Re: Universal grammar

Hans Aberg wrote:
"Rob Freeman" <groups@xxxxxxxxxxxxxxxxxxx> wrote:

How are you trying to define semantics, Hans? What is giving you
trouble with it?

The traditional metamathematics takes a syntactic approach studying object
mathematics, leading to a "formal system", a language consisting of merely
symbols composed according to certain rules. Object math is though
properly describing integers, real numbers, etc. It is hard to pin these
objects down directly, the formal system approach being simpler from
the metamathematical point of view.

I use an intermediate, trees similar to the ASTs used in computer compiler
implementations. The point is that these are syntax independent. When
using a parser generator, one will have to generate some "semantics",
i.e., code snippets, and then these ASTs are useful.

That is fine. I would just suggest you don't abstract your "formal
system" into trees until you need the "semantics"* of the trees.

That means you don't lose the full power of the formal system
consisting of sequences of symbols before you need to. In particular
you don't lose the power of sequences of symbols to be interpreted
ambiguously.

You want the information expressed in trees, and you can get the
information you need from sequences of symbols. But once you change
your representation to trees you lose the ability to represent
ambiguous information. Going from sequences of symbols to trees
involves a choice of information. You must be sure the information you
choose is that which is relevant to your problem.

I still don't see why you said "it proves difficult to define
semantics".

What difficulties are you having? The difficulty is not that you are
trying to define a representation in terms of trees which still
captures all the power of sequences of symbols to express ambiguity, is
it?

*It seems you are defining "semantics" as the relationships between
tokens expressed in your trees. Is that true?

-Rob

.

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