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Question 1 of 60 Quiz ID: q1

What is the primary difference between a problem-solving agent and a knowledge-based agent?

Problem-solving agents use logic, knowledge-based agents use search

Problem-solving agents execute a given solution, knowledge-based agents reason and adapt

Knowledge-based agents are faster, problem-solving agents are more accurate

Problem-solving agents have goals, knowledge-based agents do not

Question 2 of 60 Quiz ID: q2

In the context of agent representations, what does a 'structured' representation consist of?

A single state with no internal details

A set of variable assignments

Objects, relations, and facts about those relations

A sequence of actions to be performed

Question 3 of 60 Quiz ID: q3

The core functions a Knowledge Base (KB) must support are TELL and ASK. What do these functions do?

TELL deletes information, ASK adds information

TELL adds new information, ASK retrieves information via inference

TELL checks for consistency, ASK performs learning

TELL queries the user, ASK answers user queries

Question 4 of 60 Quiz ID: q4

In the Wumpus World, why is the environment characterized as 'partially observable'?

Because the agent is blindfolded

Because the agent can only perceive its immediate surroundings (e.g., adjacent squares)

Because the map is randomly generated each time

Because the Wumpus can hide

Question 5 of 60 Quiz ID: q5

Which of the following is NOT a property of the Wumpus World as described?

Deterministic

Sequential

Continuous

Static

Question 6 of 60 Quiz ID: q6

In logic, what defines the 'syntax' of a language?

The meaning of its sentences

The set of models where sentences are true

The rules for constructing valid sentences

The inference algorithms used

Question 7 of 60 Quiz ID: q7

What is a 'model' in the context of logical semantics?

A simplified version of an inference algorithm

An abstraction of a possible world where truth values are assigned

The knowledge base of an agent

A type of logical connective

Question 8 of 60 Quiz ID: q8

The notation M(α) refers to:

The logical equivalence of α

The set of all models in which the sentence α is true

The model checking algorithm for α

The main connective in sentence α

Question 9 of 60 Quiz ID: q9

What does it mean for a sentence α to logically entail a sentence β (α ⊨ β)?

β is true in some models where α is true

β is true in every model where α is true

α and β are true in the same models

α is a stronger statement than β

Question 10 of 60 Quiz ID: q10

An inference algorithm i that derives α from KB (KB ⊢i α) is considered sound if:

It can derive any sentence that is entailed

It derives α only if α is entailed by KB (KB ⊨ α)

It is very fast and efficient

It uses model checking instead of theorem proving

Question 11 of 60 Quiz ID: q11

Model checking as an inference method:

Applies inference rules to the KB

Is only sound if the KB is in CNF

Enumerates all possible models to verify entailment

Is primarily used for first-order logic

Question 12 of 60 Quiz ID: q12

The concept of 'grounding' ensures that:

All sentences are in propositional logic

If the KB is true in the real world, sound inferences are also true

The agent's sensors are calibrated correctly

The inference algorithm is complete

Question 13 of 60 Quiz ID: q13

In propositional logic, which of these is an atomic sentence?

P ∨ Q

¬P

Wumpus1,2

P ⇒ (Q ∧ R)

Question 14 of 60 Quiz ID: q14

What is the correct precedence for these logical operators (highest to lowest)?

¬, ∧, ∨, ⇒, ⇔

∧, ∨, ¬, ⇒, ⇔

¬, ∧, ∨, ⇔, ⇒

⇔, ⇒, ∨, ∧, ¬

Question 15 of 60 Quiz ID: q15

For the sentence P ⇒ Q to be false, what must be true?

P is false and Q is true

P is true and Q is false

P is false and Q is false

P is true and Q is true

Question 16 of 60 Quiz ID: q16

In the Wumpus world KB, what does the proposition symbol B₂,₁ represent?

