X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2F_week10_gsv.mdwn;h=4ff29764874b83c02a7bef3918c29319e58e14d5;hp=63bd071126216eac7ad6449c94dce5e324bb8b47;hb=291555207a30b07dd33b3d493ca863bc64ea9edb;hpb=aa3fa8ee79bd50b6371da340227b2144026ae3a7

diff --git a/topics/_week10_gsv.mdwn b/topics/_week10_gsv.mdwn
index 63bd0711..4ff29764 100644
--- a/topics/_week10_gsv.mdwn
+++ b/topics/_week10_gsv.mdwn
@@ -13,7 +13,8 @@ of discourse update.  One way of looking at this paper is like this:
         
     GS = Dynamic theories of binding of Groenendijk and Stokhof, e.g.,
          Dynamic Predicate Logic L&P 1991: dynamic binding, donkey anaphora
-         Dynamic Montague Grammar 1990: generalized quantifiers, discourse referents
+         Dynamic Montague Grammar 1990: generalized quantifiers and
+         discourse referents
 
     V = a dynamic theory of epistemic modality, e.g., 
         Veltman, Frank. "Data semantics." 
@@ -25,14 +26,16 @@ of discourse update.  One way of looking at this paper is like this:
 That is, Groenendijk and Stokhof have a well-known theory of dynamic
 semantics, and Veltman has a well-known theory of epistemic modality,
 and this fragment brings both of those strands together into a single
-system.  
+system.  The key result, as we'll discuss, is that adding modality to
+dynamic semantics creates some unexpected and fascinating
+interactions.
 
 ## Basics of GSV's fragment
 
 The fragment in this paper is unusually elegant.  We'll present it on
 its own terms, with the exception that we will not use GSV's "pegs".
 See the discussion below below concerning pegs for an explanation.
-After presenting the paper, we'll re-engineering the fragment using
+After presenting the paper, we'll re-engineer the fragment using
 explicit monads.
 
 In this fragment, points of evaluation are not just worlds, but pairs
@@ -45,10 +48,9 @@ information about the world (which possible worlds are live
 possibilities?) as well as information about the discourse (which
 objects to the variables refer to?).
 
-The formal language the fragment interprets is Predicate Calculus with
-equality, existential and universal quantification, and on unary
-modality (box and diamond, corresponding to epistemic necessity and
-epistemic possibility).
+The formal language the fragment interprets is the Predicate Calculus
+with equality, existential and universal quantification, and one unary
+modality, interpreted as epistemic possibility.
 
 An implementation in OCaml is available [[here|code/gsv.ml]]; consult
 that code for details of syntax, types, and values.  [[An implementation
@@ -65,12 +67,13 @@ Immediately following are the recipes for context update (GSV's
 definition 3.1).  Following GSV, we'll write `update(s, φ)` (the
 update of information state `s` with the information in φ) as `s[φ]`.
 
-    s[P(t)] = {(w,g) in s | w P (ref((w,g),t))}
+    s[P(t)] = {(w,g) in s | extension w P (ref((w,g),t))}
 
 So `man(x)` is the set of live possibilities `(w,g)` in s such that
-the set of men in `w` given by `w(man)` maps the object referred to by
-`x`, namely, `g("x")`, to `true`.   That is, update with "man(x)"
-discards all possibilities in which "x" fails to refer to a man.
+the set of men in `w` given by `extension w "man"` maps the object
+referred to by `x`, namely, `g("x")`, to `true`.  That is, update with
+"man(x)" discards all possibilities in which "x" fails to refer to a
+man.
 
     s[t1 = t2] = {i in s | ref(i,t1) == ref(i,t2)}
 
@@ -85,10 +88,11 @@ Existential quantification is somewhat intricate.
 
 Here's the recipe: given a starting infostate s, choose an object a
 from the domain of discourse.  Construct a modified infostate s' by
-adjusting the assignment function of each possibility so as to map the variable x to a.
-Then update s' with φ.  Finally, take the union over the results of
-doing this for every object a in the domain of discourse.  If you're
-unsure about this, examine the [[code|code/gsv.ml]].
+adjusting the assignment function of each possibility so as to map the
+variable x to a.  Then update s' with φ.  Finally, take the union over
+the results of doing this for every object a in the domain of
+discourse.  If you're unsure about exactly what this recipe does,
+examine the implementations linked above.
 
