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Adam Funk · Guest

On 2008-07-15, Peter T. Daniels wrote:

[quote]Youu mean, the bit of mathematics that Chomsky apparently had some
influence on 50 years ago? Has virtually nothing to do with
linguistics today (or then, either, for that matter).
[/quote]
But very useful in computer science, logic, and some interdisciplinary
fields such as natural language processing.

[quote]The closest you might find to mathematical formulations in linguistics
was "Montague Grammar," an attempt to meld symbolic logic with syntax/
semantics. There were a couple of textbooks on it.
[/quote]
"English as a formal language" in _Formal philosophy: selected papers
of Richard Montague_ (a book which I think is quite hard to find) is
the basis for trying to do compositional semantics on natural
language.

[quote]There>s also the obscure discipline of mathematical linguistics, which
tries to describe patterns formally, and the very popular
computational linguistics, which involves data processing applications
to just about anything.
[/quote]
Partee, ter Meulen, and Wall: _Mathematical methods in linguistics_,
Kluwer, 1990. I think it>s out of print but second-hand copies are
available.

But I wouldn>t recommend these books for someone without reasonable
math skills!

--
The wonderful thing about standards is that there are so
many of them to choose from. [Grace Murray Hopper]

Nathan Sanders · Guest

In article
<b44a265d-de0e-43d9-8bc0-b0b07de0dec1@y38g2000hsy.googlegroups.com>,
"Peter T. Daniels" <grammatim@verizon.net> wrote:

[quote]On Jul 16, 9:06 am, Adam Funk <a24...@ducksburg.com> wrote:
On 2008-07-15, Peter T. Daniels wrote:

Youu mean, the bit of mathematics that Chomsky apparently had some
influence on 50 years ago? Has virtually nothing to do with
linguistics today (or then, either, for that matter).

But very useful in computer science, logic, and some interdisciplinary
fields such as natural language processing.

But not in linguistics, which is OP>s concern and the nominal topic of
this newsgroup.
[/quote]
And yet, many linguists are aware of formal language theory, for a
variety of reasons: simple intellectual curiosity, familiarity of the
topic from their own mathematical or computational backgrounds, and
even for its occasional use in linguistics.

[quote]"English as a formal language" in _Formal philosophy: selected papers
of Richard Montague_ (a book which I think is quite hard to find) is
the basis for trying to do compositional semantics on natural
language.

He was murdered by his lover before he could work out the details.
[/quote]
"Lover" seems a bit strong, implying a long-term relationship. I
thought it was generally suspected that he was killed by a one-night
stand. Did he even have a (long-term) lover at the time?

Nathan

--
Nathan Sanders
Linguistics Program
Williams College
http://wso.williams.edu/~nsanders/

galathaea · Guest

On Jul 14, 8:03 pm, py.oh...@gmail.com wrote:
[quote]I>m looking for an undergraduate text on formal grammars that would be
suitable for self-study for someone who plans to enter the field of
linguistics at university. My aim is to teach him about mathematical
thought in a way that would familiar and entertaining.

Any recommendations appreciated.
[/quote]
there are a number of possible directions you could take such a course
and it would probably be best done
using what the directions your friend is most amenable to

here is a short list of possibilities

1 - cognitive grammar
the work of langacker and others here
is much more focused on the meat-and-potatoes of linguistics
and the math presented is much simpler
mostly the simpler logical and mereological connectives

this might be appropriate
if your friend is very mathophobic
but _really_ like linguistics

2 - formal grammars
chomsky was important here
not really for the formalisation part
which had already actually been done in computer science
(or recursion theory, etc.)
but because he brought the work into
what was basically humanities at the time

it was a step past saussure

better here than reading chomsky
(whose work on anarchism i _do_ recommend)
would perhaps be to read tarski and his work on model theory

this is where the theory really becomes one of meaning
and his work on the foundations of science
is really a foundation of meaningful language

