Stochastic Reasoning in Hybrid Linear Logic

Ordinary linear implication can represent unconstrained state transition, but stateful systems often operate under temporal and stochastic constraints which impede the use of linear logic as a framework for representing stateful computations. We propose a general modal extension of linear logic where the worlds represent the constraints, and hybrid connectives combine constraint reasoning with ordinary logical reasoning. Among the merits of this logic is a generic focused sequent calculus that can be used to internalize the rules of particular stateful systems; we illustrate this with a simple adequate encoding of the synchronous stochastic pi-calculus.