Date: Tue, 12 May 2015 09:18:44 0400
Subject: [PATCH] edits

topics/_week15_continuation_applications.mdwn  20 ++++++++++++++++
1 file changed, 16 insertions(+), 4 deletions()
diff git a/topics/_week15_continuation_applications.mdwn b/topics/_week15_continuation_applications.mdwn
index ec0cb5d6..cc5c9e29 100644
 a/topics/_week15_continuation_applications.mdwn
+++ b/topics/_week15_continuation_applications.mdwn
@@ 104,11 +104,14 @@ Raising closely resembles the reduction rule for shift:
Quantifier Raising: given a sentence [... [QDP] ...], build a new
sentence [QDP (\x.[... [x] ...])].
+Here, QDP is a scopetaking 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)))))
+ .
_____
 
@@ 119,11 +122,13 @@ a _____
d ___
 
S e
+
First we QR the lower shift operator
\tree (. (S) ((\\x) ((a)((S)((d)((x)(e)))))))
+ .
______
 
@@ 138,11 +143,13 @@ S ______
d ___
 
x e
+
Next, we QR the upper shift operator
\tree (. (S) ((\\y) ((S) ((\\x) ((a)((y)((d)((x)(e)))))))))
+ .
______
 
@@ 161,6 +168,7 @@ S _______
d ___
 
x e
+
We then evaluate, using the same value for the shift operator proposed before:
@@ 174,6 +182,7 @@ form:
\tree (. (S) ((\\y) ((a)((y)((d)(((a)((y)((d)(("")(e)))))(e)))))))
+ .
______
 
@@ 196,6 +205,7 @@ S _______
d ____
 
"" e
+
Repeating the process for the upper shift operator replaces each
@@ 203,6 +213,7 @@ occurrence of y with a copy of the whole tree.
\tree (. ((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(((a)((((a)(("")((d)(((a)(("")((d)(("")(e)))))(e))))))((d)(("")(e)))))(e))))))
+ .

____________
@@ 235,8 +246,10 @@ a _______  
d ____
 
"" e
+
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 doubleshifted tree.
Exercise: the result is different, by the way, if the QR occurs in a
different order.
@@ 285,15 +298,14 @@ manipulates a list of information. It is natural to imagine
separating a box into two regions, the payload and the hidden scratch
space:
+ _______________ _______________ _______________
 [x>2, y>3]   [x>2, y>3]   [x>2, y>3] 
  
  Â¢   =  
 +2   y   5 
______________ ______________ ______________


(Imagine the + operation has been lifted into the Reader monad too.)
+
For people who are familiar with Discourse Representation Theory (Kamp
1981, Kamp and Reyle 1993), this separation of boxes into payload and

2.11.0