[FOM] Logic and Linguistics

John McCarthy jmc at cs.Stanford.EDU
Sun Apr 1 22:01:18 EDT 2007

It's not hard to give a phrase structure grammar for first order
logic, but such a grammar will not do syntactic justice to bound
variables.  Something more is needed for any language with bound
variables that will at least do justice to their substitutivity.

One approach keeps a list of free variables along with the phrase
structure of the expressions and removes variables from the list
where they are bound.

This is a response John Baldwin's 
> On the one hand it is a common place to regard first order logic as 
> developed in a `formal language'.  On the other hand, some `Chomskian' 
> positions claim (e.g. Devlin, The Math Gene page 157)  that phase 
> structure grammars give an underlying structure for all natural languages.
> First order logic is often thougt of as expressing a very specific subset 
> of  what natural language expresses. (a collection of declarative 
> sentences).
> Can one analyze first order logic in terms of phase structure grammars. 
> If so, does someone have a reference.  If I am mixing apples and oranges 
> perhaps someone can explain which is which.
> John T. Baldwin
> Director, Office of Mathematics Education
> Department of Mathematics, Statistics, 
> and Computer Science  M/C 249
> jbaldwin at uic.edu
> 312-413-2149
> Room 327 Science and Engineering Offices (SEO)
> 851 S. Morgan
> Chicago, IL 60607
> Assistant to the director
> Jan Nekola: 312-413-3750
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