3 - connectionist theory

maybe thinking in terms of words-as-primitives
could be against some of your friends strongly-held notions

there was a time in my life when i had such barriers
and chomskian theory was quite a turnoff

the connectionists
people like paul churchland
brought the budding theory of neural nets into linguistics

the math here is that of vector transforms
attractor basins
and basic (discrete and continuous) dynamics

4 - logical schools of linguistics
although logicism died out because of it>s narrowly defined focus
the foundations of logic have always been strongly linguistic
and the continued use of epistemological principles
(like hume>s)
in neologicism and related foundational studies
continues to argue for the importance of linguistics in logic
and conversely through application

the mathematics here varies from an intro-to-logic course
on up to proof theory and constructivism and later

frege>s work here is a standard jumping point
but more recent work in things like mereotopology
also point to some of tarski>s works as foundational

which brings...

5 - computational semantics

really
this is where chomsky>s work came from
albeit in a much more simplified distillation

nowadays
this field is huge
and incredibly mathematically sophisticated

usually i recommend
"semantics of programming languages:
structures and techniques"
by gunter (carl a.)
as a very nicely composed introduction to the field
but it does require a good familiarity with programming languages
and already pretty solid reasoning about recursion

if recursion is what you are after
recursion theory is basically where computation linguistics came
from
and the book by boolos and jeffrey
"computability and logic"

however
type theory and domain theory and other more intensive programmes
lay just over the horizon here

all of these suggestions overlap and intersect
in many interesting ways
so if one approach starts out favorably but loses its favor
moving to another will not only provide new direction
it may reinforce some of the ideas from the prior approach

the mathematical spectrum is quite large
so perhaps this type of variety may help you adjust
to the particular skill level of your friend

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

Brian M. Scott · Guest

On Wed, 16 Jul 2008 10:58:16 -0400, Nathan Sanders
<nsanders@williams.edu> wrote in
<news:nsanders-B4C6E4.10581616072008@news.newsguy.com> in
sci.lang,sci.math:

[...]

[quote]And yet, many linguists are aware of formal language theory, for a
variety of reasons: simple intellectual curiosity, familiarity of the
topic from their own mathematical or computational backgrounds, and
even for its occasional use in linguistics.
[/quote]
Besides, it>s pretty.

[...]

Brian

Nathan Sanders · Guest

In article <1cuqy8j5ph42a$.zfubmetyzuc3$.dlg@40tude.net>,
"Brian M. Scott" <b.scott@csuohio.edu> wrote:

[quote]On Wed, 16 Jul 2008 10:58:16 -0400, Nathan Sanders
nsanders@williams.edu> wrote in
news:nsanders-B4C6E4.10581616072008@news.newsguy.com> in
sci.lang,sci.math:

And yet, many linguists are aware of formal language theory, for a
variety of reasons: simple intellectual curiosity, familiarity of the
topic from their own mathematical or computational backgrounds, and
even for its occasional use in linguistics.

Besides, it>s pretty.
[/quote]
That too.

Nathan

--
Nathan Sanders
Linguistics Program
Williams College
http://wso.williams.edu/~nsanders/

Quinn Tyler Jackson · Guest

<py.ohlin@gmail.com> wrote in message
news:627167f5-3fff-418d-b522-7b9c037a44e3@k30g2000hse.googlegroups.com...

[quote]
Frankly, I>m not sure how much formal grammars are used practically[/quote]
outside parsing—unrestricted grammars are obviously a less tidy
description of something like English. Again, that>s why I x-posted.
[quote]
[/quote]
Formal grammars are used in practical and theoretical ways in everything
from drug discovery, genomic research (motif discovery), computational and
corpus linguistics, to voice recognition and OCR error-correction. "Less
tidy" than what? Formal grammar theory as it applies to natural language has
come a long way from Chomsky>s application.

