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```LIN241 Intro to Semantics
Winter 2019
Tutorial 7
Learning objectives

Review the semantics of Generalized Quantifiers and Definite Descriptions
Exercise 1
Translate the following sentences into GQL with the iota operator
(1)
(2)
Mary introduced the speaker to some professors.
SOMEx[PROFESSOR(x)][INTRODUCED(m,ιy[SPEAKER(y)],x)]
Note: although we introduced pluralization in the semantics of definite descriptions, we will
ignore it in the analysis of generalized quantifiers, in order to keep things simple.
(3)
The witch picked a leaf from every tree in the forest.
ALLx[TREE(x) & IN(x, ιy[FOREST(y)])]
[SOMEy[LEAF(y) & FROM(y,x)][PICKED(ιz[WITCH(z)],y)]]
Paraphrase: “for every tree in the forest, there is some leaf from it (the tree) such that the witch
picked it (the leaf)”
The general form of the translatioon is:
ALLx[...][SOMEy[…][…]]
For every … there is some … such that ...
The restriction of “every” is “tree in the forest”: TREE(x) & IN(x, ιy[FOREST(y)])
The restriction of “some” is “leaf from it”, where “it” is bound by “every tree in the forest”:
LEAF(y) & FROM(y,x)
The nuclear scope of “some” is “the witch picked it”, where “it” is bound by “some leaf from
it”: PICKED(ιz[WITCH(z)],y)
The nuclear scope of “every” is “there is some leaf from it such that the witch picked it”:
SOMEy[LEAF(y) & FROM(y,x)][PICKED(ιz[WITCH(z)],y)]
Exercise 2
Part A. Answer the following questions as clearly and succinctly as you can:

According to the uniqueness theory of definite descriptions, in what conditions can speakers use
a definite description?
According to the uniqueness theory, a speaker can use a definite description when it has a
uniquely identifiable referent in the context of utterance.

According to the familiarity theory of definite descriptions, in what conditions can speakers use
a definite description?
According to the familiarity theory, a speaker can use a definite description when its referent is
already familiar in the context of utterance.

What are the novelty and familiarity conditions?
The novelty condition states that indefinite descriptions can only be used to introduce new
referents in a discourse, i.e. referents that have not previously been mentioned.
The familiarity condition states that definite descriptions can only be used to pick up old or
familiar referents in a discourse, e.g. referents that have already been mentioned.

Explain the difference between weak and strong uses of definite descriptions in English.
Strong definite descriptions have referents that have been explicitly mentioned in the ongoing
discourse.
Weak definite descriptions have referents that have not previously been mentioned in the
ongoing discourse, but that are familiar to the discourse participants because they are salient in
the situation of utterance.
Part B. Classify the definite descriptions in each example as weak, strong or bridging:
(1)
Orlando has a dog and a cat. The cat is always hungry.
This is a strong definite descriptions: its referent has already been introduced by “a cat”.
(2)
Terence bought a used car. The windshield is damaged.
This is a bridging definite description: its referent was not previously mentioned, but it is
related to the referent that was introduced by “a car”.
(3)
Staring at the sun is a bad idea.
This is a weak definite description: its referent was not previously mentioned, but it is familiar
to everyone (we are all familiar with the sun).
Part C. Consider the following model M:
D = {anne, beatrice, charles, dennis, …, anne + beatrice, ...}
I(COOK) = {anne}
I(SINGER) = {beatrice, charles}
What is the extension of the following predicates in M?

PL(COOK)
I(PL(COOK)) = {anne}

MAX(COOK)
I(MAX(COOK)) = {anne}

PL(SINGER)
I(PL(SINGER)) = {beatrice, charles, beatrice + charles}

MAX(PL(SINGER)
I(MAX(PL(SINGER))) = {beatrice + charles}

MAX(SINGER)
I(MAX(SINGER)) = {beatrice, charles}
What is the denotation of the following definite descriptions in M?

the cook
⟦ιx[MAX(COOK)(x)]⟧x[MAX(COOK)(x)]⟧M,g = anne

the cooks
⟦ιx[MAX(COOK)(x)]⟧x[MAX(PL(COOK))(x)]⟧M,g = anne

the singer
⟦ιx[MAX(COOK)(x)]⟧x[MAX(SINGER)(x)]⟧M,g is undefined

the singers
⟦ιx[MAX(COOK)(x)]⟧x[MAX(PL(SINGER))(x)]⟧M,g = beatrice + charles
Exercise 3
The discontinuous determiners in the next examples relate three sets. Give the set theoretic truth
conditions for the sentences.
a.
More architects than bricklayers are cricketers.
|I(ARCHITECT) ∩ I(CRICKETERS)| > |I(BRICKLAYERS) ∩ I(CRICKETERS)|
notes:
I(ARCHITECT) = {x: x ∈ I(ARCHITECT)}
|I(ARCHITECT) ∩ I(CRICKETERS)| is the number of architects who are cricketers
b.
Exactly as many pies as cookies are cooked.
|I(PIES) ∩ I(COOKED)| = |I(COOKIES) ∩ I(COOKED)|
c.
Fewer autobiographers than biographers are candid.
|I(AUTOBIOGRAPHER) ∩ I(CANDID)| < |I(BIOGRAPHER) ∩ I(CANDID)|
Exercise 4 (adapted from de Swart 1998)
The general constraints on determiner denotations (conservativity, extension and quantity) allow us to
represent the space of possible determiner concepts in natural language graphically by means of a tree
of numbers. Let A and B be sets, let a =| A - B |, and let b=| A ∩ B |. Then we can construct a tree of
numbers corresponding to the possible pairs (a, b):
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
To illustrate, the determiner “both” is represented by the point (0,2) on the tree, since whenever a
sentence of the form “Both As are B” is true, the number of A's that are not B is 0, and the number of
A's that are B is 2. The determiner “some” is represented by the region of the tree that contains all pairs
(i,j) such that i is any number but j ≥ 1, and only those pairs, since whenever a sentence of the form
“some As are Bs is true”, there might be any number of As that are not B, but at least one A is B.
Indicate how the following determiners can be represented on the tree of numbers:
a.
neither: (2,0); underlined in the following tree:
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
b.
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
at most two: all pairs (i,j) of numbers such that j ≤ 2
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
e.
3,0
4,0
0,1
1,1
most: all pairs (i,j) of numbers i and j such that i < j
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
d.
1,0
2,0
every: all pairs of the form (0,j), for any number j
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
c.
0,0
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
not all: all pairs (i,j) of numbers such that i > 0
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
f.
exactly one or exactly three: all pairs (i,1) and (i,3), for any number i:
a+b = 0
a+b = 1
a+b = 2
a+b = 3
a+b = 4
…
0,0
1,0
2,0
3,0
4,0
0,1
1,1
2,1
3,1
0,2
1,2
2,2
…
0,3
1,3
0,4
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