Exercise-ch5

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:

	frodo•hobbit
	hobbit•frodo

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

	walk•frodo
	(walk•e)•frodo
	(walk•frodo)•e

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

	((help•e)•frodo)•aragorn
	((help•e)•aragorn)•frodo
	((help•aragorn)•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. (hobit•x)_

2 Add the semantic types for complex expressions:

a. ((walk_ • e_ ) • aragorn_ )_

b. (hobbit_ • y_ )_

Basic combinatorics

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

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

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

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

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

	-+---- Pat
	--++++ waited
	+----- for
	+----- Chris

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