Analyzing generalized planning under nondeterminism

In automated planning, there has been a recent interest in solving class of problems, where single solution applies for multiple, possibly infinitely many, instances. This necessitates generalized notion plans, such as plans with loops. However, the correctness is non-trivial to define, making it difficult provide clear specification what we should be looking for. an influential paper, Levesque proposed formal analyzing plans. He motivated logical characterization within situation calculus that included binary sensing actions. argued from each state considered possible initially, plan terminate while satisfying goal. Increasingly, classical structures are being applied stochastic environments robotics applications. raises question look like, since Levesque's account makes assumption actions deterministic. this work, aim generalize handle nondeterministic outcomes, which may also accorded probabilities. By appealing extension probabilistic nondeterminism, will show definition, well goal achievability by Lin and Levesque, have limited appeal under nondeterminism. essence, they correspond one correct execution, unlikely adequate. Rather, propose delineate between satisfaction termination leading range criteria. To better study these criteria, position results broader context still allowing generality calculus, consider abstract framework loops, domains unbounded, and/or stochastic, continuous. Within framework, then prove numerous relationships including some impossibility categorically goals. Finally, notions more granular view than those discussed literature, strong planning cyclic planning.