Understanding planning with incomplete information and sensing Original Research Article

PKS is the framework for planning with incomplete information and sensing recently introduced by Bacchus and Petrick [Proc. KRʹ98, pp. 432–443]. The fact that PKS generalizes STRIPS to domains with incomplete information and sensing opens up the possibility of proposing it as a reference for comparisons with other formalisms that approach the problem from different perspectives. To this end we first provide a formal semantics for PKS, then analyze and extend it. The formal definition of the extended PKS entails the identification of a number of properties of this planning framework. In particular, we prove that for any finite instance of the PKS planning problem the reachable states are finite; on the basis of this result we propose an improved planning algorithm that is not only sound, as the one proposed by Petrick and Bacchus [Proc. AIPSʹ02, pp. 212–221], but also complete. 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.