The agent is in square [2,1]

There is a breeze in square [2,1]

There is a pit in square [2,1]

Square [2,1] is safe

Question 17 of 60 Quiz ID: q17

The rule 'A square is breezy if and only if there is a pit in a neighboring square' for square [1,1] is logically represented as:

B₁,₁ ⇒ (P₁,₂ ∨ P₂,₁)

B₁,₁ ⇔ (P₁,₂ ∧ P₂,₁)

B₁,₁ ⇔ (P₁,₂ ∨ P₂,₁)

(P₁,₂ ∨ P₂,₁) ⇒ B₁,₁

Question 18 of 60 Quiz ID: q18

If an agent perceives nothing (no stench, no breeze) in [1,1], what sentence should be added to the KB?

B₁,₁ ∧ S₁,₁

¬B₁,₁ ∧ ¬S₁,₁

B₁,₁ ∨ S₁,₁

¬(B₁,₁ ∨ S₁,₁)

Question 19 of 60 Quiz ID: q19

From the rules R₂: B₁,₁ ⇔ (P₁,₂ ∨ P₂,₁) and R₄: ¬B₁,₁, what can be directly inferred about pits near [1,1]?

There must be a pit in [1,2]

There must be a pit in [2,1]

There cannot be a pit in [1,2] or [2,1]

The rules are inconsistent

Question 20 of 60 Quiz ID: q20

The process of applying inference rules (like Modus Ponens) directly to the KB to construct a proof is called:

Model checking

Theorem proving

Grounding

Satisfiability checking

Question 21 of 60 Quiz ID: q21

Which rule of inference is represented by this form? 'α ⇒ β, α, therefore β'

And-Elimination

Modus Ponens

Biconditional Elimination

Resolution

Question 22 of 60 Quiz ID: q22

The equivalence (α ⇒ β) ≡ (¬α ∨ β) is known as:

De Morgan's Law

Implication Elimination

Double Negation Elimination

Contraposition

Question 23 of 60 Quiz ID: q23

According to De Morgan's Law, ¬(α ∧ β) is equivalent to:

¬α ∧ ¬β

¬α ∨ ¬β

α ∨ β

α ∧ β

Question 24 of 60 Quiz ID: q24

A sentence that is true in every possible model is called:

Satisfiable

Valid (or a Tautology)

A contradiction

An axiom

Question 25 of 60 Quiz ID: q25

A sentence is 'satisfiable' if:

It is true in all models

It is false in all models

It is true in at least one model

It is not a tautology

Question 26 of 60 Quiz ID: q26

How are validity and satisfiability connected? A sentence α is valid if and only if:

α is satisfiable

¬α is satisfiable

¬α is unsatisfiable

α is not satisfiable

Question 27 of 60 Quiz ID: q27

The property that states 'if KB ⊨ α then KB ∧ β ⊨ α' is called:

Completeness

Soundness

Monotonicity

Logical Equivalence

Question 28 of 60 Quiz ID: q28

Which of these is an application of the And-Elimination inference rule?

Deriving α from α ∧ β

Deriving β from α ⇒ β and α

Deriving α ⇒ β from α ⇔ β

Deriving ¬α from ¬(α ∧ β)

Question 29 of 60 Quiz ID: q29

From the biconditional α ⇔ β, which two new sentences can be derived using biconditional elimination?

α ∧ β

α ∨ β

α ⇒ β and β ⇒ α

¬α ⇒ ¬β and ¬β ⇒ ¬α

Question 30 of 60 Quiz ID: q30

In the Wumpus proof, from R₂: B₁,₁ ⇔ (P₁,₂ ∨ P₂,₁) and R₄: ¬B₁,₁, what rule is used to derive ¬(P₁,₂ ∨ P₂,₁)?

Modus Ponens on the forward implication

Modus Tollens on the backward implication

And-Elimination

Biconditional Elimination

Question 31 of 60 Quiz ID: q31

The final goal of the search in the 'proof as a search' problem is:

To find the gold

To kill the Wumpus

To reach a state containing the sentence we want to prove

To find a model that satisfies the KB

Question 32 of 60 Quiz ID: q32

The Resolution inference rule requires sentences to be in what form?

