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Re: RDFCore Update

From: pat hayes <phayes@ai.uwf.edu>
Date: Thu, 30 Aug 2001 16:04:08 -0700
Message-Id: <v04210113b7b46f06e24c@[130.107.66.237]>
To: nejdl@kbs.uni-hannover.de
Cc: www-rdf-logic@w3.org
> > The minutes of the RDFCore WG face to face meeting
> >
> >   http://www.w3.org/2001/sw/RDFCore/20010801-f2f/
> >
> > have just been approved and this seemed like a good time to report on our
> > progress.
> >
> > Most of the people I have spoken to have said we had a good meeting and we
> > have made good progress.  Pat Hayes presented a strawman model 
>theory for RDF.
> > which was well received.  This is a technique borrowed from the logicians
> > which provides a formal mathematical foundation for RDF.  I am hopeful that
> > this will prove to be a useful technique for grounding many of the semantic
> > issues that have arisen.
> >
> > We did spend a lot of time discussing anonymous resources, but it was time
> > well spent as this was an issue that the WG had been struggling to move
> > forward on email and teleconferences.  In the end we made significant
> > progress, deciding that anonymous resources are indeed part of the RDF
> > model, not just syntactic entities.  We also made good progress with
> > understanding their semantics.
> >
> > Other decisions the WG made include:
> >
> >   o The model theory will be defined for RDF graphs, not n-triples.
> >
>
>Brian,
>
>Why did you decide to define it for RDF graphs?

Let me answer this one. The real reason was 'anonymous nodes'. These 
have given rise to an astonishing (to a logician) amount of 
discussion and debate, and we found during a recent F2F meeting that 
almost all of this confusion could be resolved very elegantly and 
clearly by distinguishing between two rather different issues: how a 
linear notation specifies an RDF graph, on the one hand; and what 
that graph 'means' in the model-theoretic sense, on the other. The 
resulting picture was both elegant and apparently in better 
conformity to both the intent and the wording adopted in the original 
RDF M&S, and clearly resolved and settled what had been several weeks 
of detailed email discussions which seemed likely to go on for ever, 
so we decided to adopt it.

The technical point is that anonymous nodes, of course, correspond to 
existentially quantified variables; but RDF has no syntactic 
construct corresponding to the existential quantifier, and no way to 
indicate scope. (One could be introduced, of course, but only by 
extending the formal language in some way.) This seems to have been a 
major source of confusion: eg what is the meaning of adding a new 
assertion to a document, or merging two documents?. (Moreover, the 
XML serialisation of RDF has many 'implicit' anonymous nodes (eg in 
the use of containers) so that it is particularly tricky to attach a 
model theory directly to that syntax. ) The use of nodes in a graph 
eliminates the technical issue, since there are no 'multiple 
occurrences' of any 'existential variable' in the graph, so no need 
for any notion of quantifier scope other than the graph itself.

RDF graphs and Ntriple documents are in 1:1 correspondence, modulo 
re-ordering of lines and renamings of anonymous node labels, so it is 
relatively trivial to map between them in any case; and it is also 
easy to map directly between graphs and (existential-conjunction) 
expressions in a linear logical notation, should you wish to do so. 
In fact, if one is willing to put up with the awkwardness of somehow 
distinguishing between 'free' and 'bound' anonymous nodes, the model 
theory could be applied directly to the n-triples syntax.

>Specifying the
>semantics on n-triples is probably closer to the usual first order
>logic formalisms (or Datalog), see e.g. our formalization of the
>O-Telos-RDF variant (comparable to RDFS),
>http://lists.w3.org/Archives/Public/www-rdf-logic/2001Aug/0064.html).

There really is no 'usual' first order logic formalization. Every 
notational variation (of which I know about 10) seems to have its own 
devoted user community. I myself find the LISP-like prefix notation 
used by KIF most congenial, but I have come to respect the clarity of 
graph-based notations such as CGs. It is interesting to note that 
this is in fact the oldest notational style for first-order logic 
(used by both Peirce and Frege) and was replaced by what is now often 
called 'normal' notations largely for commercial reasons; the graphs 
were too expensive to print using normal typesetting. The resulting 
complexities arising from bound variable clashes produced technical 
headaches for many years. (This one of the very, very few things that 
even Alonzo Church once got wrong in print.)  Perhaps we should not 
have been surprised that it would produce some confusion here also. 
However, the point is that this is really a notational complication, 
rather than a semantic one: a distinction that RDF now also respects.

Pat Hayes

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Received on Thursday, 30 August 2001 19:03:01 GMT

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