Sensorless planning chooses one action sequence that succeeds from every possible initial physical state without receiving distinguishing observations during execution. A belief state is a set of possibilities. For a deterministic search transition model , an applicable action maps to ; for nondeterministic outcomes, take the union of all possible successors. Applicability must hold for every member of , and success requires the resulting belief state to be a subset of the physical goal set.
Every fixed action sequence preserves inclusion of the initial belief states. Consequently, a successful plan for also succeeds for every subset of . Success on a superset is an additional requirement, so cannot be inferred from success on alone. This property supports incremental belief-state search.
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