 Negation is natural enough:
 
@@ -177,7 +181,8 @@ hungry* will also be empty, as indicated above.
 In order for update with *Alice might be hungry* to be non-empty,
 there must be at least one possibility in the input state in which
 Alice is hungry.  That is what epistemic might means in this fragment:
-the prejacent must be possible.  But update with *Alice isn't hungry*
+there must be a possibility in the starting infostate that is
+consistent with the prejacent.  But update with *Alice isn't hungry*
 eliminates all possibilities in which Alice is hungry.  So the
 prediction of the fragment is that update with the sequence in (1)
 will always produce an empty information state.
@@ -192,6 +197,9 @@ We'll start with the same two possibilities.
     = {hungry, full}[Alice isn't hungry]
     = {full}
 
+This is a very different result: the two sentences are consistent, and
+do not guarantee an empty output infostate.
+
 GSV comment that a single speaker couldn't possibly be in a position
 to utter the discourse in (2).  The reason is that in order for the
 speaker to appropriately assert that Alice isn't hungry, that speaker
@@ -207,32 +215,35 @@ speaker assumes that as far as the listener knows, Alice might be
 hungry, they can utter the discourse in (2).  Here's a variant that
 makes this thought more vivid:
 
-    3. Based on public evidence, Alice might be hungry.  
-       But in fact I have private knowledge that she's not hungry.
+    3. (Based on public evidence,) Alice might be hungry.  
+       (But in fact I have private knowledge that) she's not hungry.
 
 The main point to appreciate here is that the update behavior of the
-discourses depends on the order in which the updates due to the
-individual sentence occur.  
+discourses depends on the order in which the sentences are processed.
 
-Note, incidentally, that there is an asymmetry in the fragment
-concerning negation.
+Note, incidentally, that the treatment of modality contains an
+asymmetry related to negation.
 
     4. Alice might be hungry.  Alice *is* hungry.
     5. Alice is hungry.  (So of course) Alice might be hungry.
 
 Both of these discourses lead to the same update effect: all and only
-those possibilites in which Alice is hungry survive.  You might think
-that asserting *might* requires that the prejacent be not only
-possible, but undecided.  If you like this idea, you can easily write
-an update rule for the diamond on which update with the prejacent and
-its negation must both be non-empty.
+those possibilites in which Alice is hungry survive.  So negating an
+assertion rules out the possibility, but asserting the non-negated
+version does not. 
+
+You might think that asserting *might* requires that the prejacent be
+not merely possible, but undecided.  If you like this idea, you can
+easily write an update rule for the diamond on which update with the
+prejacent and its negation must both be non-empty.
 
 ## Order and binding
 
 The GSV fragment differs from the DPL and the DMG dynamic semantics in
-important details.  Nevertheless, it says something highly similar to
-DPL about anaphora, binding, quantificational binding, and donkey
-anaphora (at least, when modality is absent, as we'll discuss below).
+important details.  Nevertheless, it is highly similar to DPL with
+respect to anaphora, binding, quantificational binding, and donkey
+anaphora (at least, until we add modality into the mix, as we will
+below).
 
 In particular, continuing the theme of order-based asymmetries,
 
@@ -241,7 +252,9 @@ In particular, continuing the theme of order-based asymmetries,
 
 These discourses differ only in the order of the sentences.  Yet the
 first allows for coreference between the indefinite and the pronoun,
-where the second discourse does not.  In order to demonstrate, we'll
+where the second discourse does not.  
+
+In order to demonstrate how the fragment treats these discourses, we'll
 need an information state whose refsys is defined for at least one
 variable.
 
@@ -312,11 +325,11 @@ The outcome is different if the order of the sentences is reversed.
 
        = {(w,g[x->b][x->b]), (w,g[x->b][x->c])}
 
-The result is different than before.  Before, there was only one
-possibility: that x refered to the only person who both entered and
-sat.  Here, there remain two possibilities: that x refers to Bob, or
-that x refers to Carl.  This makes predictions about the
-interpretation of continuations of the dialogs:
+Before, there was only one possibility: that x refered to the only
+person who both entered and sat.  Here, there remain two
+possibilities: that x refers to Bob, or that x refers to Carl.  This
+makes predictions about the interpretation of continuations of the
+dialogs:
 
     11. A man^x entered.  He_x sat.  He_x spoke.
     12. He_x sat.  A man^x entered.  He_x spoke.
@@ -354,7 +367,8 @@ following dynamic equivalence:
 
     (∃x.enter(x)) and (sit(x)) ≡ ∃x (enter(x) and sit(x))
 
-In words, existentials take effective scope over subsequent clauses.
+In words, existentials can bind pronouns in subsequent clauses even if
+they don't take syntactic scope over those clauses.
 
