11. Consider using abductive diagnosis on the problem in the previous question, with the following elaborations.

• Valves can be open or closed. Some of valves may be specified as open or closed.

• A valve can be ok, in which case the gas will flow if the valve is open and not if it is closed; broken, in which case gas never flows; stuck, in which case gas flows independently of whether the valve is open or closed; or leaking, in which case gas flowing into the valve leaks out instead of flowing through.

• There are three gas sensors that can detect gas leaking (but not which gas); the first gas sensor detects gas from the rightmost valves (v1, …, v4), the second gas sensor detects gas from the center valves (v5, …, v12), and the third gas sensor detects gas from the leftmost valves (v13, …, v16).

(a) Axiomatize the domain so the system can explain thrust or no thrust in engine e1 and the presence of gas in one of the sensors. For example, it should be able to explain why e1 is thrusting. It should be able to explain why e1 is not thrusting and there is a gas detected by the third sensor.

(b) Test your axiomatization on some non-trivial examples.

(c) Some of the queries have many explanations. Suggest how the number of explanations could be reduced or managed so that the abductive diagnoses are more useful.