Exercise 11.11 [alt-vacuum-exercise]

Conditional effects were illustrated for the ${Suck}$ action in the vacuum world—which square becomes clean depends on which square the robot is in. Can you think of a new set of propositional variables to define states of the vacuum world, such that ${Suck}$ has an unconditional description? Write out the descriptions of ${Suck}$, ${Left}$, and ${Right}$, using your propositions, and demonstrate that they suffice to describe all possible states of the world.