 The presence of modal possibility, however, disrupts this
 generalization.  GSV illustrate this with the following story.
@@ -385,11 +399,11 @@ least one possibility in which a person in the closet is guilty.  In
 this scenario, world w' is the verifying world: Carl is in the closet,
 and he's guilty.  It remains possible that there are closet hiders who
 are not guilty in any world.  Alice fits this bill: she's in the
-closet in world w', but she is not guilty in any world.
+closet in world w, but she is not guilty in any world.
 
 Let's see how this works out in detail.
 
-    14. Someone^x is in the closet.  He_x might be guilty.
+    14. Someone^x is in the closet.  They_x might be guilty.
 
          {(w,g), (w',g}[∃x.closet(x)][◊guilty(x)]
 
@@ -434,9 +448,10 @@ Now we consider the second half:
 
        = {(w',g[x->c])}
 
-The result is different.  Fewer possibilities remain.
-We have elminated both possible worlds and possible discourses.
-So the second formula is more informative.
+The result is different.  Fewer possibilities remain.  We have one of
+the possible worlds (w is ruled out), and we have ruled out possible
+discourses (x cannot refer to Alice).  So the second formula is more
+informative.
 
 One of main conclusions of GSV is that in the presence of modality,
 the hallmark of dynamic treatments--that existentials bind outside of 
@@ -447,9 +462,10 @@ has a detectable effect on truth conditions.
 As we discovered in class, there is considerable work to be done to
 decide which expressions in natural language (if any) are capable of
 expressing which of the two translations into the GSV fragment.  We
-can certainly grasp the truth conditions, but that is not the same
-thing as discovering that there are natural language sentences that
-express one or the other or both.
+can certainly grasp the two distinct sets of truth conditions, but
+that is not the same thing as discovering that there are natural
+language sentences that conventionally express one or the other or
+both.
 
 
 ## Binding, modality, and identity
@@ -466,7 +482,7 @@ The fragment correctly predicts the following contrast:
         -- This is a contradition: there is no single person who might be Bob
         -- and who simultaneously might be someone else
 
-These formulas are expressing extensional, de-reish intuitions.  If we
+These formulas are expressing extensional, de-re-ish intuitions.  If we
 add individual concepts to the fragment, the ability to express
 fancier claims would come along.
 
@@ -483,14 +499,14 @@ object that it can refer to.  Here is what GSV say:
     A term is an identifier per se if no mattter what the information
     state is, it cannot fail to decie what the denotation of the term is.
 
-## Digression on pegs
+## About the pegs
 
 One of the more salient aspects of the technical part of the paper is
 that GSV insert an extra level in between the variable and the object:
 instead of having an assignment function that maps variables directly
 onto objects, GSV provide *pegs*: variables map onto pegs, and pegs
 map onto objects.  It happens that pegs play no role in the paper
-whatsoever.  We'll demonstrate this by providing a faithful
+whatsoever.  We've demonstrated this by providing a faithful
 implementation of the paper that does not use pegs at all.
 
 Nevertheless, it makes sense to pause here to discuss pegs briefly,
@@ -570,10 +586,10 @@ to refer to that object, at least, not with a variable, since there is
 no variable that is associated with the peg that points to the
 relevant object.  So the information is present, but not accessible. 
 
-That does not mean that there aren't other expression types that are
-able to latch onto peg.  An intriguing suggestion based on an example
-in Vermeulen is that "former" might be able to provide access to a
-hidden peg:
+That does not mean that there aren't other expression types besides
+pronouns or variables that might be able to latch onto pegs.  An
+intriguing suggestion based on an example in Vermeulen is that
+"former" might be able to provide access to a hidden peg:
 
     19. Someone entered.  Someone spoke.  The former was a woman.
 
@@ -584,5 +600,5 @@ established peg, no matter whether there is a variable still pointing
 to that peg, the desired effect is achieved. 
 
 But none of this is relevant for any of the explanations or analyses
-provide by the GSV fragment, and it is considerably simpler to see
+provided by the GSV fragment, and it is considerably simpler to see
 what their fragment is about if we leave referent systems out of it.