Exercise 8.16 [wumpus-diagnostic-exercise]

Equation (pit-biconditional-equation) on page pit-biconditional-equation defines the conditions under which a square is breezy. Here we consider two other ways to describe this aspect of the wumpus world.

1. We can write [diagnostic rule] leading from observed effects to hidden causes. For finding pits, the obvious diagnostic rules say that if a square is breezy, some adjacent square must contain a pit; and if a square is not breezy, then no adjacent square contains a pit. Write these two rules in first-order logic and show that their conjunction is logically equivalent to Equation (pit-biconditional-equation).

2. We can write [causal rule] leading from cause to effect. One obvious causal rule is that a pit causes all adjacent squares to be breezy. Write this rule in first-order logic, explain why it is incomplete compared to Equation (pit-biconditional-equation), and supply the missing axiom.