Exercise 4.8 [belief-state-superset-exercise]

This exercise explores subset–superset relations between belief states in sensorless or partially observable environments.

1. Prove that if an action sequence is a solution for a belief state $b$, it is also a solution for any subset of $b$. Can anything be said about supersets of $b$?

2. Explain in detail how to modify graph search for sensorless problems to take advantage of your answers in (a).

3. Explain in detail how to modify and–or search for partially observable problems, beyond the modifications you describe in (b).