Question

Knowledge Base:

Everyone who loves all animals is loved by someone.

Anyone who kills animals is loved by noone.

Jack loves all animals

Either curiosity or Jack killed the cat, who is named Tuna.
Query: Did curiosity kill the cat?

Inference procedure:

1. Express sentence in FOL

2. Eliminate existential quantifier

3. Convert to CNF and negated query.

Answer 1

Answer: The first order equivalent sentences for given sentences are

1. ∀x [∀y Animal(y) ⇒ Loves(x,y)] ⇒ [∃y Loves(y,x)]

2. ∀x [∃z Animal(z)∧Kills(x,z)] ⇒ [∀y ¬Loves(y,x)]

3. ∀ x Animal (x) ⇒ Loves (Jack , x)

4. Kills(Jack,Tuna)∨Kills(Curiosity,Tuna)

5. Cat(Tuna)

6. ∀ x Cat (x) ⇒ Animal (x)

Negated goal query=>¬Kills(Curiosity, Tuna)

Eliminating existential quantifiers(∀,∃) and the CNF Form is:

1. Animal (F (x)) ∨ Loves (G(x), x)

2. ¬Loves (x, F (x)) ∨ Loves (G(x), x)

3. ¬Loves(y,x)∨¬Animal(z)∨¬Kills(x,z)

4. ¬Animal (x) ∨ Loves (Jack , x)

5. Kills(Jack,Tuna)∨Kills(Curiosity,Tuna)

6. Cat(Tuna)

7. ¬Cat (x) ∨ Animal (x)

8. ¬Kills(Curiosity, Tuna)