Moreover, in terms of the study of formal grammar thoery, the symbol
manipulation involved can come in very handy in other branches of
mathematics -- for example, sometimes providing a formal proof can be
approached by translation of a numerics problem into a formal language
problem, manipulated in language theory space in the standard fashion, et
cetera. For instance, I>ve read of attempts at the Collatz Conjecture proof
that reduce it to a formal language problem and then an examination of what
is known about the resulting grammar and/or machines. (I even tried my hand
at that approach myself.)

Cheers,
Quinn

Adam Funk · Guest

On 2008-07-16, Nathan Sanders wrote:

[quote]And yet, many linguists are aware of formal language theory, for a
variety of reasons: simple intellectual curiosity, familiarity of the
topic from their own mathematical or computational backgrounds, and
even for its occasional use in linguistics.
[/quote]
And vice versa.

[quote]"English as a formal language" in _Formal philosophy: selected papers
of Richard Montague_ (a book which I think is quite hard to find) is
the basis for trying to do compositional semantics on natural
language.

He was murdered by his lover before he could work out the details.

"Lover" seems a bit strong, implying a long-term relationship. I
thought it was generally suspected that he was killed by a one-night
stand. Did he even have a (long-term) lover at the time?
[/quote]
I didn>t know anything about his personal life until now, although I
had noticed that his work in this area seemed to stop rather suddenly.

--
I heard that Hans Christian Andersen lifted the title for "The Little
Mermaid" off a Red Lobster Menu. [Bucky Katt]

Adam Funk · Guest

On 2008-07-16, Peter T. Daniels wrote:

[quote]Partee, ter Meulen, and Wall: _Mathematical methods in linguistics_,
Kluwer, 1990. I think it>s out of print but second-hand copies are
available.

Barbara Partee was the principal continuator of Montague Grammar. This
volume postdates those efforts, so it might receive a chapter or so.
[/quote]
Parts A, B, & C cover set theory, logic, formal systems, etc; D is
"English as a Formal Language"; and E covers the Chomsky hierarchy and
related matters.

[quote]But I wouldn>t recommend these books for someone without reasonable
math skills!

You can read around the many formulas in some of the chapters and
discover what they>re talking about.
[/quote]
That>s what I meant by "reasonable"!

--
Is one language more powerful than another? Compare, for example,
English with Yiddish. Sure, it>s hard to describe a carburetor in
Yiddish, but try describing a schlemiel in English. (Stoll 1995)

Peter T. Daniels · Guest

On Jul 17, 4:35 pm, Adam Funk <a24...@ducksburg.com> wrote:
[quote]On 2008-07-16, Peter T. Daniels wrote:

Partee, ter Meulen, and Wall: _Mathematical methods in linguistics_,
Kluwer, 1990. I think it>s out of print but second-hand copies are
available.

Barbara Partee was the principal continuator of Montague Grammar. This
volume postdates those efforts, so it might receive a chapter or so.

Parts A, B, & C cover set theory, logic, formal systems, etc; D is
"English as a Formal Language"; and E covers the Chomsky hierarchy and
related matters.
[/quote]
Then Montague Grammar would appear in Part D.

[quote]But I wouldn>t recommend these books for someone without reasonable
math skills!

You can read around the many formulas in some of the chapters and
discover what they>re talking about.

That>s what I meant by "reasonable"!
[/quote]
Rather impolite of you to conceal that my comment immediately above is
abot a book quite other than the Partee et al.

Adam Funk · Guest

On 2008-07-17, Peter T. Daniels wrote:

[quote]On Jul 17, 4:35 pm, Adam Funk <a24...@ducksburg.com> wrote:
On 2008-07-16, Peter T. Daniels wrote:

Partee, ter Meulen, and Wall: _Mathematical methods in linguistics_,
Kluwer, 1990. I think it>s out of print but second-hand copies are
available.

Barbara Partee was the principal continuator of Montague Grammar. This
volume postdates those efforts, so it might receive a chapter or so.

Parts A, B, & C cover set theory, logic, formal systems, etc; D is
"English as a Formal Language"; and E covers the Chomsky hierarchy and
related matters.

