Re: Universal grammar

"Hans" == Hans Aberg <haberg@xxxxxxxxxx> writes:

Hans> When developing a metamathematical theory, notational
Hans> problems do not occur, because one just skips over them! :-)
Hans> For example, Shoenfield, "Mathematical Logic", defines his
Hans> formal system in Lukasiewicz style prefix notation, thus
Hans> writing "A B =>", but as this becomes unreadable to humans,

Unreadable to you maybe. But I guess the Japanese would find this
notation very user-friendly and perfectly readable.


Hans> he later just says let "A => B" be a different notation for
Hans> "A B =>". This way of glossing over details is typical for
Hans> human written mathematics. You can't do that when working
Hans> with a computer.

Why not? Heard of reverse-Polish notation or postfix notation? All
of prefix, infix and postfix notations are employed in computing.


Hans> Also, the practice is very confusing to non-mathematicians,
Hans> which rather want to define a common notation.

I don't think a postfix notation would be more confusing than the
infix notation to a Japanese or any other person whose mother tongue
is in SOV or OSV order. And a native speaker of a VSO or VOS language
wouldn't find the infix notation less confusing than the prefix
notation.

At least, with prefix and postfix notations, one doesn't need
parenthesis -- a big win over the infix notation for people who can't
easily handle more than 3 levels of nesting.


Hans> I think you probably think of the capability of LR blowing
Hans> up exponentially in compilation. The same applies to NFA to
Hans> DFA conversions used in lexer generators such as Flex and
Hans> Lex. These cases do not seem to occur in naturally occurring
Hans> grammars.

Because naturally occurring grammars are so complicated (non-regular)
that they can't be modelled as DFAs nor NFAs.



--
Lee Sau Dan 李守敦 ~{@nJX6X~}

E-mail: danlee@xxxxxxxxxxxxxxxxxxxxxxxxxx
Home page: http://www.informatik.uni-freiburg.de/~danlee
.

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