CS827: Adv. Artificial Intelligence

Unit 4: Logic (Assignment 4, answers by: A.Aziz Altowayan)


Ch.8

Exercise 8.9 (answers in red)

Exercise 8.10

  1. Emily is either a surgeon or a lawyer.
    Occupation(Emily, Surgeon) ∨ Occupation(Emily, Lawyer)

  2. Joe is an actor, but he also holds another job.
    Occupation(Joe, Actor) ∧ ∃oo ≠ Actor ∧  Occupation(Joe, o)

  3. All surgeons are doctors.
    xOccupation(x, Surgeon) ⇒ Occupation(x, Doctor)   ≡   ∀xSurgeon(x) ⇒ Doctor(x)

  4. Joe does not have a lawyer (i.e., is not a customer of any lawyer).
    ¬ Customer(Joe, Lawyer)

  5. Emily has a boss who is a lawyer.
    ∃ xBoss(x, Emily) ⇒ Occupation(x, Lawyer)   ≡   ∃ xBoss(x, Emily) ∧ Occupation(x, Lawyer)

  6. There exists a lawyer all of whose customers are doctors.
    ∃ xOccupation(x, Lawyer) ∧ ∀ yCustomer(y, x) ⇒ Occupation(y, Doctor)

  7. Every surgeon has a lawyer.
    ∀ xOccupation(x, Surgeon) ∧ ∃ yCustomer(x, y)   ≡   ∀ xOccupation(x, Surgeon) ⇒  ∃ yCustomer(x, Occupation(y, Lawer)) * 
    * complex sentence syntax