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Re: ACTION: task force unasserted triples

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Wed, 24 Apr 2002 16:07:43 -0500
Message-Id: <p05101538b8ecc69a7e0b@[65.217.30.94]>
To: Dan Connolly <connolly@w3.org>
Cc: www-archive@w3.org
>[copy to www-archive, not www-webont-wg; i.e. feel free
>to show this to anybody you like, but I don't think
>it's worth the WG's time...]

Sure, I concur. Im just sloppy about CC lines, I tend to use the ones 
that get put in automatically.

>
>On Tue, 2002-04-23 at 12:14, Pat Hayes wrote:
>[...]
>>  The situation can be summed up as follows.
>
>This just looks like hand-waving and appeal to Authority,
>not an actual technical argument.

I wasn't giving an argument. As Guus requested, I was trying to give 
clarification on what the issue was.

>
>Not to say that the burden of persuasion is necessarily
>on you; but if you're trying to persuade me, this doesn't
>do it. I would like to understand the technical argument.
>
>>  The WebOnt language is
>>  obliged by the layering requirements
>
>which layering requirements?

That OWL syntax be RDF syntax and that OWL interpretations include 
the same commitments as RDF interpretations (ie that an OWL 
interpretation of X which makes X true contains, or is an extension 
of, an RDF interpretation of X which also makes X true.)

>Definite descriptions
>without clear referents don't help much.
>
>>  to treat its own syntactic
>>  constructions
>
>What do you mean by 'syntactic constructions' here?
>By my reckonning, the syntactic constructions of
>WebOnt are exactly the same as those of RDF:
>
>   terms: literals, bnodes, and URIref names
>   atoms: S P O triples.
>   formulas: conjunctions of atoms.

Well, that is obviously wrong, even of DAML, since the DAML meanings 
of the RDF graphs are not *conjunctions* of the RDF meanings of the 
DAML triples.

>
>Please give an example of what you mean by syntactic
>construct.

In the case of DAML, I mean the lists in things like intersectionOf. 
The DAML MT treats them (correctly) as syntactic primitives, not as 
implicit existential assertions.

>
>>  as assertions of the existence of a class corresponding
>>  to the syntactic construct(and in fact of a great deal else as well,
>>  eg lists). This is because the RDF meaning of the RDF encoding of
>>  every piece of the WebOnt language amounts to an assertion of the
>>  existence of that class.
>
>Quite. That's by design, and seems quite natural to me.

Even when the class that RDF says exists is the Russell set in OWL? 
Why would that be natural?

>
>>  And, as Peter has shown, such a requirement
>>  is very dangerous,
>
>He has shown that it *can* be very dangerous.
>He has not shown, to my satisfaction, that it
>is must be dangerous in every case; that
>there is no design that avoids the problems.

Right. OK, if you want to get involved with foundations of set theory 
every time a web language is created, then I guess you are entitled 
to take your life in that direction. Seems pointless to me. Apart 
from the waste of time, I would have no confidence that Id be able to 
do it. Proving consistency of set theories is heavy work.

>
>>  since it can rapidly lead to paradoxes or
>>  contradictions of various well-known kinds when the language is
>>  reasonably expressive. (It may be worth emphasizing that the kind of
>>  problems that Peter is talking about have been well-known now for
>>  close to a century, are widely studied, and that there is no easy or
>>  cute way to hack around them. Some very smart people (Hilbert,
>>  Russell, Church, Turing, Goedel, Quine, Kripke, Montague) have
>>  wrestled with these problems, and the consensus seems to be that
>>  there isn't any way to avoid them.
>
>Look, if it's that well-studied, just spell out (or at
>least point to) the argument. An appeal to authority
>only makes me more suspicious of your position;
>recall our exchange about orthodoxy and Des-Cartes
>experiences.

Im thinking of the Russell paradox in set theory, Goedel 
incompleteness, Turing undecideability, Tarski's results on 
meta-descriptions (a consistent language can't be the same expressive 
power as its own metatheory), Montague's paradox (showing that even 
quite weak languages can't consistently describe their own 
semantics), and Quine's attempts to construct set theories that 
avoided the ZF constructions by using more 'natural' comprehension 
principles, like his New Foundations and the odd system in Set Theory 
and Its Logic - the first logic book I ever read! - which are now 
considered to be historical curiosities. (If Quine could't do it, I 
certainly can't do it.) Oh, and Kripke's demolition job on the 
substitutional interpretation of modal quantifiers.  All of these 
have a common theme: they are all variations on the liar paradox, 
which all lead to the conclusion that when you try to let a language 
define itself, or use definitions of its own semantics or meanings at 
all 'freely' (ie except under *very* tightly 'layered' conditions, eg 
ramified type theory, say, or Tarski's strict heirarchy of 
meta/meta-meta/..languages, each stronger than the one below it) then 
you get paradoxes. People have tried just about every dodge to get 
round it and none of them have worked.

Im not appealing to MY authority, in case you think I am, by the way. 
I'm not an expert in this stuff. Chris Menzel for example knows this 
area much better than I do. Feel free to ask anyone else about it.

>  > Certainly they cannot be avoided
>>  by appeals to other kinds of logic, such as multi-valued logics or
>>  abandoning the law of excluded middle. They have the same kind of
>>  status in foundations of mathematics as, say, the conservation of
>>  energy has in physics. A blithe confidence that some way will be
>>  found to hack around them should be treated rather like a patent
>>  application for a perpetual-motion machine: its really not worth
>>  getting into the details of what is wrong with it.)
>
>Meanwhile, you found it worthwhile to read and criticize
>Jeremy's attempt to do exactly this, no?

Come on!!  I only read the damn thing because you yelled at me during 
the telecon about it. Normally I don't bother to read ideas about how 
to re-do set theory properly, unless they come with a VERY good 
provenance.  But you asked me to look at it and say what was wrong 
with it, and I said I would, so I did.

>   http://lists.w3.org/Archives/Public/www-webont-wg/2002Apr/0202.html
>
>That criticism doesn't seem to say that it's hopeless to
>persue this line of work.

Perhaps I didnt express myself forcefully enough. It was meant to 
convey that general idea.

>I don't understand how to reconcile your messages.

I think Ive been fairly consistent on this issue. Maybe Ive been too 
polite at times, but we all have to try to get along.

Pat

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Received on Wednesday, 24 April 2002 17:07:49 GMT

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