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From: rickw@eskimo.com (Richard Wojcik)
Subject: Re: Chomsky's Theorem
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Date: Tue, 21 Mar 1995 05:03:07 GMT
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In article <3kjtta$a57@riscsm.scripps.edu>,
Mark Israel <misrael@scripps.edu> wrote:
>In article <D4xAx7.86@eskimo.com>, rickw@eskimo.com (Richard Wojcik) writes:
>>> Chomsky's Theorem
>>> From any context-free grammar, one can construct a strongly
>>> equivalent grammar in Chomsky normal form (a.k.a. normal form).
>>>
>>> Greibach's Theorem
>>> From any context-free grammar, one can construct a strongly
>>> equivalent grammar in Greibach normal form (a.k.a. standard form).
>>
>> You seem to have pulled these "theorems" 
>
>   Why do you put "theorems" in quotation marks?  Are you insinuating 
>that they're not really theorems?
>
>   You said:  "Chomsky's Theorem.  I think that you don't know 
>anything about it.  Please prove me wrong."  I *did*.  You should be 
>eating crow now.

As I said before, most linguists would not be able to state what "Chomsky's
Theorem" is by that name, although the rubric is sometimes used in texts on
formal linguistics.  Every linguist knows what a context-free grammar is
and, usually, what "Chomsky-Normal Form" is.

>> out of a text on formal languages, possibly even compiler theory.  
>> They pertain to a special branch of linguistics that deals with 
>> artificial languages, not natural languages. [...]  Basically, you 
>> have confused a very esoteric branch of mathematics with general 
>> linguistic theory.
>
>   Well, if I must have pulled it out of a textbook on formal
>languages or compiler theory, I couldn't possibly have found it in an
>encyclopaedia of linguistics, could I?

Sure you could.  An encyclopedia is a compendium of terms, not a
textbook.

>   Let's take a look at The International Encyclopedia of Linguistics, 
>edited by William Bright.  Hullo, what have we here?
>
># CONTEXT-FREE LANGUAGES AND GRAMMARS.  Context-free languages 
># constitute one of the most important classes of formally defined
># languages.  Linguists are most familiar with the definition of
># CFLs first given formally by Chomsky 1959 [...].  Many useful 
># theorems have been proved about CFLs. [...]   CFGs are clearly 
># reminiscent of traditional statements about phrase structure:  
># e.g. the rule A -> B C [...] or the rule D -> d [...].  (By a 
># theorem of Chomsky, any CFG can be replaced one whose rules are 
># restricted  to the two forms shown above.  Such grammars are 
># called CHOMSKY NORMAL FORM grammars; Chomsky first called them 
># 'regular', but this term is now used as a synonym for 'finite 
># state'.)  Traditional and structuralist grammarians may be 
># regarded as having tacitly assumed that natural languages were 
># CFLs.  During the early 1960s, Chomsky and others gave arguments 
># intended to establish that this was not so.  These purported 
># demonstrations of the inadequacy of CFGs for natural language 
># description were invalid because of technical errors (Pullum & 
># Gazdar 1982); but the claim seems to have been correct, since 
># non-context-free languages are no known to exist.
>
>   Thus, not only is Chomsky's Theorem mentioned:  the immediate
>context talks about natural languages!

Read the passage again, Mark.  "A theorem of Chomsky" is not "Chomsky's
Theorem".  What Chomsky said was not that natural languages come in CHOMSKY
NORMAL FORM, but that all CFGs can be >replaced< by Chomsky Normal Form
grammars.  Pullum & Gazdar were not saying that natural languages could be
described in Chomsky Normal Form, but that Chomsky's arguments against
construing natural languages were not valid.  If you were to convert their
CFG of a natural language into Chomsky Normal Form, the resulting grammar
would produce unnatural phrase structures for the language.  I could
explain this further to you, but this subject is entirely off the point.
No linguist promotes the view that "Chomsky's Theorem" or "Greibach's
Theorem" have anything to do with natural language, contrary to the
impression that you have been struggling to maintain.

>   "Traditional grammarians" may not have been linguists, but
>"structuralist grammarians" (Leonard Bloomfield et al.) certainly
>were.  And the encyclopaedia considers these demonstrations
>important.

This is completely lost on me.  Why are you mentioning Bloomfield here?  He
has nothing to do with Chomsky.

>   Context-free grammars were an early attempt at generative
>grammar.  Linguists realised their limitations, and abandoned
>them in favour of more complex mechanisms.  But *all* such 
>generative grammars are foredoomed to failure IM(H, of course)O, 
>because:
>
>1) The generative grammars are binary:  either a string is in
>   the language or it is not.  Real natural languages have (as the
>   OED editors sagely put it) "a well-defined centre but no
>   discernible circumference."

This is total gobbledegook.  You are totally ignorant about Chomsky's
theory of generative grammar.  He has never advocated a CFG analysis of
natural languages.  His theory of transformationalism was an attack on CFG
analysis.  Gazdar et al. were among the first to attack Chomsky's view on
natural languages and CFGs, but that was years after Chomsky's claims.

>2) The generative grammars attempt to specify syntax completely 
>   in isolation from semantics, which is not how humans process
>   language.

This has nothing to do with the "failure" or "success" of CFGs.  Moreover,
classical generative theory explicitly denies that it is an attempt to
characterize how humans "process" language.  Surely you've heard of the
competence/performance dichotomy (a dichotomy, BTW, that I do not defend).

>3) The generative grammars are static, whereis in human parsing,
>   the rule set is dynamically enhanced by case-based reasoning.
>   How do you parse "He is hard of thinking"?  Answer:  you
>   retrieve the cliche "hard of hearing", and induce a new rule
>   from it.

If you wish to attack the competence/performance dichotomy, then I am on
your side on this one.  However, don't forget that it takes more than glib
assertions to make a case.

>[snip]
>   My question "What do Chomsky's Theorem and Greibach's Theorem tell 
>you about natural language?" was a rhetorical question, addressed to
>Dennis Baron, and intended to elicit the answer "Nothing" from him.
>Thus, it implies the exact opposite of what you say it implies.  My 
>point was that linguists spend much of their time on mathematical 
>constructs that have little to do with what their discipline purports 
>to study:  natural language.  For the sake of rhetoric, I chose as an 
>example the thing furthest removed from natural language that I 
>could think of: Chomsky's Theorem.  I make no apologies for that.

And yet you fulminate over my mild little statements about prescriptivists.
You angrily denounce me for not letting prescriptivists define their own
positions, even though linguists were the first to use the term.  I am not
demanding an apology from you.  I only point out that you are making a very
sweeping generalization.  It conveys the false impression that most
linguists are more interested in formal linguistic theory than in the study
of natural languages.  That is utterly false.  You confuse a rather
esoteric branch of linguistics with the entire field.

>   I "raised the issue" in an incidental mention in a rhetorical 
>question that would be forgotten by now had you not pounced on it.

Rhetorical questions have rhetorical consequences.  I was within my rights
to criticize your rhetorical misrepresentation of linguists.
-- 
Rick Wojcik  rickw@eskimo.com     Seattle (for locals: Bellevue), WA
             http://www.eskimo.com/~rickw/
