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[ontolog-forum] Languages, Structures, and Diagramming

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 02 Jun 2014 09:13:56 -0400
Message-id: <538C7894.9050507@xxxxxxxxxxx>
Andrea and Leo,    (01)

I agree with Leo that the automatic generation of diagrams for
OWL RDF/XML ontologies is useful.  But I changed the subject line
to broaden the scope to a wider range of issues -- including a
recent note by Noam Chomsky to Lotfi Zadeh (copy below).    (02)

> Recently, there were some emails on the Linked Data community
> distribution list about the tools used to generate the LOD cloud
> diagram. One of the replies discussed a very simple approach -
> using GraphML and the yEd editor
> http://www.yworks.com/en/products_yed_applicationfeatures.html    (03)

One thing that's great about yEd is the ability to generate an
open-ended variety of diagram styles to highlight the structures
that may be significant for various problems, applications,
ontologies, and methodologies.    (04)

This raises another question about the relationships among various
kinds of languages -- natural, artificial, controlled natural -- and
diagramming techniques for analyzing or representing what they say.    (05)

That leads to a point by Chomsky (from the note below):    (06)

> it’s necessary to distinguish sharply between the theory of formal
> languages and the study of natural language.  There’s almost no
> connection between the two...    (07)

I agree that the theories are different.  But they can express the
same information, which can be (and has been) diagrammed with the
same kinds of methods.    (08)

NLs can represent anything and everything that anybody has ever said
in any formal notation, but they're not as tightly structured.  Many
people use diagrams as intermediate notations for mapping NLs to
formal languages of various kinds.    (09)

Question:  How can we develop the informal methods into a more
systematic methodology for relating NLs to various formalisms?    (010)

John    (011)

-------- Original Message --------
Subject:     FW: grammaticality and grammar/Chomsky
Date:   Sat, 31 May 2014 16:28:21 +0000
From:   Noam Chomsky <chomsky@xxxxxxx>
To:     zadeh@xxxxxxxxxxxxxxxxx <zadeh@xxxxxxxxxxxxxxxxx>    (012)

Am travelling around Europe giving endless talks and interviews on all
sorts of things, and very little free time, but I’d like to try a few
words about the issues you’re raising.    (013)

First, it’s necessary to distinguish sharply between the theory of
formal languages and the study of natural language.  There’s almost no
connection between the two, as I repeatedly emphasized in the work of
mine in the 1950s and since.  In fact, in Logical Structure of
Linguistic Theory, my long 1955 book (partially published finally in
1975), I didn’t even mention formal language theory because the book
was about human language.  Syntactic Structures, as perhaps you know,
was basically notes for an MIT undergrad class, engineers and
mathematicians.  All were indoctrinated at the time in beliefs about
Markov processes, statistical approximation, behaviorism, etc.  So
therefore the early part of the monograph discusses briefly why none
of this can be true, and then the rest goes on to the theory of human
language.  Same in my “three models” paper at the IRE symposium in ’56.
Unfortunately, it hasn’t been understood, since few looked beyond the
introductory passages on formal languages and refutation of prevalent
errors.    (014)

There are, in my opinion, only two results in formal language theory
that have any bearing on human language.  The first is the (trivial)
observation that even the richest class of finite automata (hence
Markovian systems far richer than those presupposed as adequate at the
time) cannot deal with even the most elementary properties of language
(nested dependencies).  There are, incidentally, “proofs” in the
computational linguistics literature “refuting” this trivial
observation, based on complete failure to comprehend it, more evidence,
if that is needed, that a little knowledge (of math) is a dangerous
thing.    (015)

The second result has to do with strong generative capacity, the only
aspect of formal language theory that has anything to do even remotely
with language (apart from the triviality just mentioned):  namely,
strong equivalence of CF grammars and non-deterministic linear-bounded
automata, a result that covers virtually all parsing systems.  It’s not
mathematically interesting.    (016)

The rest of the literature on formal language theory consists of some
interesting mathematics of no linguistic significance, and gross
misunderstandings involving weak context sensitivity, (NP-hard) weak
equivalence to CF grammars, etc. won’t go into that.    (017)

Let’s then put aside formal language theory and turn to the study of
human language.    (018)

