Paykin, JenniferZdancewic, Stephan A2023-05-222023-05-222014-02-272014-04-02https://repository.upenn.edu/handle/20.500.14332/7965This 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 that reflect 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 the category theory. The work also presents several concrete instances of the LPC model, including one based on finite vector spaces.Computer EngineeringComputer SciencesReport