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Re: finite universes

From: pat hayes <phayes@ai.uwf.edu>
Date: Sat, 28 Sep 2002 22:50:53 -0500
Message-Id: <p05111b03b9bc128579b8@[]>
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: bgrosof@mit.edu

(Webont members: I am BCCing this to webont as well as the DAML JC as 
I think the issue is relevant to our forthcoming F2F discussions. 
Hopefully BCC will avoid accidental cross-posting.  -Pat)

Hi Ian.

>Axioms that I write down do not assert anything about *the* universe,
>whatever that is,

I meant in the sense 'universe of discourse'. And in this sense, that 
is exactly what they do.

>they just constrain the kinds of of models I want to
>reason over in some particular context.

This is the central point: how does one know what kind of context is 
appropriate, on the SW? One never can know, unless it is made 
explicit, in which case it is no longer a context.

>E.g., in a database context,
>querying could be viewed as saying something like "assuming that what
>I have here are all the tuples/elements in the universe, does it
>follow that ...". This does not mean that I am asserting that what I
>have here really are all the tuples/elements in *the* universe.
>Taking your argument to its logical conclusion would mean rejecting
>pretty much any assertion you could make as it is bound to be false
>w.r.t. something somewhere on the web.

I strongly disagree with that. Where on the web is going to be false 
that there are infinitely many integers? Where is it going to be 
false that Paris is the capital of France? Etc. Surely the point of 
having information publicly available on the SW is so that agents can 
assume that it is all just plain true, rather than true only in some 
unknown context.
(There is a possible reply to this, along the lines that nothing is 
every just plain true, and all assertions have to be understood as 
made relative to a surrounding context, which might itself be 
contextual or incomplete. I doubt if you want to go there, though, 
Ian: it leads to things like Barwise situation theory and 
Guha/McCarthy style context logics. You can kiss DLs goodbye if we 
start along that road.)

I don't like the word 'context', but let me try to re-state my point using it.

What we (on these WGs) are trying to do is to design languages for 
use by agents on the semantic web, to be used to express content and 
transmit content across the web so that it can be used elsewhere. 
This presupposes, therefore, that the content expressed in these 
languages is being *published*, and once published, it might be used 
in ways, and by mechanisms, which are operating in contexts 
completely different from the context in which the content was 
originally stated; and moreover, those contexts are not known to the 
publisher of the content. Given this, it follows that publishing any 
assertion which is meant to be understood in a particular context, 
and only means what it is supposed to mean when that context is 
shared by its reader and its publisher, is at best misleading and at 
worst irresponsible. We cannot presuppose any - or at least, more 
than a tiny amount of - shared context, so our web languages must 
make all - or at least, as many as possible - of their contextual 
presuppositions explicit. They need to be decontextualized. For 
example, rather making a closed world *assumption* (..... are 
employees) where we all just 'know' that these lists are complete, so 
do not bother to say so, the SW publication should always make the 
closure of the world explicit (employee owl:oneOf [......] ). 
Otherwise, the publication is liable to be misunderstood.

On these grounds, I would claim that in a well-designed SW language 
it should ideally be *impossible* to make any assertion which implies 
that the universe is finite, ie which is true only in finite 
interpretations, since that is obviously only true in a restricted 
set of special contexts.  The intended content should always be 
expressed by saying that some named class is finite (or, in more 
advanced languages, maybe that for certain kinds of transaction it is 
OK to temporarily assume that the universe is finite for certain 
purposes: one could do that in a contextual logic like CYCL, for 
example) , but never that the universe of discourse is finite. It 
does not make that claim "in a database context", when published: it 
simply makes it. The context is lost by the act of publication, so 
this asks the entire planet to assent to it in all their contexts, 
which is ridiculous. In pure abstract-syntax OWL one can say that the 
universe is finite, but in OWL/RDF one cannot; which makes OWL/RDF a 
candidate SW language but *rules out* pure OWL, in my view. In other 
words, this is a (serious) bug, not a feature.

