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Linear implication can represent state transitions, but real transitionsystems operate under temporal, stochastic or probabilistic constraints thatare not directly representable in ordinary linear logic. We propose a generalmodal extension of intuitionistic linear logic where logical truth is indexedby constraints and hybrid connectives combine constraint reasoning with logicalreasoning. The logic has a focused cut-free sequent calculus that can be usedto internalize the rules of particular constrained transition systems; weillustrate this with an adequate encoding of the synchronous stochasticpi-calculus. We also present some preliminary experiments of direct encoding ofbiological systems in the logic.

A Hybrid Linear Logic for Constrained Transition Systems with Applications to Molecular Biology