Up to now we have assumed that actions arc only executed in the appropriate situations. Let us see what propositional successor-state axioms such as Equation (11.1) have to say about actions whose preconditions are not satisfied.
a. Show that the axioms predict that nothing will happen when an action is executed in a state where its preconditions are not satisfied.
b. Consider a plan p that contains the actions required to achieve a goal but also includes illegal actions, is it the case that initial state A successor-state axioms ^ p │= goal?
c. With first-order successor-slate axioms in situation calculus (as in), is it possible to prove that a plan containing illegal actions will achieve the goal?