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King’s College London
This paper is part of an examination of the College counting towards
the award of a degree. Examinations are governed by the College
Regulations under the authority of the Academic Board.
MA EXAMINATION
7AAN2092
Theory of Meaning
Examination Period 2 (May 2015)
TIME ALLOWED: 2 HOURS
Answer ONE question from Section A and ONE question from Section B.
Avoid overlap in your answers.
DO NOT REMOVE THIS PAPER FROM THE EXAMINATION
ROOM
TURN OVER WHEN INSTRUCTED
2015 © King’s College London
7AAN2092
Section A
1. (a) What do the basic types e and t represent?
(b) What is the semantic type of a transitive verb?
(c) Give a recursive definition of the domain of interpretation of types.
(d) What is the domain of the type (e → t) → (e → t)?
(e) Give an example of a word which would be naturally modeled with
a constant of type (e → t) → (e → t) and describe the denotation of
that constant.
(f) Assign types to the following words:
i.
ii.
iii.
iv.
v.
vi.
John
every
cat
cuddles
violently
student
(g) Using the type assignments given in (f), show that the sentence “John
violently cuddles every cat.” has type t
(h) The notion of semantic consequence is defined in type theory, but
not the notion of syntactic consequence. Explain this absence.
2. (a) Define α, β and η reduction.
(b) When is α-reduction necessary? Give an example of an expression
which requires α-reduction to be normalized.
(c) Normalise these expressions, showing each step that you take.
i. (λP.P (likes))(λQ.Q(j))
ii. (λx.λy(likes)(y)(x))(john)
(d) Define [[λx.α]] with respect to a model M and variable assignment
g.
(e) Argue that β-reduction is sound. Sketch a proof.
3. (a) What is the role of intensional types in formal semantics?
(b) Give a definition of the set of types used in intensional logic.
(c) Define the syntax and semantics of the intensional operators
∨
.
∧
and
(d) Give an example of sentences where the intensional operators
∨
are used.
∧
and
(e) Are
∧∨
α and
∨∧
α always equivalent to α? Explain your answers.
2
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7AAN2092
Section B
4. What are the advantages and limitations of representing the meaning of
a proposition as a function from possible worlds to truth values?
5. Discuss the limitations of First-Order Logic as a representation language
for natural languages, and how they can be overcome using higher-order
logic.
6. Discuss the role of meaning postulates in Montague semantics.
7. How is a uniform treatment of noun-phrases obtained in Montague semantics? Explain how this could be applied to the phrase “John and every
dog”.
3
END OF PAPER