Understanding planning with incomplete information and sensing

We extend PKS to include conditional plans with cycles and introduce the distinction between different classes of solutions: strong, strong cyclic, weak acyclic and weak cyclic. In contrast with current belief, we prove that some weak acyclic solutions are more likely to succeed for a limited execution than some strong cyclic solutions, revealing the lack of a method for judging the quality of different solutions. Finally, we introduce a quality measure for solutions of any class, and a quantitative method for comparing them.