NPTEL Artificial Intelligence : Search Methods For Problem solving Week 11 Assignment Answers 2024

1. In Mathematical Logic (Formal Logic), ________________ .

once a statement is true it will continue to be true
logical reasoning is mainly concerned with the interpretation of statements,i.e., what the statements represent (in content) in a domain of interest
all of the above

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2. Which of the following are tautologies?

[P ∧ Q] ⊃ [P ∨ Q]
[(P ∨ Q) ⊃ R] ⊃ [(P ∧ Q) ⊃ R]
[(P ∨ Q) ⊃ R] ⊃ [P ⊃ R]

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3. Which of the following are tautologies?

[(P ⊃ R) ∨ (Q ⊃ R)] ⊃ [(P ∧ Q) ⊃ R]
[(P ⊃ R) ∧ (Q ⊃ R)] ⊃ [(P ∧ Q) ⊃ R]
all of the above

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4. Given a KB, _______________ .

entailment refers to sentences that are necessarily true when the KB is true
entailment refers to sentences that are necessarily false when the KB is false
entailment refers to sentences that are derived by a proof procedure
entailment in propositional logic can be computed using truth tables

Answer :-

5. Soundness and completeness are properties associated with ______________ .

proofs
proof procedures
knowledge bases
all of the above

Answer :-

6. Modified Modus Ponens _________________ .

combines generalization and modus ponens into a single inference rule
combines universal instantiation and modus ponens into a single inference rule
is used in first order logic to reduce the number of steps in proofs
is a substitution rule

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7. Forward Chaining is an automated theorem proving algorithm ________________ .

it matches goals with rules to derive new goals
it matches goals with rules to derive new rules
it matches facts with rules to derive new facts
it matches facts with rules to derive new rules

Answer :-

8. Backward Chaining is an automated theorem proving algorithm ________________ .

it matches goals with rules to derive new goals
it matches goals with rules to derive new rules
it matches facts with rules to derive new facts
it matches facts with rules to derive new rules

Answer :-

9. In propositional logic and first-order-logic, _______________ .

a KB allows only true sentences
a KB allows false sentences to represent what is false in a domain
a KB cannot represent what is false in a domain
a KB can represent what is false in the domain

Answer :-

10. Select the correct options.

a KB is true if and only if all sentences in the KB are true
a KB is true if and only if at least one sentence in the KB is true
a KB is false if and only if all sentences in the KB are false
a KB is false if and only if at least one sentence in the KB is false

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11. In the KB, {a,b,c} denote constants and {Topper,Champion,Admission} denote unary predicates, and x is a variable. Select the sentences that are entailed by the KB.

KB = {
    ∀x[(Topper(x) ∨ Champion(x)) ⊃ Admission(x)],
    Admission(a),
    Topper(b),
    ¬Admission(c)
}

Topper(a)
Admission(b)
¬Champion(c)
∀x[Champion(x) ⊃ Admission(x)]

Answer :-

12. A unifier is _____________ .

an operator that takes the union of two knowledge bases
a set of variable-value pairs that make two different formulas to become identical to each other
a rule of substitution that replaces two formulas with an equivalent single formula

Answer :-

13. Each option contains a pair of formulas, which of these pairs are unifiable? Here Likes, Coach, Game and Travel denote predicates; Amy, Joe and Rome denote constants; ?u, ?v, ?x, and ?y denote variables.

Likes(?x,?x); Likes(Joe,?y)
Coach(?x,?y); Coach(?u,?v)
Game(Joe,?y,?y); Game(?u,Amy,Joe)
Travel(Joe,?x,?y); Travel(?u,Amy,Rome)

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END GROUP 1

BEGIN GROUP 2

KB contains the following five rules:

1. B(?x,?y) ⊃ P(?x,?y)
2. H(?x,?y) ⊃ M(?x,?y)
3. [S(?x) ∧ W(?y)] ⊃ C(?x,?y)
4. [S(?x) ∧ R(?y)] ⊃ P(?y,?x)
5. [P(?x,?y) ∧ C(?y,?z)] ⊃ M(?x,?z)

and the following set of facts (where the lowercase alphabets denote constants):

{ B(k,t), P(n,a), P(k,e), R(t), S(a), W(d) }

Use only Modified Modus Ponens and ∧-Simplification as rules of inference.

14. Let the Forward Chaining algorithm run to completion. For each rule in the KB, count the number of times that rule generated a new fact.

Enter the count for each rule 1 to 5 in that order as a comma separated list.
Answer format: 3,1,4,1,5

Answer :-

15. Let the Forward Chaining algorithm run to completion, which of the following facts will be added to the KB?

P(k,t)
P(a,t)
C(a,t)
C(a,d)
M(d,n)
M(t,d)

Answer :-

16. Let M(?u,?v) be the goal, where ?u and ?v are variables. Generate the complete goal tree (AND-OR tree). Count the number of instances of each rule 1 to 5 (in the KB) that occur in the goal tree?

Enter the count for each rule 1 to 5 in that order as a comma separated list.
Answer format: 3,1,4,1,5