Assignment 10: Negation

For each positive assertion in English, there appears to be a corresponding
negative assertion:

(1)   My beer is warm.
(2)   My beer is not warm.

(3)   Harvey has wrestled alligators.
(4)   Harvey has not wrestled alligators.

You can test this out.  Think of any positive assertion, and see if you can 
produce the corresponding negative.

This homework will be about the negative versions of sentences.  Beware,
because there are negative versions of other things.  In

(5)   Not many cats will eat dog food.
and
(6)   They found us not in the kitchen, but in the basement.

we see the negation of NPs and PPs.  In

(7)   The goat might have been not paying attention.

we see the negation of a VP.  These cases, where the thing negated is not
the whole S, are called "constituent negation".  We will not be concerned with
constituent negation in this assignment, but only with sentence negation.

In determining the syntax of sentence negation, the first task is to decide
where 'not' goes in the sentence structure.  Consider facts like:

(8)   The frog must not have eaten the grasshopper.
(9)   The frog had not eaten the grasshopper.
(10)  The frog was not eating the grasshopper.
(11) *The frog ate not the grasshopper.
(12)  The frog did not eat the grasshopper.
(13)  The frog had not been eating the grasshopper.
(14) *The frog not had been eating the grasshopper.
(15) *The frog had been eating not the grasshopper.

Come up with a generalization (in words): Where exactly does the sentential
negator 'not' have to be with respect to the various verbs of the sentence?
This is a question about what you observe in English, not about the grammar.

The next question, of course, is how to modify the grammar so that the
grammatical sentences are generated and the ungrammatical ones are not. 

This may be very hard.  Try as hard as you can.

Make sure that you clearly explain in words how your solution works, and that
you record it in appropriate notation. To convince us that your solution is
right, be sure to argue *against* an interesting alternative. Why is your
solution better?