

The assumption of <i>logical omniscience,</i> discussed on
page <a class="pageRef" title="" href="#">logical-omniscience</a>, is of course not true of any actual reasoners.
Rather, it is an <i>idealization</i> 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:<br>

1.  Partial knowledge adversary games, such as card games. Here one
    player wants to reason about what his opponent knows about the state
    of the game.<br>

2.  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.<br>

3.  A shopping agent in an environment in which there are costs of
    gathering information.<br>

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