From: Chris Barker <barker@kappa.linguistics.fas.nyu.edu>
Date: Mon, 1 Nov 2010 19:14:53 +0000 (-0400)
Subject: Added assignmemnt 6
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=01979f60c8474ffe20e4a1a20d59bfff5d3950c6;ds=sidebyside

Added assignmemnt 6
---

01979f60c8474ffe20e4a1a20d59bfff5d3950c6
diff --cc intensionality_monad.mdwn
index 6887487f,36a0cddd..3b69ef9f
--- a/intensionality_monad.mdwn
+++ b/intensionality_monad.mdwn
@@@ -1,43 -1,35 +1,41 @@@
- The intensionality monad
- ------------------------
 -The "intensionality" monad
 ---------------------------
 -
+ Now we'll look at using monads to do intensional function application.
+ This really is just another application of the reader monad, not a new monad.
+ In Shan (2001) [Monads for natural
+ language semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that
+ making expressions sensitive to the world of evaluation is conceptually
+ the same thing as making use of the reader monad.
+ This technique was beautifully re-invented
+ by Ben-Avi and Winter (2007) in their paper [A modular
+ approach to
++>>>>>>> f879a647e289a67b992caaafd497910259a81040
+ intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
+ though without explicitly using monads.
+ 
+ 
+ All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
+ To run it, download the file, start OCaml, and say 
  
- In the meantime, we'll look at several linguistic applications for
- monads, based on what's called the *reader monad*, starting with
- intensional function application.  
+ 	# #use "intensionality-monad.ml";;
+ 
+ Note the extra `#` attached to the directive `use`.
  
 -Here's the idea: since people can have different attitudes towards
 -different propositions that happen to have the same truth value, we
 -can't have sentences denoting simple truth values.  If we did, then if John
 -believed that the earth was round, it would force him to believe
 -Fermat's last theorem holds, since both propositions are equally true.
 -The traditional solution is to allow sentences to denote a function
 -from worlds to truth values, what Montague called an intension.  
 -So if `s` is the type of possible worlds, we have the following
 -situation:
 +First, the familiar linguistic problem:
 +
 +       	   Bill left.  
 +	   Cam left.
 +	   Ann believes [Bill left].
 +	   Ann believes [Cam left].
 +
 +We want an analysis on which all four of these sentences can be true
 +simultaneously.  If sentences denoted simple truth values or booleans,
 +we have a problem: if the sentences *Bill left* and *Cam left* are
 +both true, they denote the same object, and Ann's beliefs can't
 +distinguish between them.
 +
- In Shan (2001) [Monads for natural language
- semantics](http://arxiv.org/abs/cs/0205026v1), Ken shows that making
- expressions sensitive to the world of evaluation is conceptually the
- same thing as making use of a *reader monad*.  This technique was
- beautifully re-invented by Ben-Avi and Winter (2007) in their paper [A
- modular approach to
- intensionality](http://parles.upf.es/glif/pub/sub11/individual/bena_wint.pdf),
- though without explicitly using monads.
- 
- All of the code in the discussion below can be found here: [[intensionality-monad.ml]].
- To run it, download the file, start OCaml, and say 
- 
- 	# #use "intensionality-monad.ml";;
- 
- Note the extra `#` attached to the directive `use`.
- 
 +The traditional solution to the problem sketched above is to allow
 +sentences to denote a function from worlds to truth values, what
 +Montague called an intension.  So if `s` is the type of possible
 +worlds, we have the following situation:
  
  
  <pre>