  We reformulate the signal temporal logic (STL) synthesis problem as a maximum
a-posteriori (MAP) inference problem. To this end, we introduce the notion of
random STL~(RSTL), which extends deterministic STL with random predicates. This
new probabilistic extension naturally leads to a synthesis-as-inference
approach. The proposed method allows for differentiable, gradient-based
synthesis while extending the class of possible uncertain semantics. We
demonstrate that the proposed framework scales well with GPU-acceleration, and
present realistic applications of uncertain semantics in robotics that involve
target tracking and the use of occupancy grids.
