Re: Universal grammar

In article <1162358621.139447.159490@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Rob
Freeman" <groups@xxxxxxxxxxxxxxxxxxx> wrote:

I don't know what you mean by "higher cognitive processing". But you
leave it undefined, so it is perhaps not important. You could redefine
it to be a search for patterns over text, and close the loop
completely.

It just refers to how the human brain is organized. Higher, more
structured thinking is called cognitive thinking, and is thought to be
mainly situated in the frontal lobe system.

The consequences of accepting "there are more patterns in text than can
be captured by any one summarization" are however profound. It means no
complete grammar can ever be found.

From the formal (mathematical) point of view, it can always be found: just
list all valid sentences.

That any single grammar will always
appear random (or alternatively that interpretation of any single
grammar will always appear ambiguous.)

And Lojban <http://www.lojban.org/> has a complete grammar, though being a
constructed language.

Language itself will appear
"polyvalent".

Many-valuedness is in itself not something making a formal
grammar description possible.

If grammar is equated with meaning, it means "truth" will
always be subjective. That the fundamental definition of truths will
always be in terms of "paradigms" (sets of examples), and no logical
argument for one or other truth will make sense in terms of the other
(because they will each define their own logic.) This also means the
logical foundations of any discipline based on "truth" will be
"uncertain".

If the grammar is tied to human cognitive thinking, then that is is a
problem. It is not clear this is so with human languages, though.

The analogy with the logical paradoxes of maths would be interesting to
explore. But I understand you are looking for a solution within your
own theory.

I sort of just got curious on the Prolog programming style in the form of
language implementation. After experimenting awhile with CLP, I decided to
try out the theorem prover variation.

I think you were right to ask in a language group.
Linguistics has dealt extensively with the search for universal
representation.

I got new ideas from it (see below).

As I say, Dependency Grammar sounds very similar to
your idea for syntax independence using trees.

I am just using standard math; thus, as far as I could see, nothing of
that you mention.

I don't recall what kind
of trees Aravind Joshi's "Tree-Adjoining Grammar" uses. Perhaps Lexical
Functional Grammar..., Wiki: "The LFG approach has had particular
success with ... languages in which the relation between structure and
function is less direct than it is in languages like English; for this
reason LFG's adherents consider it a more plausible universal model of
language." There will be others. Plenty has been done. But be careful.
In my opinion the salient point is that they have all failed. No-one
has come up with a complete grammar, let alone a universal grammar.

One might explore the Prolog pattern matching idea in various context,
including the processing of human language. In this setup, one has, in
each given context, a set of rules. If one has an input x that should be
structured, the one applies the unification u(x, p_i) for all applicable
patterns p_i, producing a substitution s which tells how an an applicable
rule should be specialized. Then, the applicable rules says how x should
be altered in order to be able to repeat this process.

So this is essentially what Prolog does, and a theorem prover does, and I
thought it might be applicable to other situations as well, like parsing.

From your standpoint, it would not ,matter how general your examples are,
as they can be specialized via a substitution.

--
Hans Aberg
.

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