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Re: finite universes

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Wed, 2 Oct 2002 23:18:29 +0100
Message-ID: <15771.28853.113626.588849@merlin.horrocks.net>
To: www-webont-wg@w3.org


I see logic as a simple piece of machinery. It takes some input that
conforms to a syntactic specification and produces some output based
on a semantic specification of conforming syntax. I don't want to make
any judgements about what kind input it is reasonable to handle beyond
that of conforming to the syntax, and I want to promise that for all
such input the output will be determined solely by the
semantics. That's it.


On September 28, pat hayes writes:
> (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.
> >Pat,
> >
> >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.
> Pat
> 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.
> >
> >Ian
> >
> >
> >
> >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
> >>  --
> >>  ---------------------------------------------------------------------
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> >>  40 South Alcaniz St.			(850)202 4416   office
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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 Wednesday, 2 October 2002 18:18:25 UTC

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