[FOM] Fwd: Re: expressive power of natural languages

[Camilo Thorne]

Hi,

Just a small follow-up to Jakub's pointers. As he correctly mentioned,
formal (higher order) logic
has gathered a substantial consensus among linguistics as a means of
modelling NL semantics.
Montague in the 70s (and later Kennan, Barwise, Cooper, Heim) showed how
first and
higher order logic can be used to model (chiefly) the (i) compositionality
of NL meaning, (ii)
function argument structure and (ii) its truth functionality and
denotation. In this sense, every
NL quantifier (typically, noun phrases like "every man", "most men", etc.)
expresses/conveys/denotes a *generalized* quantifier, which need not be
first-order. In fact,
it is easy to prove that the formal semantics of "most" is *not* first
order (it does not verify
compactness), as shown by Barwise and Cooper in (suggested reading -
seminal paper):

http://philpapers.org/rec/BARGQA

which may be wise to read before you read the papers mentioned by Jakub.
Also, I would
recommend you to check the Handbook of Computational Linguistics and
Natural Language
Processing, Ch 15, for a basic introduction

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1405155817.html

Otherwise, there is the classical Gamut textbook

http://www.press.uchicago.edu/ucp/books/book/chicago/L/bo3628700.html

Similarly, function words express/convey/denote logical operations and
content words,
entities and their classes and relations.  Also notice that the semantics
of, e.g., tense
and aspect, requires temporal modalities, temporal interval algebras or
dynamic logic.

Cheers,

Camilo

On Sat, Dec 3, 2011 at 7:00 PM, Avril Styrman <Avril.Styrman at helsinki.fi>wrote:

> Dear FOMmers, I forward the below message on behalf of John Sowa.
>
> ----- Edelleenvälitetty viesti lähettäjältä sowa at bestweb.net -----
>
> John Kadvany:
>
>  My sense is also that Jackendoff, long of the generative school,
>>> also sees much of linguistic complexity as being handled by human
>>> cognition rather than being coded up via some mathematical
>>> representation.
>>>
>>
> Vaughn Pratt:
>
>  Are these necessarily mutually exclusive?  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 agree with Jackendoff that human cognition is more capable of
> understanding and reasoning about linguistic complexity than any
> formal system that we currently have.
>
> But I also agree with Pratt that mathematics is the best available
> tool for analyzing both complexity *and* human cognition. Furthermore,
> I believe that it's impossible to design and implement a system that
> can come close to the power of human cognition without using some
> high-powered mathematics.
>
> For an overview of my thoughts about how a deeper understanding
> of neuroscience and psycholinguistics can help us discover
> better mathematical techniques, see the following slides:
>
>   http://www.jfsowa.com/talks/**goal.pdf<http://www.jfsowa.com/talks/goal.pdf>
>   The goal of language understanding
>
> John Sowa
>
>
>
> ----- Välitetty viesti päättyy -----
>
>
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>



-- 
Camilo Thorne

Research Fellow
KRDB Research Centre for Knowledge and Data
Free University of Bozen-Bolzano
3, Piazza Domenicani
39100,Bolzano, Italy
tel:  (+39)0471016123
fax: (+39)0471016009
http://www.inf.unibz.it/~cathorne

"Exegi monumentum aere perennius"
(Horatius, Ode III-30)
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