[FOM] Natural language expressive power and complexity

[Valeria de Paiva]

hi Alex,

>I was wondering if there is any (at least semi-)conclusive view about the
> expressive power of a natural language like english resulting in a statement
> like "whatever it is, it is a language of at least 2nd order".

Being a lazy person I was hoping someone more officially
representative of the community of Natural Language Semantics was
going to reply to your question.
But since I haven't seen anyone yet(maybe I haven't seen all the
replies), here  goes my take on it.

Most of the more interesting work I've seen has turned your question around, ie
what are the complexity results we can prove for fragments of English
that seen sensible fragments?
There is a very rich literature on the question as above, of which I'd
recommend  the work of Ian Pratt-Hartmann and Larry Moss, check their
webpages for loads of good information.

as for Vaughan's point:
>Absence of a mathematical representation sounds more like a symptom of either lack of >progress towards understanding human cognition, or rejection of mathematics as an
>aid to description and analysis, than a property of language and how it's understood.
I'd say that there mathematical representations, many of them. The
issue, at least when you change the question to the one above is to
decide:
1.  what are the interesting fragments?
2. how to choose the representations so that we get as large as
possible coverage of the language?

cheers,
Valeria de Paiva


-- 
Valeria de Paiva
http://www.cs.bham.ac.uk/~vdp/
http://valeriadepaiva.org/www/