Logical Inference Quiz

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Questions and Answers

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?

<p>Two (A)</p> Signup and view all the answers

What does KB ⊨ R signify?

<p>KB entails R (A)</p> Signup and view all the answers

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

<p>Adding all the cues to the knowledge base (A)</p> Signup and view all the answers

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

<p>It is raining (C)</p> Signup and view all the answers

Why is Model Checking not considered an efficient algorithm?

<p>It considers every possible model before giving an answer (C)</p> Signup and view all the answers

What does the horizontal bar in inference rules typically represent?

<p>Premise and conclusion (A)</p> Signup and view all the answers

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

<p>16 (C)</p> Signup and view all the answers

What knowledge is part of the premise in inference rules?

<p>Existing information (A)</p> Signup and view all the answers

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

<p>By checking all models where the knowledge base is true for R (C)</p> Signup and view all the answers

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

<p>Exclusive Or requires both arguments to be true, while inclusive Or requires only one of the arguments to be true. (B)</p> Signup and view all the answers

Which example best illustrates an exclusive Or?

<p>Having either cookies or ice cream for dessert. (C)</p> Signup and view all the answers

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

<p>⊕ (D)</p> Signup and view all the answers

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

<p>When either P or Q is true. (B)</p> Signup and view all the answers

What does implication (→) represent in logical structures?

<p>A statement where if P is true, then Q must also be true. (A)</p> Signup and view all the answers

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

<p>Only Q (A)</p> Signup and view all the answers

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

<p>Eliminate biconditionals (D)</p> Signup and view all the answers

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

<p>(¬P ∨ R) ∧ (¬Q ∨ R) (C)</p> Signup and view all the answers

What inference algorithm is typically run on Conjunctive Normal Form?

<p>Resolution algorithm (D)</p> Signup and view all the answers

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

<p>An empty clause () (D)</p> Signup and view all the answers

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

<p>(KB ∧ ¬α) must be a contradiction (C)</p> Signup and view all the answers

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

<p>It signifies a contradiction (A)</p> Signup and view all the answers

What is the main difference between implication and entailment?

<p>Implication involves deriving new sentences, while entailment involves checking if all information in one proposition is true based on another. (D)</p> Signup and view all the answers

What does inference refer to?

<p>The process of deriving new sentences from existing ones. (A)</p> Signup and view all the answers

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

<p>Checking if KB entails R based on the model checking algorithm. (D)</p> Signup and view all the answers

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

<p>All information in α is true based on all information in KB being true. (D)</p> Signup and view all the answers

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

<p>By enumerating all possible models and checking if α is true in each model where KB is true. (C)</p> Signup and view all the answers

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

<p>It makes the KB false in all models where P is not true. (B)</p> Signup and view all the answers

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