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Propositional Temporal Logic (PTL)

Description: This quiz is designed to test your knowledge of Propositional Temporal Logic (PTL). PTL is a formal system used to represent and reason about temporal properties of systems. It is widely used in computer science, artificial intelligence, and other fields.
Number of Questions: 15
Created by:
Tags: propositional temporal logic temporal reasoning formal systems
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Which of the following is a valid formula in PTL?

  1. G(p -> q)

  2. F(p & q)

  3. X(p U q)

  4. Y(p R q)

Show answer
Correct Option: C
Explanation:

X(p U q) means that in the next moment, p will hold until q holds.

What is the dual of the formula G(p -> q)?

  1. F(p & q)

  2. F(!p | q)

  3. G(!p | q)

  4. G(p & q)

Show answer
Correct Option: B
Explanation:

The dual of a formula is obtained by replacing all temporal operators with their duals and negating the formula.

What is the meaning of the formula F(p U q)?

  1. p will hold eventually

  2. p will hold until q holds

  3. p will hold in the next moment

  4. p will hold forever

Show answer
Correct Option: A
Explanation:

F(p U q) means that there exists a future moment where p holds and q holds or p holds forever.

Which of the following is a valid inference rule in PTL?

  1. From G(p -> q) and p, infer q

  2. From F(p & q), infer G(p)

  3. From X(p U q), infer F(q)

  4. From Y(p R q), infer G(q)

Show answer
Correct Option: A
Explanation:

This is a valid inference rule because if p holds forever and p implies q, then q must also hold forever.

What is the semantics of the formula G(p -> q)?

  1. In every possible execution, p implies q

  2. In some possible execution, p implies q

  3. In every possible execution, p holds

  4. In some possible execution, q holds

Show answer
Correct Option: A
Explanation:

G(p -> q) means that in every possible execution, if p holds then q also holds.

Which of the following is a valid formula in PTL?

  1. G(p & q)

  2. F(p | q)

  3. X(!p)

  4. Y(p -> q)

Show answer
Correct Option: A
Explanation:

G(p & q) means that both p and q hold forever.

What is the dual of the formula F(!p)?

  1. G(p)

  2. F(p)

  3. G(!p)

  4. F(!p)

Show answer
Correct Option: C
Explanation:

The dual of a formula is obtained by replacing all temporal operators with their duals and negating the formula.

What is the meaning of the formula X(!p)?

  1. p will not hold in the next moment

  2. p will hold in the next moment

  3. p will hold eventually

  4. p will hold forever

Show answer
Correct Option: A
Explanation:

X(!p) means that in the next moment, p will not hold.

Which of the following is a valid inference rule in PTL?

  1. From F(p & q), infer F(p)

  2. From G(p -> q), infer G(q)

  3. From X(p U q), infer X(q)

  4. From Y(p R q), infer Y(q)

Show answer
Correct Option: A
Explanation:

This is a valid inference rule because if p and q hold eventually, then p must also hold eventually.

What is the semantics of the formula F(p | q)?

  1. In some possible execution, p or q holds

  2. In every possible execution, p or q holds

  3. In some possible execution, p holds

  4. In every possible execution, q holds

Show answer
Correct Option: A
Explanation:

F(p | q) means that there exists a future moment where either p or q holds.

Which of the following is a valid formula in PTL?

  1. G(p -> q)

  2. F(p & q)

  3. X(p U q)

  4. Y(p R q)

Show answer
Correct Option: A
Explanation:

G(p -> q) means that in every possible execution, if p holds then q also holds.

What is the dual of the formula X(p U q)?

  1. F(!p | q)

  2. G(!p | q)

  3. F(p & !q)

  4. G(p & !q)

Show answer
Correct Option: A
Explanation:

The dual of a formula is obtained by replacing all temporal operators with their duals and negating the formula.

What is the meaning of the formula Y(p R q)?

  1. p will hold until q holds

  2. p will hold eventually

  3. p will hold in the next moment

  4. p will hold forever

Show answer
Correct Option: A
Explanation:

Y(p R q) means that p will hold until q holds, or p will hold forever.

Which of the following is a valid inference rule in PTL?

  1. From G(p -> q) and p, infer q

  2. From F(p & q), infer G(p)

  3. From X(p U q), infer F(q)

  4. From Y(p R q), infer G(q)

Show answer
Correct Option: A
Explanation:

This is a valid inference rule because if p holds forever and p implies q, then q must also hold forever.

What is the semantics of the formula Y(p R q)?

  1. In every possible execution, p holds until q holds

  2. In some possible execution, p holds until q holds

  3. In every possible execution, p holds

  4. In some possible execution, q holds

Show answer
Correct Option: A
Explanation:

Y(p R q) means that in every possible execution, p will hold until q holds, or p will hold forever.

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