Exercise-ch5

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Exercises for chapter 5: Simple LRS

Functional notation

We have introduced the functional notation and the eventuality variable in chapter 5. What are the new formulae that correspond to the formulae from chapter 2?

1 Notation from chapter 2: hobbit(frodo)
New notation:

frodohobbit
hobbitfrodo

2 Notation from chapter 2: walk(frodo)
New notation:

walkfrodo
(walke)•frodo
(walkfrodo)•e

3 Notation from chapter 2: help(aragorn,frodo)
New notation:

((helpe)•frodo)•aragorn
((helpe)•aragorn)•frodo
((helparagorn)•frodo)•e


Semantic types

Add the semantic types in the blanks. Use simple letters ("e" or "t") for simple types. Use round brackets for complex types (for example: "(e,t)").

1 Add the types for simple expressions:

a. frodo_


b. hobbit_


c. walk_


d. help_


e. (hobitx)_

2 Add the semantic types for complex expressions:

a. ((walk_

e_

) • aragorn_

)_

b. (hobbit_

y_

)_


Basic combinatorics

Basic mechanism with canonical examples

1 Sentence: Pat snored.
Logical form: (snoree) • pat
Which parts of the logical form are contributed by which word?

e ¦pat ¦ snore ¦ snoree ¦ (snoree) • pat
Pat
snored

2 Sentence: Pat likes Chris.
Logical form: ((likee) • chris) • pat
Which parts of the logical form are contributed by which word?

e ¦pat ¦ chris ¦ like ¦ likee ¦ (likee) • chris ¦ ((likee) • chris) • pat
Pat
likes
Chris


Basic mechanism with copula and argument-marking preposition

1 Sentence: Alex is happy.
Logical form: ((happye) • alex)
Which parts of the logical form are contributed by which word?

e ¦ alex ¦ happy ¦ happye ¦ (happye) • alex
Alex
is
happy

2 Sentence: Alex had been happy.
Logical form (ignoring tense and aspect!): ((happye) • alex)
Which parts of the logical form are contributed by which word?

e ¦ alex ¦ happy ¦ happye ¦ (happye) • alex
Alex
had
been
happy

3 Sentence: Pat waited for Chris
Logical form: ((waite) • chris) • pat
Which parts of the logical form are contributed by which word?

e ¦ chris ¦ pat ¦ wait ¦ waite ¦ (waite) • chris ¦ ((waite) • chris) • pat
Pat
waited
for
Chris

4 Sentence: Kim is proud of Fido
Logical form: ((proud-ofe) • fido) • kim
Which parts of the logical form are contributed by which word?

e ¦ kim ¦ fido ¦ proud-of ¦ proud-ofe ¦ (proud-ofe) • fido ¦ ((proud-ofe) • fido) • kim
Kim
is
proud
of
Fido


Nominal expletives

1 Sentence: It stormed.
Logical form: storms
Which parts of the logical form are contributed by which word?

s ¦ storm ¦ storms
It
stormed

2 Sentence: It was snowing.
Logical form: snows
Which parts of the logical form are contributed by which word?

s ¦ snow ¦ snows
It
was
snowing


Other constructions

1 Sentence: Pat did not call.
Logical form: ¬ ((call • e) • pat
Which parts of the logical form are contributed by which word?

e ¦ pat ¦ call ¦ calle ¦ (calle) • pat ¦ ¬ ((calle) • pat)
Pat
did
not
call

2 Sentence: Alex gave up on Pat.
Logical form: ((give-upe) • pat) • alex
Which parts of the logical form are contributed by which word?

e ¦ alex ¦ pat ¦ give-up ¦ give-upe ¦ (give-upe) • pat ¦ ((give-upe) • pat) • alex
Alex
gave
up
on
Pat



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