Assignment 1
PLIN3004/PLING218 Advanced Semantic Theory
1 Set membership and subsets
S1
S2
S3
S4
S5
“
“
“
“
“
(Partee et al. 1990:24)
t t H u ,t A u , A u
A
t Au
tt Auu
tt Au,Au
S6
S7
S8
S9
“
“
“
“
H
tHu
ttHuu
t H, t H u u
Of these nine sets,
i) which are subsets of S1 ?
ii)
which are members of S9 ?
iii) which are subsets of S9 ?
iv) which are members of S4 ?
v) which are subsets of S4 ?
(Example: “which are members of S1 ?” —S2 , S3 and S7 )
2 Operations on sets
(Partee et al. 1990:25)
Let A “ t a, b, c u , B “ t c, d u ,C “ t d, e, f u. What are the following sets?
i)
AY B
ii)
AX B
iii)
A Y pB X Cq
iv) C Y A
v)
BYH
vi)
A X pB X Cq
3 Optional problem: Counterexample to (T)
Find a counter-example in English to the following schema (often called (T)).
“φ” is true in a situation s iff φ in s
That is, find an English sentence φ and a situation s such that “φ” is intuitively true (or false)
in s, even though it is not the case (or is the case) in s that φ.
1