NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 4 Assignment Answers 2025

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NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 4 Assignment Answers 2025

1. Which of the following are well formed formulas in L(P, F, C)?

  • Dog(Spot) ∧ ¬Dog(Spot)
  • Likes(Joe,breed(x))
  • ∀x∃y (Dog(x) ⊃ breed(y))
  • ∀x Likes(x,Spot)
Answer :- For Answers Click Here

2. Which of the following are sentences in L(P, F, C)?

  • Dog(Spot) ∧ ¬Dog(Spot)
  • Likes(Joe,breed(x))
  • ∀x∃y (Dog(x) ⊃ breed(y))
  • ∀x Likes(x,Spot
Answer :-

3. Which of the following is an atomic formula in L(P, F, C)?

  • Dog(Spot) ∧ ¬Cat(Spot)
  • Owns(Joe, Commander)
  • Likes(Joe, breed(Commander))
  • ∀x ¬Likes(x,Commander)
Answer :-

4. Select the formula(s) that are equivalent to the Boolean function g(A,B).

  • ¬A
  • ¬((B ⊃ A) ∧ (¬B ⊃ A))
  • (¬B ⊃ ¬A) ∧ (B ⊃ ¬A)
  • All of the above
Answer :-

5. Express in FOL: “dogs are pets”.

  • ∃x(Dog(x) ∧ Pet(x))
  • ∀x(Dog(x) ⊃ Pet(x))
  • ∃x(Pet(x) ∨ Dog(x))
  • ∀x(Pet(x) ⊃ Dog(x))
Answer :-

6. Express in FOL: “dogs are not cats”.

  • ¬∀x(Dog(x) ⊃ Cat(x))
  • ∀x¬(Dog(x) ⊃ Cat(x))
  • ∀x(Dog(x) ⊃ ¬Cat(x))
  • ∀x(Cat(x) ⊃ ¬Dog(x))
Answer :- For Answers Click Here

7. Express in FOL: “those who own pets like their pets”.

  • ∀x∀y(Likes(x,y) ⊃ (Owns(x,y) ∧ Pet(y)))
  • ∃x∃y(Owns(x,y) ∧ Pet(y) ∧ Likes(x,y))
  • ∀x∀y((Owns(x,y) ∧ Pet(y)) ⊃ Likes(x,y))
  • All of the above
Answer :-

8. According to FOL semantics, select the model(s) of the sentence
∀x∀y((Owns(x,y) ∧ Pet(y)) ⊃ Likes(x,y)) in L(P, F, C) defined above.

  • Owns={ (Bush,Spot) }; Pet={ Spot }; Likes = { (Bush,Spot) }
  • Owns={ (Bush,Spot) }; Pet={ Spot }; Likes = { (Joe,Fedo) }
  • Owns={ (Bush,Spot) }; Pet={ Fedo }; Likes = { (Bush,Spot) }
  • Owns={ (Bush,Spot) }; Pet={ Fedo }; Likes = { (Joe,Fedo) }
Answer :-

9. According to FOL semantics, select the model(s) of the sentence
∃x∃y(Owns(x,y) ∧ Pet(y) ∧ Likes(x,y)) in L(P, F, C) defined above.

  • Owns={ (Bush,Spot) }; Pet={ Spot }; Likes = { (Bush,Spot) }
  • Owns={ (Bush,Spot) }; Pet={ Spot }; Likes = { (Joe,Fedo) }
  • Owns={ (Bush,Spot) }; Pet={ Fedo }; Likes = { (Bush,Spot) }
  • Owns={ (Bush,Spot) }; Pet={ Fedo }; Likes = { (Joe,Fedo) }
Answer :-

10. According to FOL semantics, which of the following are true in L(P, F, C) defined above?

  • Dogs are not cats.
  • Dogs are pets
  • Cats are pets
  • None of the above
Answer :-

11. According to FOL semantics, which of the following are true in L(P,F,C) defined above?

  • Joe refers to a person.
  • Fedo refers to an element in the domain.
  • breed(Fedo) refers to an element in the domain.
  • breed is a predicate symbol.
Answer :-

12. Consider the FOL language L( {P,Q}, {f,g,h}, {A,B,C} ) with variables x, y, z. Each option shows a pair of clauses, which of the pairs of clauses are unifiable?

  • P(?x, f(?x)); P(g(?y), ?y);
  • P(?x, f(?x)); P(g(A), ?y);
  • P(?x, f(?x)); P(g(A), f(?y));
  • Q(?x, ?x, h(?x)); Q(g(B), g(?y), h(g(?y)));
Answer :-

13. Match each FOL formula to a suitable Skolem form. Here, P and Q are predicates; x, y and z are variables; sk1, sk2, …, are Skolem constants and Skolem functions.
A. ∃x (P(x) ∧ ∀y Q(x,y))
B. ∀x ((∀y P(y)) ⊃ ∀z Q(x,z))
Skolem forms:
1. P(sk1) ∨ Q(sk1,sk2)
2. P(sk1) ∨ Q(sk1,?y)
3. P(?y) ∨ Q(?x,?y)
4. ¬P(?y) ∨ Q(?x,?z)
5. ¬P(sk3(?x)) ∨ Q(?x,?z)

For the formulas A and B, in that order, enter the matching Skolem formula numbers as a comma-separated list without brackets/spaces.
Answer format: 7,6

Answer :- For Answers Click Here

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