Then Montague Grammar would appear in Part D.
[/quote]
Yes.

[quote]But I wouldn>t recommend these books for someone without reasonable
math skills!

You can read around the many formulas in some of the chapters and
discover what they>re talking about.

That>s what I meant by "reasonable"!

Rather impolite of you to conceal that my comment immediately above is
abot a book quite other than the Partee et al.
[/quote]
Sorry, I thought you were talking (as I was) about all "these books"
including that one.

--
I put bomb in squirrel>s briefcase and who gets blown up? Me!

tommy1729 · Guest

On Jul 14, 11:27 pm, "Peter T. Daniels" <gramma...@verizon.net> wrote:

[quote]The closest you might find to mathematical formulations in linguistics
was "Montague Grammar," an attempt to meld symbolic logic with syntax/
semantics. There were a couple of textbooks on it.
[/quote]
would that be of any value to look at for symbolic maths and the use
of specific notations in mathematical proofs

MoeBlee · Guest

On Jul 31, 7:24 am, tommy1729 <tommy17...@gmail.com> wrote:
[quote]On Jul 14, 11:27 pm, "Peter T. Daniels" <gramma...@verizon.net> wrote:

The closest you might find to mathematical formulations in linguistics
was "Montague Grammar," an attempt to meld symbolic logic with syntax/
semantics. There were a couple of textbooks on it.

would that be of any value to look at for symbolic maths and the use
of specific notations in mathematical proofs
[/quote]
It is of some related interest, but not most directly. Basically, no,
Montague grammar is not the thing you should study to learn symbolic
logic and formal mathematical proof. Rather, for that purpose, I
highly recommend the book

Logic: Techniques of Formal Reasoning by Kalish, Montague and Mar.

(By the way, that is the same Montague as with Montague grammar.)

If you study that book thoroughly, really master it, then I think it
would change your life. Truly, I>m not exaggerating. It would give you
the basic tools you need to write mathematics in clear, understandable
symbolism and also to put your arguments in logical form. It is the
best book I know of for that purpose. It is written in a quite clear
way, practical, thorough, and rigorous (to just the right degree
appropriate for the level of study). I recommend it as the first book
to master before then going on the subjects of set theory and then
mathematical logic.

MoeBlee

Peter T. Daniels · Guest

On Jul 31, 2:07 pm, MoeBlee <jazzm...@hotmail.com> wrote:
[quote]On Jul 31, 7:24 am, tommy1729 <tommy17...@gmail.com> wrote:

On Jul 14, 11:27 pm, "Peter T. Daniels" <gramma...@verizon.net> wrote:

The closest you might find to mathematical formulations in linguistics
was "Montague Grammar," an attempt to meld symbolic logic with syntax/
semantics. There were a couple of textbooks on it.

would that be of any value to look at for symbolic maths and the use
of specific notations in mathematical proofs

It is of some related interest, but not most directly. Basically, no,
Montague grammar is not the thing you should study to learn symbolic
logic and formal mathematical proof. Rather, for that purpose, I
highly recommend the book

Logic: Techniques of Formal Reasoning by Kalish, Montague and Mar.

(By the way, that is the same Montague as with Montague grammar.)

If you study that book thoroughly, really master it, then I think it
would change your life. Truly, I>m not exaggerating. It would give you
the basic tools you need to write mathematics in clear, understandable
symbolism and also to put your arguments in logical form. It is the
best book I know of for that purpose. It is written in a quite clear
way, practical, thorough, and rigorous (to just the right degree
appropriate for the level of study). I recommend it as the first book
to master before then going on the subjects of set theory and then
mathematical logic.
[/quote]
Do you know how this edition, by Mar, differs from the original by
Kalish & Montague, which was my Logic class textbook at Cornell in
1970 or so?

Even in those days, the topics covered by Kalish & Montague didn>t
suffice for the study of semantics, and people who were interested
were encouraged to go on to Modal Logic. "Fuzzy Logic" was just being
invented at the time.


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