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Artificial Intelligence: Knowledge Representation And Reasoning Week 5 NPTEL Assignment Answers 2025

By / February 16, 2025

NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 5 Assignment Answers 2025

1. Select the formulas that are in CNF.

  • ¬R
  • (¬R) ∧ (¬P ∨ Q) ∧ (¬Q ∨ R)
  • (¬R) ∨ (¬P ∧ Q) ∨ (¬Q ∧ R)
  • P ⊃ Q
  • ¬P ∨ Q
Answer :- For Answers Click Here

2. Convert to CNF and simplify:

￢( [P ⊃ (Q ∨ R)] ⊃ ( [Q ⊃ A] ⊃ ( [R ⊃ A] ⊃ [P ⊃ A] ) ) )

  • (P) ∧ (¬Q) ∧ (¬R) ∧ (¬Q ∨ A) ∧ (¬R ∨ A) ∧ (¬A)
  • (¬P ∨ ¬Q ∨ ¬R) ∧ (Q ∨ A) ∧ (R ∨ A) ∧ (P) ∧ (¬A)
  • (¬P ∨ Q ∨ R) ∧ (¬Q ∨ A) ∧ (¬R ∨ A) ∧ (P) ∧ (¬A)
  • None of the above
Answer :-

3. Convert to skolem form:

∀x∀y { ( ∀y[ P(x,y) ⊃ Q(y) ] ) ⊃ [ Q(y) ⊃ R(x,y) ] }

  • ∀x∀y{ [P(x,sk(x)) ⊃ Q(sk(x))] ⊃ [Q(y) ⊃ R(x,y)] }
  • ∀x∀y{ [P(x,y) ⊃ Q(y)] ⊃ [Q(sk(x)) ⊃ R(x,sk(x))] }
  • ∀x∀y∀z{ [P(x,y) ⊃ Q(y)] ⊃ [Q(z) ⊃ R(x,z)] }
  • None of the above
Answer :-

4. Convert to clause form:

∀x∀y { ( ∀y[ P(x,y) ⊃ Q(y) ] ) ⊃ [ Q(y) ⊃ R(x,y) ] }

  • [P(?x,sk(?x)) ∨ ¬Q(sk(?x)) ∨ ¬Q(?y) ∨ R(?x,?y)]
  • [P(?x,sk(?x)) ∨ ¬Q(?y) ∨ R(?x,?y)] ∧ [¬Q(sk(?t)) ∨ ¬Q(?u) ∨ R(?t,?u)]
  • [P(?x,?y) ∨ ¬Q(?y) ∨ R(?x,?y)] ∧ [¬Q(?u) ∨ ¬Q(?u) ∨ R(?t,?u)]
  • [P(?x,?z) ∨ ¬Q(?z) ∨ ¬Q(?y) ∨ R(?x,?y)]
Answer :-

5. Consider the following two clauses from the language L({P,Q},{f,g},{a,b}) with variables x, y and z.

Clause 1: { P(a, ?y, f(?y)); }
Clause 2: { ¬P(?x, ?z, f(g(?x))); ¬P(?z, ?x, f(?x)); }

To resolve Clause 1 with Clause 2 which of the following are possible unifiers?

  • { x -> a; y -> a; z -> a; }
  • { x -> b; y -> b; z -> a; }
  • { x -> a; y -> z; z -> g(a) }
  • { x -> y; z -> a; }
Answer :-

6. For the pair of clauses in the previous question, select the most general unifier(s).

  • { x -> a; y -> a; z -> a; }
  • { x -> b; y -> b; z -> a; }
  • { x -> a; y -> z; z -> g(a) }
  • { x -> y; z -> a; }
Answer :- For Answers Click Here

7. Use the Resolution Method to derive all the resolvents for KB1.

KB1 = { ￢( [P ⊃ (Q ∨ R)] ⊃ ( [Q ⊃ A] ⊃ ( [R ⊃ A] ⊃ [P ⊃ A] ) ) ) }

Which of the following occur as a result of a resolution step?

  • A
  • ⊥ (false)(bottom)
  • ¬P ∨ ¬Q
  • R ∨ A
  • ⊤ (true)(top)
Answer :-

8. Is KB1 consistent?

  • Yes
  • No
  • Cannot be determined
Answer :-

8. A knowledge base is given in clause form where predicates symbols are A, C, L, G, P, Q; constants are Ana and Fedo; and variables are prefixed with ‘?’.

KB2 = {
1. ¬L(?a,?b) ∨ G(?a,?b)
2. ¬L(?u,?v) ∨ ¬A(?v) ∨ C(?u,?v)
3. ¬Q(?x,?y) ∨ ¬P(?y) ∨ ¬A(?z) ∨ L(?x,?z)
4. ¬P(?t) ∨ A(?t)
5. Q(Ana,Fedo)
6. P(Fedo)
}

Which of these sentences follow from KB2. Use the Resolution Refutation Method to prove it.

  • A(Fedo) ∧ L(Ana,Fedo)
  • ¬L(Ana,Fedo)
  • ∃m∃n Q(m,n)
  • ∃t A(t)
Answer :-

10. Can the Resolution Refutation Method be used to prove that KB2 entails the following statement?

∃n∃n C(m,n)

  • Yes
  • No
Answer :- For Answers Click Here

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