[FOM] Logic and Linguistics

[David Auerbach]

Which grammar (in the Chomsky hierarchy) works for the language of  
first-order logic is sensitive to the specification of language (for  
example, how the indexing of the variables is handled). I.e., there's  
no such thing as *the* language of first-order logic.  A good source  
on this is:

H. Levin - Categorical Grammar and the Logical Form of Quantification,
Bibliopolis, 1982

There may be later stuff.

On Apr 1, at 10:15 PM, Neil Tennant wrote:

> On Sun, 1 Apr 2007, John Baldwin wrote:
>
>> Can one analyze first order logic in terms of phase structure  
>> grammars.
>> If so, does someone have a reference.
>
> Linguists like Barbara Hall Partee and Gerald Gazdar worked on this  
> in the
> mid-1970s. I believe the language of first-order logic has a
> context-sensitive grammar, hence can be recognized by a linear bounded
> automaton. The main grammars, and the automata recognizing them, are
> covered in "Formal languages and their relation to automata" by  
> John E.
> Hopcroft and Jeffrey D. Ullman (Reading, Mass., Addison-Wesley Pub.  
> Co.
> 1969). (There is also a more recent edition with Aho as a third  
> author.)
>
> Neil Tennant
>
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David Auerbach
Department of Philosophy & Religion
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