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Epistemic Logic and Rationality

Epistemic Logic and Rationality is a branch of logic that deals with knowledge and belief. It is used to study how agents reason about their own knowledge and the knowledge of others. This quiz will test your understanding of the basic concepts of epistemic logic and rationality.

5 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is a valid inference in epistemic logic?

  1. If I know that P, then I know that I know that P.
  2. If I believe that P, then I know that P.
  3. If I know that P, then I believe that P.
  4. If I believe that P, then I know that I believe that P.
Question 2 Multiple Choice (Single Answer)

Which of the following is a valid inference in rational choice theory?

  1. If I prefer A to B, and B to C, then I prefer A to C.
  2. If I prefer A to B, and B is indifferent to C, then I prefer A to C.
  3. If I prefer A to B, and C is indifferent to B, then I prefer A to C.
  4. If I prefer A to B, and B is preferred to C, then I prefer A to C.
Question 3 Multiple Choice (Single Answer)

Which of the following is a valid inference in game theory?

  1. If Player 1 has a dominant strategy, then Player 2 has a dominant strategy.
  2. If Player 1 has a Nash equilibrium strategy, then Player 2 has a Nash equilibrium strategy.
  3. If Player 1 has a mixed strategy, then Player 2 has a mixed strategy.
  4. If Player 1 has a pure strategy, then Player 2 has a pure strategy.
Question 4 Multiple Choice (Single Answer)

Which of the following is a valid inference in decision theory?

  1. If I have a complete and transitive preference relation, then I can always find a unique optimal decision.
  2. If I have a complete and transitive preference relation, then I can always find a set of Pareto optimal decisions.
  3. If I have a complete and transitive preference relation, then I can always find a set of Nash equilibrium decisions.
  4. If I have a complete and transitive preference relation, then I can always find a set of dominant strategy decisions.
Question 5 Multiple Choice (Single Answer)

Which of the following is a valid inference in social choice theory?

  1. If a social welfare function is Pareto efficient, then it is also utilitarian.
  2. If a social welfare function is utilitarian, then it is also Pareto efficient.
  3. If a social welfare function is dictatorial, then it is also Pareto efficient.
  4. If a social welfare function is egalitarian, then it is also Pareto efficient.
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