Linas Vepstas wrote:
On Wed, Oct 17, 2007 at 10:25:18AM -0400, Richard Loosemore wrote:
One way this group have tried to pursue their agenda is through an idea
due to Montague and others, in which meanings of terms are related to
something called "possible worlds". They imagine infinite numbers of
possible worlds, in which all the possible variations of every
conceivable parameter are allowed to vary, and then they define the
meanings of actual things in our world in terms of functions across
those possible worlds. Such an idea is, of course, not usable in any
computer program, since it requires unthinkably large infinities [sic!],
I don't beleive the last sentence follows from the previous. There
are plenty of ways of integrating over infinities to get finite answers.
There are an infinite number of points inside a circle, yet we can still
define the area of a circle. There are an extremely large number of
ways of drawing black and white balls out of urns, and yet we can
still define averages and expectations (and these are even analytic,
differentiable, smooth functions!)
If instead of talking about black and white balls, we talked about
"is and is not a chair", and then considered some infinite number
of universes where some things were chairs and others were not,
and we drew items out of each universe, each labeled as "chair"
or "not a chair", one can still, in principle, obtain some usable
average idea of chair-ness that a real-world computer program could
approximate to some degree, just as real-world programs approximate
pi=3.14159...
You're right: I should not have slipped so easily into an "of course it
is not usable" statement without saying more.
As you point out, infinities don't stop other ideas from being useful --
in general.
The problem here is that the formalism does not come with any way to
apply it to real implementations, in such a way that is verifiably
correct rather than just a guess. Possible worlds semantics does not,
to the best of my knowledge, make any objective, counterintuitive,
falsifiable predictions about anything in the universe of things. Nor
does it supply even a hint of how it could be applied to produce a real
computation that would yield such predictions. It is post-hoc and
descriptive: it comes along after the fact and tries to impose order on
some observable characteristics of human minds.
That statement I just made is a minefield of controversy, of course. I
am sure someone will immediately start thinking of ways in which
predictions could perhaps be extracted from it, but then we would get
dragged into a minute examination of exactly where those predictions
come from, and whether they are really due to the formalism itself or
are just intuitively obvious, or built into it from the beginning.
Overall, I believe that possible-worlds semantics serves no purpose in
AI except to justify the idea that statements like "It is the case that
all cups are drinking vessels that possess a handle" can have something
like a "truth value" that is usable in a logical calculus.
In other words, it is a crutch.
Richard Loosemore.
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