# NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 4 Assignment Answers 2024

## NPTEL Artificial Intelligence: Knowledge Representation And Reasoning Week 4 Assignment Answers 2024

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

• ∃x WorksWith(x,y)
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2. Which of the following are sentences in L(P, F, C)?

• ∃x WorksWith(x,y)
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3. Which of the following is an atomic formula in L(P, F, C)?

• ¬Celebrity(Ben)
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4. Select the formulas that are equivalent to the Boolean function g(A,B).

• (A ∧ ¬B) ∨ (¬A ∧ B)
• (B ⊃ A) ∨ (A ⊃ B)
• (A ∨ B) ∧ (¬A ∨ ¬B)
• B ≡ ¬A
`Answer :- `

5. According to FOL semantics, which of the following are model(s) of the sentence ∃x∀y(WorksWith(x,y) ⊃ FriendOf(x,y)) in L(P, F, C)?

`Answer :- `

6. According to FOL semantics, which of the following are model(s) of the sentence ∃x∀y(WorksWith(x,y) ⊃ FriendOf(x,y)) in L(P, F, C)?

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7. According to FOL semantics, which of the following is/are true about predicates in L(P, F, C)?

• FOL derives the meaning of predicates like Celebrity, WorksWith and FriendOf from the meaning of the words used in the predicate name.
• The logical part of FOL uses WorksWith(x,y) to infer WorksWith(y,x).
• WorksWith is a binary predicate.
`Answer :- `

8. According to FOL semantics, which of the following is/are true?

• Ada always refers to an element in the domain.
• mother(father(Ada)) always refers to an element in the domain.
• Celebrity(x) returns an element from the domain.
• mother(father(Ada)) must be equal to one of the constants in L(P,F,C).
`Answer :- `

9. Consider the FOL language L( {P,Q}, {f,g,h}, {A,B,C} ) with variables x, y, z. Which of the following pairs of clauses are unifiable?

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

10. 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(y))
B. ∃x ((∃y R(x,y)) ⊃ Q(x))
C. ∀x (Q(x) ⊃ ∃y R(x,y))

Skolem forms:

1. ¬P(sk3) ∨ Q(?y)
2. ¬P(?x) ∨ Q(?y)
3. ¬R(sk1,?y) ∨ Q(?y)
4. ¬R(sk3,sk4) ∨ Q(sk4)
5. ¬R(?x,sk2(?x)) ∨ Q(?x)
6. R(?x,sk2(?x)) ∨ ¬Q(?x)

For the formulas A, B and C, in that order, enter the matching Skolem formula numbers as a comma separated list.

`Answer :- For Answer Click Here`

11. Use FOL to state that WorksWith is a symmetric relation. WorksWith is symmetric because: if x works with y then it also means that y works with x.

• WorksWith(x,y) ⊃ WorksWith(y,x)
• ∀x∀y (WorksWith(x,y) ⊃ WorksWith(y,x))
• ∃x∃y (WorksWith(x,y) ⊃ WorksWith(y,x))
• All of the above
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