Implications (⇒)

Biconditionals (⇔)

Clauses (disjunctions of literals)

Conjunctions of atomic sentences

Question 33 of 60 Quiz ID: q33

Converting a sentence to Conjunctive Normal Form (CNF) involves:

Expressing it as a conjunction of disjunctions of literals

Expressing it as a disjunction of conjunctions of literals

Eliminating all conjunctions

Eliminating all logical connectives

Question 34 of 60 Quiz ID: q34

What is the first step in converting the biconditional B₁,₁ ⇔ (P₁,₂ ∨ P₂,₁) to CNF?

Apply De Morgan's Law

Eliminate the biconditional

Eliminate the implication

Apply distributivity

Question 35 of 60 Quiz ID: q35

After biconditional elimination, the next step to get to CNF is to:

Apply distributivity

Eliminate implications

Apply De Morgan's Law

Remove double negations

Question 36 of 60 Quiz ID: q36

The subexpression ¬(P₁,₂ ∨ P₂,₁) ∨ B₁,₁ is transformed using De Morgan's Law into:

(¬P₁,₂ ∧ ¬P₂,₁) ∨ B₁,₁

(¬P₁,₂ ∨ ¬P₂,₁) ∨ B₁,₁

¬P₁,₂ ∨ ¬P₂,₁ ∨ B₁,₁

(P₁,₂ ∧ P₂,₁) ∨ B₁,₁

Question 37 of 60 Quiz ID: q37

The final step in achieving the full CNF for the converted sentence is to apply:

Implication Elimination

Biconditional Elimination

Double Negation Elimination

The Distributive Law

Question 38 of 60 Quiz ID: q38

The full CNF of B₁,₁ ⇔ (P₁,₂ ∨ P₂,₁) is:

(¬B₁,₁ ∨ P₁,₂ ∨ P₂,₁) ∧ (¬P₁,₂ ∨ B₁,₁) ∧ (¬P₂,₁ ∨ B₁,₁)

(B₁,₁ ∨ P₁,₂ ∨ P₂,₁) ∧ (¬P₁,₂ ∨ ¬B₁,₁) ∧ (¬P₂,₁ ∨ ¬B₁,₁)

(¬B₁,₁ ∧ P₁,₂ ∧ P₂,₁) ∨ (¬P₁,₂ ∧ B₁,₁) ∨ (¬P₂,₁ ∧ B₁,₁)

(B₁,₁ ⇒ P₁,₂ ∨ P₂,₁) ∧ (P₁,₂ ∨ P₂,₁ ⇒ B₁,₁)

Question 39 of 60 Quiz ID: q39

The primary limitation of model checking that motivates the use of theorem proving is:

It is not sound

It is not complete

It can be computationally infeasible for large models

It cannot handle propositional logic

Question 40 of 60 Quiz ID: q40

In the Wumpus world, the sentence 'There is no pit in [1,1]' (R₁: ¬P₁,₁) is an example of:

A percept sentence

An eternal truth/axiom of the environment

A derived conclusion

A goal sentence

Question 41 of 60 Quiz ID: q41

If the agent moves to [2,1] and perceives a Breeze, what new sentence is added to the KB?

B₂,₁

L₂,₁

B₂,₁ ∧ L₂,₁

B₂,₁ ∧ L₂,₁ ∧ ¬B₁,₁

Question 42 of 60 Quiz ID: q42

The query ASK(KB, MAKE-ACTION-QUERY(t)) in the KB-AGENT function returns:

A percept

An action

A new sentence for the KB

The current time step

Question 43 of 60 Quiz ID: q43

A 'sound' inference algorithm is most critical for ensuring:

The agent acts quickly

All entailed sentences can be derived

The agent's conclusions are true in the real world

The KB remains in CNF

Question 44 of 60 Quiz ID: q44

A 'complete' inference algorithm is defined as one that can:

