11.9 In this exercise we will consider the monkey-and-bananas problem, in which there is a monkey in a room with some bananas hanging out of reach from the ceiling, but a box is available that will enable the monkey to reach the bananas if he climbs on it. Initially, the monkey is at A, the bananas at B, and the box at C. The monkey and box have height Low, but if the monkey climbs onto the box he will have height High, the same as the bananas. The actions available to the monkey include Go from one place to another, Push an object from one place to another, Climb onto an object, and Grasp an object. Grasping results in holding the object if the monkey and object are in the same place at the same height.

a. Write down the initial state description in predicate calculus.

b. Write down STRIPS-style definitions of the four actions, providing at least the obvious preconditions.

c. Suppose the monkey wants to fool the scientists, who are off to tea, by grabbing the bananas but leaving the box in its original place. Write this as a general goal (i.e., not assuming the box is necessarily at C) in the language of situation calculus. Can this goal be solved by a STRIPS-style system?

d. Your axiom for pushing is probably incorrect, because if the object is too heavy, its position will remain the same when the Push operator is applied. Is this an example of the frame problem or the qualification problem?