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COS2661 Assignment 3 memo 2024

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COS2661 Assignment 3 memo 2024: QUESTION 1 [15] In this question you have to translate sentences of English sentences into First-Order Logic, using the predicates and names given in Table 1. English FOLComment TabisoTabisoThe name of a boy. StudentstudentTafaratafaraPetpet Names The name ...

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  • August 23, 2024
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  • 2024/2025
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, QUESTION 1 In this question you have to translate sentences of English
sentences into First-Order Logic, using the predicates and names given
in Table 1

1.1 Nothing to the left of Tabiso is larger than everything to the left of
Tafara.
¬∃x (LeftOf(x, Tabiso) ∧ ∀y (LeftOf(y, Tafara) → Larger(x, y)))

1.2 Anything to the left of Tabiso is smaller than something that is in
back of every pet to the right of Tafara.
∀x (LeftOf(x, Tabiso) → ∃y (Pet(y) ∧ RightOf(Tafara, y) ∧ BackOf(y, z) ∧ Smaller(x, z)))

1.3 Every student gave a pet to some other student sometime or other.
∀x (Student(x) → ∃y ∃z (Student(y) ∧ Pet(z) ∧ x ≠ y ∧ Gave(x, z, y)))

1.4 No student fed every pet.
¬∃x (Student(x) ∧ ∀y (Pet(y) → Fed(x, y)))

1.5 If Tabiso ever gave Tafara a pet, she owned it then, and he didn’t.
∃z (Pet(z) ∧ Gave(Tabiso, z, Tafara) → (Own(Tafara, z) ∧ ¬Own(Tabiso, z)))


Question 2

2.1 ∀x (¬∃y FrontOf(y, x) → Large(x))
If nothing is in front of something, then that thing is large.

2.2 ∀x ((Student(x) ∧ ∃y (Pet(y) ∧ LeftOf(x, y))) → Own(x, y))
Every student who has a pet to their left owns that pet.

2.3 ∀x∀y ((Between(tafara, x, y) ∧ x ≠ y) → (Small(x) ∧ Small(y)))
If Tafara is between two distinct objects, then both objects are small.


2.4 ∀x ((Pet(x) ∧ ∀y ¬BackOf(y, z))→¬∃z (Pet(z) ∧ x ≠ z ∧ Smaller(x, z))
If a pet has nothing behind it, then there is no other pet smaller than it.


2.5 ∃x∃y [Student(x) ∧ Student(y) ∧ x ≠ y ∧ ∀z(Student(z) → (z = x ˅ z
= y)) ∧ Smart(x) ∧ Smart(y)]
There are two distinct students who are the only smart students in the group.

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