A Linear/Producer/Consumer Model of Classical Linear Logic

Jennifer Paykin
(University of Pennsylvania)
Steve Zdancewic
(University of Pennsylvania)

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.

In Sandra Alves and Iliano Cervesato: Proceedings Third International Workshop on Linearity (LINEARITY 2014), Vienna, Austria, 13th July, 2014, Electronic Proceedings in Theoretical Computer Science 176, pp. 9–23.
Published: 16th February 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.176.2 bibtex PDF
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