w3.org
Message-ID: <OF46EB3812.3E36A05C-ONC1256C1F.004356FE@agfa.be>

> > > > > 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?

Well, I prefer Peter's option 1 as we already have it in N3 e.g.
  P log:implies C .
which is actually
  ~P log:or C .
and indeed neither ~P nor C are asserted, just their disjunction.
I really don't see any problem in selfreference as long as you
are not asserting your own truth-conditions, or as Pat once wrote

[[[
The problem comes from mixing up assertions, which just plain 
*are* true or false but don't talk about it,  with meta-assertions 
(which talk *about* truth). The point being that the truth-predicate 
isn't just any old predicate; it is required *as part of the very 
definition of the language itself* to faithfully reflect both the 
truths and the non-truths exactly (the <-> in your formula.). And its 
that exact correspondence that provides the rigidity which forces the 
situation into paradox. If we are just making simple assertions, they 
can just disagree. But that truth-predicate twists a not-true into a 
true-not, and then we are left chasing the truthvalues around in 
never-ending circles. Heres an analogy that just occurred to me: if 
you twist a piece of paper, the ends might not be aligned, but its 
still just a piece of twisted paper with two sides. But if you glue 
the ends together, it becomes a Mobius strip, and then its back *is* 
its front. The truth predicate is the glue.
]]]

-- ,
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/
Received on Saturday, 24 August 2002 08:18:13 GMT

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