  We present a general framework for risk semantics on Signal Temporal Logic
(STL) specifications for stochastic dynamical systems using axiomatic risk
theory. We show that under our recursive risk semantics, risk constraints on
STL formulas can be expressed in terms of risk constraints on atomic
predicates. We then show how this allows a (stochastic) STL risk constraint to
be transformed into a risk-tightened deterministic STL constraint on a related
deterministic nominal system, enabling the application of existing STL methods.
For affine predicate functions and a (coherent) Distributionally Robust Value
at Risk measure, we show how risk constraints on atomic predicates can be
reformulated as tightened deterministic affine constraints. We demonstrate the
framework using a Model Predictive Control (MPC) design with an STL risk
constraint.
