F19-Exercise
Ling 331 / 731
Spring 2016
Key
1. Distinguish a variable from a constant.
A variable’s denotation changes with respect to the assigment, while the denotation of a constant is the
same for all assignments (i.e., no matter which assignment we use.)
2. Explain why we need to split the TN rule into LT and PR.
The TN rule says that an interpretable node’s meaning is specified in the lexicon. So for mayor, the
meaning of the word is fully supplied by its lexical entry. This cannot be the case for her, because the
context must supply what’s missing. So we need to split TN into a rule for the words like mayor (LT),
and one for words like her (PR).
3. Given the following assignment, fill in the chart.


→
Gene
→
Barry 

→
Ellen 
→ Roberto
2
 3
r=
 163
75
denotation
value
extension
J x2 Kr
r(2)
Gene
J x163 Kr
r(163)
Ellen
J y75 Kr
r(75)
Robert
J y3 Kr
r(3)
Barry
4. Compose the following phrase structures. Assume assignment z.
1.
S
DP
VP
D◦
she3
V◦
slept
FA : t
slept(z(3))
[λx ∈ De . slept(x)](z(3))
NN : e
z(3)
NN : he, ti
λx ∈ De . slept(x)
PR : e
z(3)
LT : he, ti
λx ∈ De . slept(x)
1
2.
S
FA : t
pondered(z(2))
[λx ∈ De . pondered(x)](z(2))
DP
VP
D◦
he2
V◦
pondered
3.
S
VP
D◦
he5
V◦
persevered
S
DP
D◦
she1
NN : he, ti
λx ∈ De . pondered(x)
PR : e
z(2)
LT : he, ti
λx ∈ De . pondered(x)
FA : t
persevered(z(5))
[λx ∈ De . persevered(x)](z(5))
DP
4.
NN : e
z(2)
NN : e
z(5)
NN : he, ti
λx ∈ De . persevered(x)
PR : e
z(5)
LT : he, ti
λx ∈ De . persevered(x)
FA : t
in(ιx ∈ Ce [ house(x) ])(z(3))
VP
V◦
is
PP
P◦
in
DP
the house
NN : e
z(3)
PR : e
z(3)
FA : he, ti
λy ∈ De . in(ιx ∈ Ce [ house(x) ])(y)
LT : hhe, ti, he, tii
FA : he, ti
λf ∈ Dhe, ti . f
λy ∈ De . in(ιx ∈ Ce [ house(x) ])(y)
LT : he, he, tii
λx ∈ De .λy ∈ De . in(x)(y)
5.
S
DP
D◦
he2
FA : e
ιx ∈ Ce [ house(x) ]
FA : t
near(ιx ∈ Ce [ shed(x) ])(z(3))
VP
V◦
is
PP
◦
P
near
DP
the shed
NN : e
z(3)
FA : he, ti
λy ∈ De . near(ιx ∈ Ce [ shed(x) ])(y)
PR : e
z(3)
LT : hhe, ti, he, tii
λf ∈ Dhe, ti . f
FA : he, ti
λy ∈ De . near(ιx ∈ Ce [ shed(x) ])(y)
LT : he, he, tii
λx ∈ De .λy ∈ De . near(x)(y)
2
FA : e
ιx ∈ Ce [ shed(x) ]
6.
S
FA : t
called(z(1))(ιx ∈ Ce [ Tom(x)])
DP
D◦
∅
VP
V◦
called
NP
Tom
DP
D◦
her1
FA : he, ti
λy ∈ De . called(z(1))(y)
FA : e
ιx ∈ Ce [ Tom(x)]
LT : hhe, ti, ei
λf ∈ Dhe, ti .ιx ∈ Ce [ f(x) ]
NN : he, ti
λx ∈ De . Tom(x)
LT : he, he, tii
λx ∈ De .λy ∈ De . called(x)(y)
NN : e
z(1)
PR : e
z(1)
7.
S
FA : t
called(z(3))(ιx ∈ Ce [ mayor(x)])
DP
D◦
the
VP
V◦
called
NP
mayor
DP
D◦
him3
FA : he, ti
λy ∈ De . called(z(3))(y)
FA : e
ιx ∈ Ce [ mayor(x)]
LT : hhe, ti, ei
λf ∈ Dhe, ti .ιx ∈ Ce [ f(x) ]
NN : he, ti
λx ∈ De . mayor(x)
LT : he, he, tii
λx ∈ De .λy ∈ De . called(x)(y)
NN : e
z(3)
PR : e
z(3)
8.
S
DP
D◦
she2
FA : t
sought(z(7))(z(3))
VP
V◦
sought
DP
D◦
it7
FA : he, ti
λy ∈ De . sought(z(7))(y)
NN : e
z(3)
PR : e
z(3)
LT : he, he, tii
λx ∈ De .λy ∈ De . sought(x)(y)
NN : e
z(7)
PR : e
z(7)
3