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Re: A Rough Guide to Notation3

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Fri, 23 Aug 2002 23:20:19 -0400 (EDT)
Message-Id: <20020823.232019.65661617.pfps@research.bell-labs.com>
To: sandro@w3.org
Cc: seth@robustai.net, sean@mysterylights.com, www-rdf-interest@w3.org

From: Sandro Hawke <sandro@w3.org>
Subject: Re: A Rough Guide to Notation3 
Date: Fri, 23 Aug 2002 16:41:48 -0400

> 
> > > 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 their
> > 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?
> 
>      -- sandro
> 


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.

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.


peter
Received on Friday, 23 August 2002 23:20:31 GMT

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