Exercise 12.24

The assumption of logical omniscience, discussed on page logical-omniscience, is of course not true of any actual reasoners. Rather, it is an idealization of the reasoning process that may be more or less acceptable depending on the applications. Discuss the reasonableness of the assumption for each of the following applications of reasoning about knowledge:

  1. Chess with a clock. Here the player may wish to reason about the limits of his opponent’s or his own ability to find the best move in the time available. For instance, if player A has much more time left than player B, then A will sometimes make a move that greatly complicates the situation, in the hopes of gaining an advantage because he has more time to work out the proper strategy.

  2. A shopping agent in an environment in which there are costs of gathering information.

  3. An automated tutoring program for math, which reasons about what students understand.

  4. Reasoning about public key cryptography, which rests on the intractability of certain computational problems.

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