Exercise-ch2

Additional Exercises for Chapter 2: Predicate Logic

The syntax of predicate logic

For the following exercises we use names and properties from the The Lord of the Rings novels.

Names: frodo, sam, gandalf, aragorn
1-place predicates: hobbit, wizard
2-place predicates: know, help

Formulae without variables

1 Click on the items that are well-formed expressions of the semantic representation language.

	gandalf
	hobbit
	sauron
	frodo ∧ gandalf
	know(gandalf)
	help(aragorn,frodo)

2 Click on the expressions that are well-formed formulae.

	hobbit
	frodo
	hobbit(aragorn)
	hobbit(frodo) ∧ wizard(gandalf)
	hobbit(frodo) ¬ wizard(sam)

Formulae with variables

1 Click on the items that are well-formed expressions of the semantic representation language.

	y
	x ∧ frodo
	∃x

2 Click on the expressions that are well-formed formulae.

	∀x (hobbit(x) ⊃ x = gandalf)
	∃y(hobbit(x) ∨ wizard(gandalf))