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In this paper, we propose Belief Behavior Trees (BBTs), an extension to Behavior Trees (BTs) that allows to automatically create a policy that controls a robot in partially observable environments. We extend the semantic of BTs to account for the uncertainty that affects both the conditions and action nodes of the BT. The tree gets synthesized following a planning strategy for BTs proposed recently: from a set of goal conditions we iteratively select a goal and find the action, or in general the subtree, that satisfies it. Such action may have preconditions that do not hold. For those preconditions, we find an action or subtree in the same fashion. We extend this approach by including, in the planner, actions that have the purpose to reduce the uncertainty that affects the value of a condition node in the BT (for example, turning on the lights to have better lighting conditions). We demonstrate that BBTs allows task planning with non-deterministic outcomes for actions. We provide experimental validation of our approach in a real robotic scenario and - for sake of reproducibility - in a simulated one.