Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cut-free sequent calculus that can be used to internalize the rules of

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... r constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus. We also present some preliminary experiments of direct encoding of biological systems in the logic.