more semantics

[Joan Bresnan]

Hi, Alex.  I just wanted to make one observation about the
representation of quantifier scope ambiguities in LF that you may not
be aware of.   

Some years ago Jaakko Hintikka (see his "Quantifiers and
Quantification Theory", in LI 5.2, 1974) introduced to generative
linguistics the phenomenon that has come to be called "branching
quanitifiers".  These are cases of natural language quantification
which cannot be translated into the language of quantification theory
(first order logic, which was the basis of both the early generative
semantics representations and LF in Chomskyan theory starting with
May).  Some examples are:

1) Some relative of each villager and some relative of each townsman
hate each other.
2) Some element of each A contains some element of each B.

See Hintikka's paper for a very nice discussion of the analysis of
these examples and their significance.  Hintikka argued that the
correct semantic interpretation of theses examples is impossible to
state in first-order logic, which has a linear ordering of quantifiers
corresponding to their scoping, but could be captured in
game-theoretic semantics, which can be expressed in second order
quantification theory (using Skolem functions).  In these examples,
quantifiers are not linearly ordered as ExVy(formula) or VyEx(formula),
but partially ordered with respect to each other:

Ex
  \(formula in x and y)
  /
Vy

Several interesting results follow from this; for example, Hintikka
argues that given the enormous logical power of natural language
semantics implied by this phenomenon, "there is an enormous difference
between syntax and semantics" (p. 174).

But for present purposes, I think we can conclude that logical form
(in a theory-neutral sense) could have partially ordered quantifiers,
which would yield several distinct interpretations from a single
representation.

After this work, Chomskyan LF had to be beefed up to allow equivalent
formulations. 

>>From these assumptions it follows that, in GB, ambiguity, which has to
do with meaning, must be captured at LF; in other words, in GB, an
ambiguous string of words must have alternative grammatical
representations, distinct at least at LF, one for each of the
alternative meanings.  If this is not correct, it must be because one

Now I *think* the above shows that your latter assumption is not
correct.

Joan