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arXiv · 1502.04770

A Linear/Producer/Consumer Model of Classical Linear Logic

Jennifer Paykin·Steve Zdancewic
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Abstract

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.

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Jennifer Paykin, Steve Zdancewic. 2015-02-17. A Linear/Producer/Consumer Model of Classical Linear Logic. https://doi.org/10.4204/eptcs.176.2

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