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Re: finite universes

From: Lynn Andrea Stein <las@olin.edu>
Date: Sun, 29 Sep 2002 15:00:35 -0400
Message-ID: <3D974DD8.83A21DE9@olin.edu>
To: pat hayes <phayes@ai.uwf.edu>
CC: Ian Horrocks <horrocks@cs.man.ac.uk>, bgrosof@mit.edu

pat hayes wrote:

> (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)

Unfortunately, I can't make the F2F (though I'm still hoping there's some
opportunity for remote participation) and so will miss that part of the

> Ian writes:
> >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.

> Pat responds:
> 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.

Well, to a C programmer int is restricted to 32 bits and in certain parts of
Texas Paris is the town next door.  I realize that one response to this is that
what a C programmer means by an int is not the thing you meant pjh:integer to
describe (and similarly pjh:Paris is different from at least some Texan's
notions), but I don't consider that an adequate response.  There is NO definitive
objective interpretation of what, e.g., Paris means, and although I'm confident
that you can constrain pjh:Paris in ways that would make it clear that
texas:Paris is a different thing, the same issues with subtler shading will arise
over and over again.  I have said before that the only way to truly understand
web ontologies is in terms of communities of interpretation -- social context --
and I will say it again now.  The trick is going to be the ability to say
something about being in the same social context and therefore using Paris to
mean France, not Texas.  (Said differently:  If the trick involves its being TRUE
that Paris can only mean France, the trick ain't gonna work on the web.)

> (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,

There is nowhere else to go.

> 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.

In fact, we're not going to be able to know the context, but we WILL be able to
(and need to) say:  For the purposes of the following, assume that you are in the
same context as the author of this information.  Your assumption may be wrong --
people coopt terminology and misuse it all the time -- but your reasoning will
need to be based on this presumed sharing of context.   For the most part, that
presumed sharing of context will have to be indicated by human beings or webs of

> 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.

I agree with almost all of your reasoning about what is or isn't possible on the
web but draw somewhat different conclusions.  I agree that maximum possible
decontextualization is a Very Good Thing, so I guess I don't disagree with most
of this text (including large portions I've omitted from this response).  But I
fundamentally doubt that decontextualization is POSSIBLE, in general.   That is,
even with maximal decontextualization, we're going to need the web of trust/it's
OK to just assume you're in the same context as this ontology.

> 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.

Fine, but logic presumes there is *A* universe of discourse and, unfortunately,
on the web there are many localized universes that partially overlap and slip and
slide against one another.  That is, you can't decontextualize everything so that
there can be a single universe behind it all.  And if you think you can, you're
missing the idea that mutually inconsistent pockets of reasoning happen *all* the
time in the world (not to mention within a single human brain, naive theories of
belief notwithstanding).

Received on Sunday, 29 September 2002 15:00:37 GMT

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