NPTEL Fundamentals of Artificial intelligence Week 5 Assignment Answers 2024

1. Q1. Formalization of knowledge in a declarative form begins with a __________.

A. conceptualization
B. semantics
C. interpretation
D. model

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2. P, Q and R are logical propositions. Identify the statements as tautology, and / or contradiction?
I. ((P∨Q)∧R)↔((P∧R)∨(Q∧R))
II. (P ↔Q)∧(Q↔R)∧¬(P↔R)

A. I. Tautology; II. Contradiction.
B. I. Contradiction; II. Tautology.
C. Both Tautologies.
D. Both Contradictions

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3. Consider which of the following statements are correct w.r.t. entailment in first-order logic being semi-decidable. I. Algorithms exist that say yes to every entailed sentence II. No algorithm exists that says no to every non-entailed sentence.

A. Both Statement I and II.
B. Either Statement I or II.
C. Statement I only.
D. Statement II only.

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4. Skolemization is a procedure for systematic elimination of the ___________ in a first-order formula in a prenex form, by introducing new constant and functional symbols.

A. existential quantifiers
B. universal quantifiers
C. variable
D function

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5. Consider the predicate Likes(x,y): x likes y. Everyone likes ice cream. Is it possible to convey the same meaning using an existential statement? If yes, give the existential statement.

A. No.
B. Yes. ∀x Likes(x,Icecream)
C. Yes. ∃x Likes(x,Icecream)
D. Yes. ¬ ∃x ¬Likes(x,Icecream)

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6. A definition of a predicate is a biconditional, and can be decomposed into a necessary and sufficient descriptions. Which of the following statement are true with regards to definition of ‘Brother’ I. Being a ‘Male’ is a necessary condition for being a ‘Brother’, but it is not sufficient. II. Being a ‘Male’, ‘Sibling’ is a necessary and sufficient condition for being a ‘Brother’.

A. I Only
B. II Only
C. Both I and II
D. None

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7. Assertion A: Any predicate calculus well-formed formula can be converted to a set of clauses. Reason R: The prenex form consists of a string of quantifiers called prefix followed by a quantifier-free formula called the matrix.

A. Both A and R are true and R is the correct explanation for A
B. Both A and R are true but R is not the correct explanation for A
C. A is True but R is False
D. A is false but R is True

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8. For the following pair of atomic sentences, give the most general unifier, if it exists: a. Older(Father(y), y) b. Older(Father(x), John)

A. {y/x, x/John}
B. {x/y}
C. {y/John, x/John}
D. Cannot unify

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9. For the following pair of atomic sentences, give the most general unifier, if it exists: a. Q(y, G(A, B)) b. Q(G(x, x), y)

A. {y/G(x,x), x/A}
B. {y/G(x,x), x/B }
C. {y/G(A,B), x/A}
D. Cannot unify

Answer :-

10. Assertion A: A proof requires axioms to build on i.e., axioms can be used to prove theorems in a given domain. Reason R: Axioms are facts and rules that attempt to capture all of the foundational principles i.e., important facts and concepts about the domain.

A. Both A and R are true and R is the correct explanation for A
B. Both A and R are true but R is not the correct explanation for A
C. A is True but R is False
D. A is false but R is True