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Re: DTTF: summary (gasp!)

From: Jonathan Borden <jonathan@openhealth.org>
Date: Thu, 23 May 2002 16:39:34 -0400
Message-ID: <00d601c20299$f35bd990$0a2e249b@nemc.org>
To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: <www-webont-wg@w3.org>
Jeremy Carroll wrote:

> (Short message, with long PS)
> Both Peter and Jim ask me to expand a bit, which isn't really somewhere
> I want to go.
> Suggested change
> ================
> I think a useful way of saying why DTs help solve the problem is:
> ....
> Mainstream Description Logic research is paradox free.
> Description Logic makes a distinction between the A-Box and the T-Box.
> We will use darkness to identify the T-Box; whereas A-Box semantics will
> extend RDFS semantics.
> ....

I must confess to be unaware of the details of T vs. A boxes but what you
say, a priori, seems ok, and not at all in opposition to the concept of
unasserted triples. Now _how_ the OWL MT is itself constructed given the
triple _syntax_ is a different story, and not something, frankly, that I
have a strong opinion on at the moment. In essence, my singular goal at the
moment is to close the issue to the extent that we can make a request of the
RDFCore WG which will allow both WG to continue with their work (i.e.

> This still isn't enough to fully satisfy me (see below), but may be
> enough to help DanC!
> Jeremy
> PS (longer)
> I believe that my analysis of the problem is sufficiently off from the
> rest of the DTTF that trying to integrate it is not valuable,
> particularly since I buy the conclusion.
> Basically the three conditions that Jonathan identifies:
> 1) all RDF triples to be asserted i.e. "truths"
> 2) classes as instances
> 3) OWL's need to support commonsense entailments
> should, in my opinion, be augmented with a fourth,
> 4) the state of the art in description logic
> and I do not find the arguments about paradox compelling.
> (I see each of these as a contradiction rather than a paradox).
> The argument from paradox is essentially the only argument Jonathan
> gives.
> I see the perpetual motion machine quote as a derogatory misreading of
> standard computer science practice of maximally using any mechanism that
> you are building in its own construction:
> [[
> This idea of a self-extending language that can, in
> principle, describe extensions to itself and then in some sense
> become those extensions, like a railway locomotive laying its own
> tracks ahead of itself, is a powerful vision, and one that I can see
> might excite considerable enthusiasm.  However, so is a
> perpetual-motion machine, and for much the same reasons.
> ]]

Well, I think we are not talking about "standard computer science" rather
Model Theory and Semantics. And since _that_ is what we are talking about,
how to integrate the _semantics_ of RDF and OWL _not_ how to write an RDF or
OWL reasoner, then we need to look
at what Pat is talking about.

In my reading I have become concerned that this argument may indeed be along
the lines of Hilbert's attempt, in the early part of the century, to
develop, essentially an axiomatized formulation of arithmetic which we call
"PM" for "Principia Mathematica". Godel convincingly proved that not only
can this not be done, but that any attempt to build a comprehensive
axiomatization of "PM" _within_ "PM" is doomed to failure.

It seems to me that if we substitute "CE" for "PE" in, for example, Nagel's
"Godel's Proof" -- which is a relatively nontechnical read, then "CE" may
indeed be stuck with the same essential problem as "PM".

This is _not_ to suggest that arithmetic doesn't work, hardly, rather that
it is not possible to formulate arithmetic _within_ arithmetic which is the
point that Pat is making, strongly, but correctly.

> But given the state of the art in DL, I think that Peter has adequately
> shown that my attempts at comprehensive entailment were research rather
> than development, but I am not yet convinced that they were
> fundamentally misguided research.

Yes, well I am not convinced that the analogy between "CE" and "PM" is
perfect, and so I think it _might be_ possible to get "CE" to work, but this
might be a major effort, and in the end might find itself right up against
Godel, and hence risky.

> If the argument from paradox is correct and the perpetual machine jibe
> is fair then the goal of the comprehensive entailments work is mistaken.
> I understand Peter, Pat and Jonathan as believing that; I still don't.
> It's a difference. I don't think we need to loose sleep over it. It
> will, in my view, be adequately conveyed by an abstention. Also, the
> only real way to substantiate my position is to do the necessary
> research.

Yes, well if you could indeed prove some form of "CE" free of paradox, my
understanding is that would indeed be a major accomplishment, deserving of
probable fame, (and possible fortune :-)

> I think my position (#4 above) does make it easier to articulate why
> dark triples help solve the problem.
> Description Logic makes a distinction between the A-Box and the T-Box;
> we have tried and failed to remove this distinction while not "doing
> research". We will use darkness to identify the T-Box; whereas A-Box
> semantics will extend RDFS semantics.

Ok, can you give me some specific, relatively non-technical language, that I
could incorporate into a message appropriate for RDFCore WG? Or does RDFCore
need be concerned with this distinction (i.e. that's something we can
discuss amonst ourselves)?

Received on Thursday, 23 May 2002 16:44:13 UTC

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