Exercise 11.8

Consider the following argument: In a framework that allows uncertain initial states, nondeterministic effects are just a notational convenience, not a source of additional representational power. For any action schema $a$ with nondeterministic effect $P \lor Q$, we could always replace it with the conditional effects ${~R{:}~P} \land {~\lnot R{:}~Q}$, which in turn can be reduced to two regular actions. The proposition $R$ stands for a random proposition that is unknown in the initial state and for which there are no sensing actions. Is this argument correct? Consider separately two cases, one in which only one instance of action schema $a$ is in the plan, the other in which more than one instance is.