SHEBS@UTAH-20.ARPA (10/01/84)
From: Stan Shebs <SHEBS@UTAH-20.ARPA>
(My my, people seem to get upset, even when I think I'm making
noncontroversial statements...)
It wasn't clear whether Tom Dietterich (and maybe others) understood
my remark on induction. I was merely pointing out that "induction on
one case" is indistinguishable from "generalization". Simple-minded
generalization IS easy. Suppose I have as input a Lisp list (A B),
(presumably the first in a stream), and I tell my machine to create
some hypotheses about what it expects to see next. Possible hypotheses
are:
(A B) - the machine expects to see (A B) forever
(?X B) - the machine expects to see 2nd element B
(A ?X) - similarly
(?X ?Y) - 2-element lists
Since these are lists, presumably one could get more elaborate...
(?X ?Y optional ?Z)
...
And end up with "the most general hypothesis":
?X
All of these patterns can be produced just by knowing how to form
Lisp lists; I don't think there's any hidden assumptions or biases
(please enlighten me if there are). I would say that in general,
one can exhaustively generate all hypotheses, when the domains
are completely specified (i.e. a pattern like (<or A B> B) for the
above example has an undefined entity "or" which has nothing to do
with Lisp lists; one would have to extend the domains in which one
is operating). Generating hypotheses in a more reasonable order is
completely domain-dependent (and no general theory is known).
Getting back to the example, all of the hypotheses are equally
plausible, since there is only one case to work from (unless one
wants to arbitrarily rank these hypotheses somehow; but none can
be excluded at this point).
I agree that selecting representations is very hard; there's not
even any consensus about what representations are useful, let alone
about how to select an appropriate one in particular cases.
(Have I screwed up anywhere in this? I really wasn't intending
to flame...)
stan shebs