- 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>