LIN 617 - First written homework assignment [due on stapled paper in class on Tuesday, February 4]
(Spring 2014)
In class, we have analyzed sentences such as (1) and (2); you may find it helpful to review our analyses.
(1)
(2)
Otis croons.
Alfred likes Marion.
Suppose now that these sentences are interpreted in the context of the following universe U:
U:
The set D of individuals is {Alfred, Carla, Marion, Otis}.
The set of truth values is {0, 1}.
The individuals in D exhibit the following properties.
croons
Alfred
no
Carla
yes
Marion
no
Otis
yes
A.
likes Alfred likes Carla likes Marion likes Otis
Alfred
yes
yes
yes
yes
Carla
yes
yes
no
no
Marion
no
yes
no
yes
Otis
no
yes
yes
yes
Fill in the blanks in the following table. In the third column, each denotation should be represented as either an
individual, a truth value, or a function. Functions should be presented in the general format in (7) on p.11 of Heim
& Kratzer (i.e. as tables in which arguments and values are linked by arrows). Where relevent, employ right-to-left
Schönfinkelization. The first row is done for you.
Expression
The
expression’s
semantic type
The expression’s denotation in universe U
e
Alfred
(Table continued on next page)
2
Expression
B.
The
expression’s
semantic type
The expression’s denotation in universe U
Fill in the blanks in the folloiwng table. Here, don’t represent functional denotations extensionally (as tables
with arrows from arguments to values in universe U); instead, specify the functional denotations by means of
the λ-notation.
Expression
The expression’s denotation represented in λ-notation
Now consider a new expression, the adverb now in sentences such as (3).
3
(3)
Note that the traditional grammatical terminology is a little misleading: “adverb” suggests that now modifies verbs, but
as the tree diagram shows, it modifies a full sentence in (3).
C.
Judging from (3), what is the semantic type of now? What is its denotation domain? (You may find it helpful to
review pp.26-29 of Heim & Kratzer.)
D.
Write a lexical entry specifying the value of ⟦ now ⟧. (Cf. p.15 of Heim & Kratzer.)
E.
Write a semantic interpretation rule for the topmost node in (3). (Cf. pp.15f.)
F.
Does your semantic interpretation rule conflict in any way with rule (S1) on p.16? Explain your reasoning. How
would you try to resolve this conflict? (No single correct answer!)