Assignment 2 memo Formal Logic II (COS2661)

COS2661
ASSIGNMENT 03 Memo
Question 1
Translate English sentences into sentences of First-Order Logic, using the predicates given in
Table 1 below. (20)

No. Predicate

1 Brown(x)

2 dog(x)

3 hairy(x)

4 Corgi(x)

5 Person(x)

6 Loves(x, y)

7 Pancakes(x)

8 Knows(x, y)

9 TasteSimilar(x, y)



1.2 Every brown dog is hairy. (4)

∀x (Brown(x) ∧ dog(x)) → hairy(x)

1.2 There is a Corgi that loves everyone. (4)

∃x (Corgi(x) ∧ ∀y (Person(y) → Loves(x, y)))

1.3 Everybody loves at least one Corgi. (4)

∀x (Person(x) → ∃y (Corgi(y) ∧ Loves(x, y)))

1.4 Any two pancakes taste similar. (4)

∀x ∀y (Pancakes(x) ∧ Pancakes(y) → TasteSimilar(x, y))

1.5 Everyone knows at least two people. (4)

∀x ∃y ∃z (Person(x) ∧ Person(y) ∧ Person(z) ∧ y ≠ z ∧ Knows(x, y) ∧ Knows(x, z))

, Question 2 (20)
Translate sentences of First-Order Logic into English sentences, using the predicates and
names given in Table 2.
English FOL


Names

Faro faro

Rudo rudo

“Days and Years” days

“Fourth Street” fourth

“Enemies or not?” enemies

Predicates

x is an actor Actor(x)

x is a soap opera Soap(x)

x plays in y Play(x, y)

x watches y Watch(x, y)



2.1 x (¬ Actor(x)  Play(x, days)  ¬ Watch(x, days)) (4)
There exists a person who is not an actor, plays in 'Days and Years,' and does not watch 'Days
and Years'.

2.2 Play(faro, fourth)  Play(faro, enemies))  (¬ Play(faro, fourth)  ¬ Play(faro,
enemies)) (4)
Faro plays either in 'Fourth Street' or in 'Enemies or not?', and it is not the case that Faro
plays in both 'Fourth Street' and 'Enemies or not?' (4)

2.3 (¬ Soap(fourth)  Soap(days)) → (Watch(faro, enemies)  Watch(rudo, enemies))
If 'Fourth Street' is not a soap opera but 'Days and Years' is, then Faro or Rudo watches
'Enemies or not?'

2.4 ∀x ((Play(x, enemies)  ¬Watch(x, enemies)) → Play(x, fourth)) (4)
For all individuals, if they play in 'Enemies or not?' but do not watch it, then they play in 'Fourth
Street'.