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<body><><><><><><><><><><><><>--This is the Language List--<><><><><><><><><><><><><><BR>
<BR>
<br>
<br>
Steven D'Aprano wrote:<br>
<blockquote type="cite"
cite="mid0209090403583X.01114@localhost.localdomain">
<pre wrap=""><!---->And language is too important to let the essential meaning of the word
be diluted by those who would talk about the language of art. Art does
not communicate, any more than words use language. Art is the medium of
communication, not the body that communicates.
</pre>
</blockquote>
<br>
I wrote earlier that language is very-well-defined. I am copying this out
of a book. I think<br>
it should be read carefully, and saved and referred to regularly by anyone
who has<br>
an interest in this topic. I am copying from this book because it is short,
concise and<br>
has other wonderful applications which will interest the readers.<br>
<br>
The relevance of this will be shown below. If I am going thru all this trouble
of typing<br>
it seems those who want to comment should at least read carefully and think
a while<br>
about what all this means.<br>
<br>
{Note": The set inclusion sign is denoted by @, or I use the word "is-in"
to mean the<br>
same thing. The symbol "->" and "=>" are both arrows, and used differently.<br>
The notation P(i+1) used once means P subscript i+1. Elsewhere the subscript<br>
is simply lower case e.g. Pi is P sub i except where integers are used e.g.
P2, P3, etc) )<br>
<br>
<br>
>From page 331 of Banks, Signal Processing, Image Processing and Pattern<br>
Recognition, Prentice-Hall, 1990.<br>
<br>
----------------------------------start here -----------------------------------------<br>
[1] We begin by abstracting the basic elements of an ordinary (written)
language. An alphabet<br>
is a finite nonempty set V whose elements are called letters. A word w (over
V) is a finite<br>
string of zero or more letters of V, and its length is |w| being the number
of letters in the string.<br>
... The set of all words over V is denoted by W(V) or just W if no confusion
over the set of<br>
letters is likely.<br>
<br>
[2] If P, Q @W [mine: e.g. P,Q is-in W) then PQ (or P*Q) denotes their concatenation.
Note that <br>
concatenation is associative ... P is a subword of Q if Q=P1*P*P2 for some
P1,P2 @W. <br>
Subsets of W are called languages (over V).<br>
<br>
[3] A generative grammar (or phrase structure grammar is a quadruple G=(Vn,Vtm,S,F)
where Vn and Vt <br>
are disjoint alphabets, S@Vn, and F is a finite set of ordered pairs (P,Q)
such that P,Q@W(V),<br>
where V=Vn.union.Vt and P contains at least one letter of Vn. The elements
of Vn are called<br>
nonterminals, and those of Vt terminals, while S is called the initial letter.
If (P,Q)@F we write<br>
P ->Q <br>
<br>
[4] Such an element (P,Q) is called a rewriting rule or production. We say
that P generates Q directly<br>
and write P=>Q is there exist words R,T and a production P1->Q1 @F
such that P=R*P1*T and <br>
Q=R*Q1*T. Similarly, we say that P generates Q and write P=>*Q if there
exists a finite<br>
sequence of words P0,..., Pk such that Po=P, Pk=Q and Pi=>P (i+1) for
0<=i<=k-1. Thus<br>
P=>* Q = P= P0=>P1...=>Pk=Q.<br>
<br>
[5] The language L(G) generated by G is then defined by<br>
L(G) = {P: P@W(Vt), S=>*P}<br>
....<br>
The rules of production (i.e. elements of F) defined above are very general
and without<br>
some restrictions lead to significant problems in formal language theory.
A hierarchy of grammars<br>
is therefore introduced, each being more general than the following grammar.
The four main<br>
types may be defined as follows:<br>
<br>
[6] Type 0 or unrestricted grammar allows productions as defined above.<br>
Type 1 or context-sensitive grammar allows only production of the form.....<br>
Type 2 or context-free grammar allows productions of form A -> P where
A@Vn, <br>
and P@W(V).<br>
Type 3, or finite-state or regular grammar allows productions of the forms
A -> BP, <br>
or A -> P, where A,B @Vn, P@W(Vt).<br>
---------------------------------------------end here -----------------<br>
<br>
Before Larry gets boringly pedantic, we should notice that the restriction
to<br>
"letters" is for simplicity. We can assume that we use a phonemic or phonetic<br>
alpahbet ( and that there are no extra monstrocities such as English "two,
too, to"<br>
etc. These certainly make things more complicated but do not add to the <br>
discussion.<br>
<br>
Now the real problems are elsewhere. (I numbered the paragraphs to make <br>
it easier for later discussion and referral, but I will not put comments
here now<br>
because it will get too long.)<br>
<br>
Arguments against this from linguists (not all linguists) are various kinds.
Probably<br>
the most common one (and the most confusing one) is this one:<br>
<br>
THIS LANGUAGE PRODUCES ALL KINDS OF THINGS! WHAT<br>
KIND OF A LANGUAGE IS THAT? <br>
<br>
Yes it does, and so it should. Indeed, I give an example right from this<br>
book, on page 339, and I will quote.<br>
<br>
--------------------------start here --------------------<br>
In this section we shall describe some of the more widely used pattern<br>
languages and their primitives. The first was developed to deal with<br>
two-dimensional picture type objects which do not link together naturally<br>
at single points. This means that simple concatenation of symbols cannot<br>
be applied without some simplification of picture primitives. In order to<br>
reduce the problem to a concatenation language the picture description<br>
language (PDL) is defined in terms of primitives, each of which has only<br>
two points (head and tail) which can be joined to other primitives.....<br>
-----------------------end here-----------------------------------<br>
<br>
<br>
Note: No circularity. There are primitives.<br>
<br>
Now, here is the main problem. And it is a very general one. Some linguists<br>
want to know why these grammars can be used for things other than<br>
natural language such as English. The answer is quite simple. Did they ask<br>
their teacher why there are no integers for counting only apples? Did they<br>
ask their physics teachers what kind of physics uses equations for electrical<br>
circuits (e.g. TV tuner) the same equation that can be used to model the<br>
sugar-insulin cycle ? Did they ask why the equation for the propagation
of<br>
sound waves after an integral transform happens to be the same equation <br>
as that of a pendulum? There are many many such examples.<br>
<br>
The best answer is yet another question:<br>
<br>
Why should the mathematical formulation of language not be able to<br>
also model other things?<br>
<br>
I deleted many things but they are all trivially non-germane. What is really<br>
required is what is called "maturity" (mathematical maturity). That is the<br>
crux of the problem. The rest is boring detail.<br>
<br>
The historical explanation is simply that because of the development of<br>
digital computers, the field suddently went on a trip on a super-highway
and it is much<br>
different than riding on a donkey cart. There is a book called "Thirty Years
That<br>
Shook Physics" (about the relativistic and quantum explosion). That also
lost a lot of<br>
old-time physicists. That is how life is. The same thing happened to economics.
So now<br>
it is the time of linguistics.<br>
<br>
<br>
<pre class="moz-signature" cols="$mailwrapcol">--
M. Hubey
<a class="moz-txt-link-abbreviated" href="mailto:hubeyh@mail.montclair.edu">hubeyh@mail.montclair.edu</a> /\/\/\/\//\/\/\/\/\/\/<a class="moz-txt-link-freetext" href="http://www.csam.montclair.edu/~hubey">http://www.csam.montclair.edu/~hubey</a></pre>
<br>
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