  This paper defines a new proof- and category-theoretic framework for
classical linear logic that separates reasoning into one linear regime and two
persistent regimes corresponding to ! and ?. The resulting
linear/producer/consumer (LPC) logic puts the three classes of propositions on
the same semantic footing, following Benton's linear/non-linear formulation of
intuitionistic linear logic. Semantically, LPC corresponds to a system of three
categories connected by adjunctions reflecting the linear/producer/consumer
structure. The paper's metatheoretic results include admissibility theorems for
the cut and duality rules, and a translation of the LPC logic into category
theory. The work also presents several concrete instances of the LPC model.
