Artificial Intelligence - Knowledge Representation and Reasoning - Unit 6 - Week 3

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Week 3 : Assignment
payment status The due date for submitting this assignment has passed.
Due on 2024-02-14, 23:59 IST.
Course Assignment submitted on 2024-02-13, 19:51 IST

outline
IMPORTANT: Your short answers MUST FOLLOW THE FORMAT STATED IN EACH
About QUESTION. DO NOT ENTER EXTRANEOUS BLANKS, DOTS, TABS, PARENTHESIS or
NPTEL ()
UNWANTED CHARACTERS in your answers. By default, enter lists as COMMA separated
values WITHOUT PARENTHESIS, BLANKS OR EXTRANEOUS CHARACTERS. Any deviation
How does an will result in ZERO MARKS because the answers are EVALUATED BY STRING MATCHING.
NPTEL
online
Marking scheme for MCQs with more than one correct answer:
course
● Full marks, if all correct options are selected and no wrong option is selected.
work? ()
● Partial marks, if some correct options are selected and no wrong option is selected.
● Zero marks, if at least one wrong option is selected.
Prerequisite
● Zero marks, if no options are selected.
Assignment
()
Abbreviations: Knowledge Base (KB), Propositional Logic (PL).
We treat “proof” and “derivation” as synonyms.
Week 1 ()
Week 2 () 1) In propositional logic, NAND stands for NOT AND, and NOR stands for NOT OR. 1 point
Which of the following are propositional logic sentences that are composed from the atomic
Week 3 () sentences A,B,C,D?
Propositional (A ¬(B ⊃ C))

Logic (unit?
A ¬∧ B
unit=40&lesso
n=41) A ¬∨ C
B ¬⊃ C
Propositional ¬(A ∧ B)
Logic: Syntax
¬(A ∨ C)
(unit?
unit=40&lesso ¬¬D
n=42) No, the answer is incorrect.
Score: 0
Propositional
Accepted Answers:
Logic:
¬(A ∧ B)
Semantics
¬(A ∨ C)
(unit?
unit=40&lesso ¬¬D
n=43)
2) Let the propositional variables A, B, and C denote three distinct statements that are 1 point
Proofs: Natural equivalent to each other, then we can use the propositional formula (A ≡ B ≡ C) to express the
Deduction equivalence between A, B, and C.
(unit?
unit=40&lesso True
n=44) False
The Deduction No, the answer is incorrect.
Theorem Score: 0
(unit? Accepted Answers:
unit=40&lesso False
n=45)
Models (unit? 3) Represent the formula ¬[(A ⊃ B) ⊃ (P ⊃ Q)] using only the connectives {¬,∧ }. 1 point
unit=40&lesso
n=46)
A ∧ ¬B ∧ ¬(P ∧ ¬Q)
¬A ∧ B ∧ P ∧ ¬Q
The Tableau
Method (unit?
¬(A ∧ ¬B) ∧ P ∧ ¬Q
unit=40&lesso ¬(A ∧ ¬B) ∧ ¬P ∧ ¬Q
n=47)
Yes, the answer is correct.
Lecture Score: 1
material (unit? Accepted Answers:
unit=40&lesso ¬(A ∧ ¬B) ∧ P ∧ ¬Q
n=48)
4) A model for a KB in propositional logic is a list of __________ . 1 point
Week 3
Feedback form
truth values assigned to all sentences in the KB
: Artificial
Intelligence: truth values assigned to all atomic propositions such that all sentences in the KB evaluate
Knowledge to true
Representatio all atomic propositions in the KB
n And
all atomic propositions in the KB and their negations
Reasoning
(unit? Yes, the answer is correct.
unit=40&lesso Score: 1
n=49) Accepted Answers:
truth values assigned to all atomic propositions such that all sentences in the KB evaluate to
Practice: Week
true
3 : Assignment
(Non Graded)
(assessment? 5) Select the correct option. 1 point
name=195)
KB: { (A ∨ B) ⊃ (A ∧ B) }
Quiz: Week 3
: Assignment KB ⊨ (A ⊃ B)
(assessment? KB ⊨ (B ⊃ A)
name=210)
KB ⊨ (A ≡ B)
Week 4 () All of the above

Week 5 () Score: 1
Accepted Answers:
Week 6 () All of the above
6) Select the sentences that can be derived from the given KB? 1 point
Week 7 ()
KB: { If there is no balance or the battery is dead then Kailash cannot make a call. If the battery is
Week 8 ()
not charged then the battery is dead. Kailash made a call. Therefore, the battery was charged. }
Week 9 () Kailash did not make a call.

Kailash made a call.
Week 10 ()
The battery is dead.
Week 11 () The battery is not dead.

The battery is charged.
DOWNLOAD The battery is not charged.
VIDEOS ()
The phone has balance.
Text The phone has no balance.

Transcripts () Partially Correct.
Score: 0.5
Books () Accepted Answers:
Kailash made a call.
Problem The battery is not dead.
Solving The battery is charged.
Session - The phone has balance.
Jan 2024 ()
7) Let α, β, γ, and δ be formulas over the set of propositions {P, Q, R}. Given the 1 point
conjunction (α ∧ β ∧ γ ∧ ¬δ) as input, the Tableau Method may be used to show that __________
.
the conjunction is satisfiable

the conjunction is unsatisfiable
(α ∧ β ∧ γ) ⊃ δ is a tautology
δ can be derived from the formulas α, β, γ

Score: 1
Accepted Answers:
the conjunction is satisfiable
the conjunction is unsatisfiable
(α ∧ β ∧ γ) ⊃ δ is a tautology
δ can be derived from the formulas α, β, γ
8) Select the valid tableau expansion rules. 1 point

Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
Rule 6

Score: 1
Accepted Answers:
Rule 3
Rule 4
Rule 6
9) Which of these expansion trees show the correct application of tableau expansion 1 point
rules?
Tree 1
Tree 2
Both 1 and 2
None of the above
No, the answer is incorrect.
S 0
Score: 0
Accepted Answers:
Both 1 and 2
10) Which of the tableau expansion trees in the previous question show a proof, by 1 point
Tableau Method, of the statement (P ⊃ (Q ⊃ R)) ⊃ ((P ⊃ Q) ⊃ (P ⊃ R))?
Tree 1
Tree 2
Both 1 and 2
None of the above

Score: 0
Accepted Answers:
Tree 1
11) In an expansion tree produced by the Tableau Method __________ . 1 point
a closed branch produces a model for the formula at the root of the tree
a closed branch produces a model for the NEGATION of the formula at the root of the
tree
a fully expanded open branch produces a model for the formula at the root of the tree
a fully expanded open branch produces a model for the NEGATION of the formula at the
root of the tree

Score: 0
Accepted Answers:
a fully expanded open branch produces a model for the formula at the root of the tree

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NPTEL (https://swayam.gov.in/explorer?ncCode=NPTEL) » Artificial Intelligence: Knowledge Representation

And Reasoning (course)

Course Assignment submitted on 2024-02-13, 19:51 IST

Propositional (A ¬(B ⊃ C))

Yes, the answer is correct.

Week 9 () Kailash did not make a call.

Week 11 () The battery is not dead.

Text The phone has no balance.

the conjunction is satisfiable

Yes, the answer is correct.

8) Select the valid tableau expansion rules. 1 point

Yes, the answer is correct.

No, the answer is incorrect.

No, the answer is incorrect.

11) In an expansion tree produced by the Tableau Method __________ . 1 point

No, the answer is incorrect.

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