First, we have to recognize that the term “language” is used in ways
that make serious inquiry impossible.  Thus we say that Chinese is a
language but Romance isn’t, though the Romance languages are at least as
close as the Chinese “dialects” to mutual intelligibility.  More so in
fact.  There’s talk about “computer languages,” “animal language,”
“formal languages,” and on, and on, even the language of the stars.  We
therefore confront the problem that has been familiar in the sciences
since their modern origin.  In the period of Galileo through Newton and
beyond, the “hard problem” was motion.  For the scientists of the day,
it included growth of flowers, motions caused by the will, etc., etc.
Science took off when Galileo and his successors recognized that they
must construct a highly idealized concept of motion, remote from
ordinary usage and understanding, and try to construct precise theories
of it.    (019)

The same has been true of all of science, and it’s true of language too.
Modern linguistics took off when the concept of generative grammar was
developed in its technical sense, investigating an idealized biological
system now sometimes called “I-language.” This study has achieved quite
far-reaching results, which I won’t try to review here.  That
incidentally includes notions of grammaticality (deviance) that are
quite precise and often well understood.  E.g., the clear gradation in
status among (1) “how many cars do you wonder if the mechanics fixed”
(OK), (2) “how many cars do you wonder which mechanics fixed”
(degraded), (3) how many mechanics do you wonder if fixed the cars”
(fully ungrammatical in English-type languages, in fact it seems in all
languages when apparent exceptions are properly analyzed).    (020)

Grammaticality, a theory internal notion, is distinct from
“acceptability”, determined by informant judgments (by experiments that
can be made as careful as one likes, and results are highly reliable).
For the latter, one can construct operational definitions.  For the
former, like all notions of the sciences, the notion is not really
appropriate, except in a highly idealized theory-internal sense.    (021)

There are many dimensions of acceptability, which the theoretical study
of language seeks to explain.  The example you gave is unacceptable,
but is fully grammatical, violating no rules of English.  The
unacceptability depends on factual assumptions, and as I mentioned,
even expressions that presuppose logical contradictions can be fully
grammatical, and must be if the theory of language is to be coherent.    (022)

“Motion” in the days of early modern science would have been regarded
as a “fuzzy notion,” had the concept been developed.  That would have
been an error.  The vast range covered by informal usage consisted of
subsystems that were perfectly precise and definite.  Same is true of
language, as far as we know, at least in the domains we are discussing.    (023)

That’s not to say that fuzzy logic is not applicable in many domains.
It no doubt is.  But this doesn’t seem to be one of them.    (024)

Hope that this is helpful.    (025)

Noam    (026)

-------- Original Message --------
From: Lotfi A. Zadeh [mailto:zadeh@xxxxxxxxxxxxxxxxx]
Sent: Wednesday, May 28, 2014 9:31 PM
To: Noam Chomsky
Subject: grammaticality and grammar/Chomsky    (027)

Dear Noam,    (028)

Many thanks for your prompt and informative response.  The questions
which I pose have many answers, depending on who is asking the
questions.  My assumption is that the person who is asking the questions
has mathematical maturity and is conversant with existing theories of
natural language.  Obviously enough, dictionary-style definitions is
not what is expected.    (029)

The concept of grammar in the context of formal languages is easy to
define.  It seems to me that it is difficult to construct an operational
definition of grammar and grammaticality in the context of natural
languages.  Obviously enough, the best we can do is to construct a
grammar for a subset of a language, say English.  In the case of my
example:irst At what time was dinner tomorrow?  Putting aside some
strange worlds and cultures, the question is clearly not good English.
It violates a rule.  So far as I know, existing grammars would classify
the question as grammatical.  Are there grammars which would classify
the question as grammatically incorrect?  If grammaticality is a matter
of degree, how can the degree be associated with a given sentence?    (030)

Underlying my questions is my perception that the concept of grammar
and grammaticality are fuzzy concepts, meaning that there is no sharp
boundary between what is a grammar and what is not a grammar, and what
is grammatical and what is not grammatical.    (031)

I hope that what I said above clarifies the meaning of my questions.
I put these questions on your table because I cannot think of anyone
who can answer them as authoritatively as you.    (032)

With my thanks and warm regards    (033)

Sincerely,    (034)

Lotfi    (035)

Lotfi A. Zadeh
Professor Emeritus
Director, Berkeley Initiative in Soft Computing (BISC)    (036)

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