[Avery Andrews 951124.1437]
Here's a somewhat interesting post off the optimality theory mailing
list, I'm including the whole thing although it probably won't be
vaguely comprehensible until it gets into the description of driving.
One thing that makes interesting is that PCT has mostly focussed on
situations where all the references can be satisfied, and must be,
whereas in optimality theory, the constraints often conflict, and can't
all be satisfied at once. Some of Ed Ford's discussion of discipline
problems indicates that he thinks in terms of conficting constraints
also. Anyway, here it is....
ยทยทยท
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From list-relay@UCSD.EDU Mon Nov 20 22:58:53 1995
To: Optimal <optimal@UCSD.EDU>
Subject: Re: <OT> UG & OT
Date: Mon, 20 Nov 95 11:09:58 +0000
From: T M Ellison <marke@cogsci.ed.ac.uk>
Content-Length: 3525
Status: RO
X-Lines: 78
Gary Marcus <marcus@psych.umass.edu> writes:
? Here's why. If OT is to be learnable, something like the Tesar-Smolensky
? model of constraint-ranking has to be right.
Assumption #1. Is there a proof of this? As I understand it, the T-P work
requires that children must know the underlying forms of words (or more
particularly, the output of GEN for a given lexeme) in order to do
constraint ranking. Are these GEN-outputs innate? If not, where do they
come from. I think this is a fair argument that T-S's model does not
correspond to how children learn.
? But to rank constraints in finite time, there must be a finite number
of constraints.
Assumption #2. Is there a proof of this? Or does it depend on the T-S
model? There is no reason why infinite classes of constraints cannot be
reranked, in just the same way that interesting operations can be
performed on infinite sets of strings using regular expressions or
finite-state automata.
Here is an almost trivial example. Suppose that we had constraints like
the well-known bimoraic minimum foot constraint (call it FOOT-2), but
instead, these constraints took the form:
FOOT-n: A foot must contain at least n morae.
(I'm not saying these are likely constraints, just possible ones).
Then assume we can have any amount of epenthesis in the output of GEN
(that is, an infinite set of candidates). Then, if there are no other
constraints involved, the evidence of a single bimoraic foot is enough to
rank FOOT-2 higher than the infinite number of other constraints. We have
imposed a ranking affecting an infinite number of constraints.
? A child who
? ranked all of the possible constraints that could be derived from the
? cognitive system (or motor control), would be forced to rank-order an
? infinite set of constraints (be Faithful when you want to be clear, be
? Faithful when you are hungry, be Faithful only before sundown, etc. etc.
? etc).
? Adulthood would be delayed.
By the same argument, we should not be able to learn any motor-control
activity which requires rank ordering. But we certainly can. We learn to
drive, which involves ranking constraints like:
*) Do not collide at high speed
*) Do not collide with other vehicles or pedestrians
*) Obey policeman's directions
*) Obey road signs
*) Drive on the left (Australia/NZ/UK/etc. version)
It's fairly easy to see the more-or-less total ranking of these
constraints. It is possible to extend this list with more motor-skilly
constraints like:
*) If the engine roars, release accelerator slightly
*) Depress clutch to freewheel before slipping gear to neutral
and so on, which become a single coordinated movement in the fluent
driver.
Is driving innate? Do we have to worry about the constraint `Drive on
the right on Fridays if carrying a vegetarian passenger'? Not on its own.
The whole class of `drive on the right' constraints can be demoted except
`drive on the right when you are turning right on a street with a sign
saying one-way'. By I don't think we need to appeal to an innate Universal
Highway-Code to acheive the right ranking.
? Fortunately, an innate Universal Grammar comes to the rescue, by innately
? specifying what constraints are potentially relevant. The child's
? rank-ordering-device then needs conduct only a finite number of
? comparisons.
It may be that we have an innate Universal Grammar for motor skills. If we
don't need a UG for them, then we don't need it for phonology. If we need it
for phonology, then we need it for everything.
marke