From 88b8a69e01f705bf5000ce75cd3f70caea1a929d Mon Sep 17 00:00:00 2001 From: Chris 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 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))))) +
```   .
__|___
|    |
@@ -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 double-shifted 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