Logical Inference Quiz

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In which models is the knowledge base (KB) true?

In all models except when P is true and Q is false

In all models except when R is false

Only in the model where P is true and Q is false (correct)

Only in the model where R is true

Which proposition affects the truth value of R?

P → R

(P ∨ Q) ∧ R

P ∧ ¬Q

(P ∧ ¬Q) → R (correct)

What happens to the knowledge base if R is false?

It remains true

It becomes true

It becomes false (correct)

It depends on P

How many models are left after considering all propositions?

Two Signup and view all the answers

What does KB ⊨ R signify?

KB entails R Signup and view all the answers

What step is required after representing the rules of the game in propositional logic?

Adding all the cues to the knowledge base Signup and view all the answers

What does the symbol 'rain' represent in the code snippet provided?

It is raining Signup and view all the answers

Why is Model Checking not considered an efficient algorithm?

It considers every possible model before giving an answer Signup and view all the answers

What does the horizontal bar in inference rules typically represent?

Premise and conclusion Signup and view all the answers

How many atomic propositions are required when representing four colors in propositional logic?

16 Signup and view all the answers

What knowledge is part of the premise in inference rules?

Existing information Signup and view all the answers

How does the Model Checking algorithm determine if a query 'R' is true?

By checking all models where the knowledge base is true for R Signup and view all the answers

What is the key difference between an exclusive Or and an inclusive Or?

Exclusive Or requires both arguments to be true, while inclusive Or requires only one of the arguments to be true. Signup and view all the answers

Which example best illustrates an exclusive Or?

Having either cookies or ice cream for dessert. Signup and view all the answers

What is the symbol commonly used to represent an exclusive Or?

⊕ Signup and view all the answers

In an inclusive Or, when is the statement considered true?

When either P or Q is true. Signup and view all the answers

What does implication (→) represent in logical structures?

A statement where if P is true, then Q must also be true. Signup and view all the answers

Which part of an implication statement is known as the consequent?

Only Q Signup and view all the answers

What is the first step in converting propositions to Conjunctive Normal Form?

Eliminate biconditionals Signup and view all the answers

In the given example, what is the result of converting (P ∨ Q) → R to Conjunctive Normal Form?

(¬P ∨ R) ∧ (¬Q ∨ R) Signup and view all the answers

What inference algorithm is typically run on Conjunctive Normal Form?

Resolution algorithm Signup and view all the answers

What does resolving a literal and its negation, e.g., ¬P and P, result in?

An empty clause () Signup and view all the answers

How is it determined if KB ⊨ α in the resolution algorithm?

(KB ∧ ¬α) must be a contradiction Signup and view all the answers

Why is the empty clause () considered false in resolution algorithms?

It signifies a contradiction Signup and view all the answers

What is the main difference between implication and entailment?

Implication involves deriving new sentences, while entailment involves checking if all information in one proposition is true based on another. Signup and view all the answers

What does inference refer to?

The process of deriving new sentences from existing ones. Signup and view all the answers

In the given example with P, Q, R, and KB, what does the query 'Does KB ⊨ R?' mean?

Checking if KB entails R based on the model checking algorithm. Signup and view all the answers

What does it mean when we say 'KB entails α'?

All information in α is true based on all information in KB being true. Signup and view all the answers

How is the Model Checking algorithm used to determine if KB ⊨ α?

By enumerating all possible models and checking if α is true in each model where KB is true. Signup and view all the answers

What is the significance of knowing P is true in the example provided?

It makes the KB false in all models where P is not true. Signup and view all the answers