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From: lee@uhccux.UUCP (Greg Lee)
Newsgroups: sci.lang,comp.ai
Subject: Re: Infinte alphabets - (Turing via Berke)
Message-ID: <969@uhccux.UUCP>
Date: Sat, 17-Oct-87 15:49:58 EDT
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Posted: Sat Oct 17 15:49:58 1987
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In article <434@russell.STANFORD.EDU> goldberg@russell.STANFORD.EDU
 (Jeffrey Goldberg) writes:
>In article <959@uhccux.UUCP> lee@uhccux.UUCP (Greg Lee) writes:
>[stuff ...]

The commentary on my posting seems to me to be rather obtuse.  Rather
than proceeding point by point, I think I should restate the matter.
Perhaps this time I can make myself clearer.  Before doing that, I'll
explain that by "separated by ... constituent boundaries"  I meant
to refer to the circumstance that one item is within a constituent
and another is outside that constituent.

Now, to begin again.  Gerald Gazdar made the point that a local
context sensitivity, such as a transitive verb occurring always
with a sister noun phrase, does not prevent a language from being
context free.  And since there is evidence that such subcategorization
context sensitivity is in fact local in natural languages, this provides
us some evidence (not probative) that language is context free.

Suppose now that we apply the same reasoning in the case of phonology.
If language is phonologically context free, we would predict that
context sensitivities are local.  It is a commonplace that phonological
rules tend not to apply across major constituent breaks.  The prediction
appears to be correct, and so we have some evidence (not probative)
that language is phonologically context free.

Because of the qualification in my original posting, I concede in
advance that this does not provide a very compelling argument for
finiteness of alphabets.  But the logic, at least, seems clear
enough:
	language is context free (hypothesis supported by empirical
				  argument)
	if language is context free, the alphabet is finite (obvious)
	therefore, the alphabet is finite (well known rule of logic)

(We could talk about the logic in the Schieber article sometime,
if you like.)

Greg Lee, lee@uhccux.uhcc.hawaii.edu