PLIN3004/PLING218 Advanced Semantic Theory
1
Assignment 9
Surface Scope Reading
Compute the denotation of (1) (and make sure that the surface scope reading is derived).
(1)
DP
some linguist 5
DP
every book 1
S
t5
VP
read t 1
We assume the following type-xet, xet, tyy meanings for the quantificational determiners. You
can use either the function or set version of entries.
(2)
a.
b.
veverywa, M “ rλ f
“ rλ f
a, M
vsomew
“ rλ f
“ rλ f
P Det .rλg P Det . 1 iff for every x P De such that f pxq “ 1, gpxq “ 1ss
P Det .rλg P Det . 1 iff setp f q Ď setpgqss
P Det .rλg P Det . 1 iff for some x P De such that f pxq “ 1, gpxq “ 1ss
P Det .rλg P Det . 1 iff setp f q X setpgq ‰ Hss
You have to use the new version of Predicate Abstraction twice.
(3)
Predicate Abstraction (new ver.):
for any model M, for any assignment function a and for any index i P N,
<a, M »
4
3
;ariÑ x s, M fi
A
>
6
fl
“ – λ x P De .
5i A =
You will use this rule twice in the computation. Recall that if g is an assignment function,
gri Ñ xs is the assignment function that differs from g at most in that gpiq “ x. And g itself
could be already modified, e.g. hr1 Ñ Parissr8 Ñ Londons is the assignment function that
differs from hr1 Ñ Pariss at most in that hr1 Ñ Parissr8 Ñ Londonsp8q “ London.
2
(Optional) Type-Shifting (this exercise is difficult)
We adopted the hypothesis that quantificational DPs can covertly move in order to solve the
type-mismatch. However, there is an alternative analysis that does not involve movement.
Recall that we have a type-mismatch on the assumption that transitive verbs like ‘saw’ are of
type xe, ety, as they cannot combine with a quantificational DP of type xet, ty.
(4)
vsawwa, M “ rλ x P De . rλ y P De . 1 iff y saw x in Mss
1
What if we are wrong about this assumption, and ‘saw’ is actually of type xxet, ty , xe, tyy? We
won’t have a type-mismatch, as shown in (5).
(5)
t
DPxet ,t y
xe, ty
some boy sawxxet ,t y,xe,t yy
DPxet ,t y
every girl
As for proper names, recall from Assignment 7 that they can be analyzed as Generalized
Quantifiers too, e.g. vJohnwa, M “ rλ f P Dxe,t y . f pJohnq “ 1s, so transitive verbs of type
xxet, ty , xe, tyy can have them in object position.
So if transitive verbs are actually of type xxet, ty , xe, tyy, we won’t need QR. Propose a typexxet, ty , xe, tyy denotation for ‘saw’. Note that as before, you want ‘John saw Mary’ to denote
1 in M iff John saw Mary in M.
(6)
vsawwa, M “ rλQ P Dxet ,t y . rλ x P De . 1 iff ???ss
2