This general point about the need for decontextualizing strikes me as 
so obvious that I am amazed that anyone involved in the SW effort can 
disagree with it. But I have often met a reaction like: 'What is all 
the fuss about? All we are saying is that we want to go on using good 
old logic/logic programming/database technology/etc., what is wrong 
with that? Surely people will want to use logic/databases on the 
SW??' Ben said something like this in the telecon discussion, for 
example. I tried to respond to this kind of objection in my message, 
but maybe it didnt get through, so let me try again. Of course we 
want to allow these technologies to be used with the SW. But the SW 
is also a genuinely new idea, a project unlike any that has been 
attempted before, and requires some new thinking. All I am saying is 
that we need to take the obvious constraints of the SW into account 
when thinking about how to adapt these technologies to it. We can't 
conclude, from the fact that there will be databases on the SW , that 
conventional DB techniques can just be used exactly as they have been 
hitherto in 'database contexts' (or DLs, or logics, or logic 
programming, etc.). We have to face up to the possible need to 
re-tool some of our technology a little. If all we manage to do is to 
re-invent some old wheels in an XML syntax, without even thinking 
about the larger picture, then we won't have achieved very much.


PS. that term, 'universe of discourse', isn't just an empty label. 
The pioneers of formal logic knew very well that logics formalize an 
aspect of language use, and that all linguistic meaning depends on a 
kind of contract involved in all human language use, which is a 
shared understanding of what the communication is about, the 'common 
ground' of a discourse (or of a mathematical proof, for example). 
Apply the idea to human telephone conversation. If I feel in my 
pocket and say to you, only seven things exist, then in order for us 
to continue to share our assumptions - to have a common ground - you 
have to accept this rather questionable claim. Which is unlikely if 
you are a sane adult, and irresponsible of me if you are sufficiently 
gullible. But if I say, there are seven things in my pocket, then the 
chances of our being able to go on communicating successfully are 
greatly increased.

>On September 24, pat hayes writes:
>>  Ben and Ian, a point I should have made but didn't in todays telecon
>>  discussion. Ian introduced his example where one asserts that the
>>  universe has one thing in it. I said that it seemed crazy to me to
>>  assert that the universe was finite. Ben said in response that often
>>  one did want to work with a finite universe in databases, for
>>  example. Then we had a long discussion which I now think was beside
>>  the point. The key point, to me, is that when we are working in a
>>  web-logic context, any kind of restriction of the topic has to be
>>  made explicit, since there cannot be any kind of global guarantee
>>  that others will share those limited assumptions. This applies to
>>  things like closed-world assumptions, and to assumptions about
>>  working in a finite universe (which are really the same thing). I am
>>  not arguing that a web logic should ignore or disallow database
>>  ideas, or fail to provide for users who wish to utilize information
>>  from finite data stores, or information which depends on that
>>  finiteness; but all that can be done, and discussed, without anyone
>>  asserting the the *universe* is finite. All one needs to do, and what
>>  I think we should both say that they must do, and provide tools to
>>  enable them to do it, is to say that they are restricting themselves
>>  to some finite class of entities. But that restriction needs to be
>>  made explicit somehow - if only buried in an XML prefix in a file
>>  somewhere, not necessarily in an in-your-face kind of way - when that
>>  information is published in a web context. That is not, to emphasize
>>  the point, in any way an attack on the use of database technology or
>>  ideas, or in any way an attempt to marginalize or discourage existing
>>  applications or domains of use. But it does mean that I think that it
>  > is quite OK for a web *logic* to reject as inconsistent any assertion
>>  that the universe of discourse is finite, or only has one thing in
>>  it, or whatever: because that is not an assertion about your
>  > database, but about the entire logical universe of discourse for the
>  > whole semantic web. And saying that THAT is finite is indeed crazy,
>  > or at best a very strong philosophical claim that you had better be
>>  prepared to defend if you want to try to convince everyone else with
>>  a web browser of it. But in fact, you probably didn't want to say
>>  that in any case; you probably wanted to say that some subclass of
>>  the universe was finite, and to restrict yourself for the time being
>>  to that class; and of course I have no problem with that kind of
>>  assertion. I bet you would include the qualification, in fact, in any
>>  public data transmission, even if it were only implicit in some
>>  mutual convention that you and your friends were using.
>>  Pat
>>  --
>>  ---------------------------------------------------------------------
>>  IHMC					(850)434 8903   home
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>>  phayes@ai.uwf.edu
>>  http://www.coginst.uwf.edu/~phayes

IHMC					(850)434 8903   home
40 South Alcaniz St.			(850)202 4416   office
Pensacola              			(850)202 4440   fax
FL 32501           				(850)291 0667    cell
phayes@ai.uwf.edu	          http://www.coginst.uwf.edu/~phayes
Received on Saturday, 28 September 2002 23:50:37 UTC

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