Derive any sentence that is entailed

Derive only sentences that are entailed

Convert any sentence to CNF

Handle both propositional and first-order logic

Question 45 of 60 Quiz ID: q45

The logical equivalence (α ∨ (β ∧ γ)) ≡ ((α ∨ β) ∧ (α ∨ γ)) demonstrates:

Commutativity of ∨

Associativity of ∧

Distributivity of ∨ over ∧

De Morgan's Law

Question 46 of 60 Quiz ID: q46

In the model {P=true, Q=false}, what is the truth value of ¬P ∨ Q?

True

False

Question 47 of 60 Quiz ID: q47

Which of these sentences is satisfiable but not valid?

P ∨ ¬P

P ∧ ¬P

P ∨ Q

Question 48 of 60 Quiz ID: q48

The Wumpus world is 'static', meaning:

The agent is the only thing that can change it

It does not change while the agent is thinking

It is completely observable

It has only one solution

Question 49 of 60 Quiz ID: q49

The initial KB of a logical agent typically contains:

Only percepts

Only actions

The rules of the environment and initial percepts

A complete map of the world

Question 50 of 60 Quiz ID: q50

The inference rule Modus Tollens has the form:

α ⇒ β, β, therefore α

α ⇒ β, ¬β, therefore ¬α

α ∨ β, ¬α, therefore β

α ⇔ β, therefore α ⇒ β

Question 51 of 60 Quiz ID: q51

The Resolution rule combines two clauses to produce a new clause. What clause results from resolving (A ∨ B) and (¬A ∨ C)?

A ∨ C

B ∨ C

A ∨ ¬A

B ∧ C

Question 52 of 60 Quiz ID: q52

First-order logic, compared to propositional logic, primarily adds the ability to represent:

Logical connectives

Objects, properties, and relations

Probability

Time

Question 53 of 60 Quiz ID: q53

In the context of the KB agent function, what is the purpose of the persistent counter 't'?

To limit the number of inferences

To uniquely identify each percept and action in time

To track the agent's score

To seed the random number generator

Question 54 of 60 Quiz ID: q54

According to the lecture, real-world applications of concepts from the Wumpus World include:

Designing spreadsheets

Designing intelligent agents for autonomous vehicles and robotics

Writing natural language parsers

Optimizing database queries

Question 55 of 60 Quiz ID: q55

The sentence ¬(P₁,₂ ∨ P₂,₁) derived in the Wumpus example is equivalent to:

P₁,₂ ∧ P₂,₁

¬P₁,₂ ∨ ¬P₂,₁

¬P₁,₂ ∧ ¬P₂,₁

P₁,₂ ∨ P₂,₁

Question 56 of 60 Quiz ID: q56

If a knowledge-based agent is told a new fact that contradicts its existing KB, what property ensures that this does not automatically make every sentence entailed?

Soundness

Completeness

Monotonicity

Consistency

Question 57 of 60 Quiz ID: q57

The process of proving KB ⊨ α by proving that KB ∧ ¬α is unsatisfiable is called:

Model checking

Proof by resolution

Proof by contradiction (or reductio ad absurdum)

Forward chaining

Question 58 of 60 Quiz ID: q58

The Unit Clause heuristic used in DPLL is important because it:

Converts sentences to CNF

Forces a branching decision

Finds pure symbols

Propagates the effect of a single-literal clause, simplifying the model

Question 59 of 60 Quiz ID: q59

A 'pure symbol' in the DPLL algorithm is a symbol that:

Appears in a unit clause

Appears with only one polarity (all positive or all negative) in all remaining clauses

Has not been assigned a truth value yet

Appears in every clause

Question 60 of 60 Quiz ID: q60

Why is propositional logic often impractical for very large, complex knowledge bases?

It is not sound or complete

It cannot represent the real world

It requires a separate symbol for every atomic proposition, leading to combinatorial explosion

Its inference rules are too slow

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