Quantifier Raising: given a sentence [... [QDP] ...], build a new
sentence [QDP (\x.[... [x] ...])].
+Here, QDP is a scope-taking quantificational DP.
+
Just to emphasize the similarity between QR and shift, we can use QR
to provide insight into the tree task that mystified us earlier.
\tree (. (a)((S)((d)((S)(e)))))
+<pre>
.
__|___
| |
d _|__
| |
S e
+</pre>
First we QR the lower shift operator
\tree (. (S) ((\\x) ((a)((S)((d)((x)(e)))))))
+<pre>
.
___|___
| |
d _|__
| |
x e
+</pre>
Next, we QR the upper shift operator
\tree (. (S) ((\\y) ((S) ((\\x) ((a)((y)((d)((x)(e)))))))))
+<pre>
.
___|___
| |
d _|__
| |
x e
+</pre>
We then evaluate, using the same value for the shift operator proposed before:
\tree (. (S) ((\\y) ((a)((y)((d)(((a)((y)((d)(("")(e)))))(e)))))))
+<pre>
.
___|___
| |
d __|__
| |
"" e
+</pre>
Repeating the process for the upper shift operator replaces each
\tree (. ((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(("")(e)))))(e))))))
+<pre>
.
|
______|______
d __|__
| |
"" e
+</pre>
-The yield of this tree (the sequence of leaf nodes) is aadadeedaadadeedee.
+The yield of this tree (the sequence of leaf nodes) is
+aadadeedaadadeedee, which is the expected output of the double-shifted tree.
Exercise: the result is different, by the way, if the QR occurs in a
different order.
separating a box into two regions, the payload and the hidden scratch
space:
+<pre>
_______________ _______________ _______________
| [x->2, y->3] | | [x->2, y->3] | | [x->2, y->3] |
------------------- ------------------ ------------------
| | ยข | | = | |
| +2 | | y | | 5 |
|______________| |______________| |______________|
-
-
-(Imagine the + operation has been lifted into the Reader monad too.)
+</pre>
For people who are familiar with Discourse Representation Theory (Kamp
1981, Kamp and Reyle 1993), this separation of boxes into payload and