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A linear/producer/consumer model of classical linear logic

Published online by Cambridge University Press:  27 October 2016

JENNIFER PAYKIN  and
STEVE ZDANCEWIC
JENNIFER PAYKIN
Affiliation:
Department of Computer and Information Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Emails: jpaykin@seas.upenn.edu, stevez@cis.upenn.edu
STEVE ZDANCEWIC
Affiliation:
Department of Computer and Information Sciences, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Emails: jpaykin@seas.upenn.edu, stevez@cis.upenn.edu
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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 LPC structure. The paper's meta-theoretic 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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 5: Linearity 2014 , May 2018 , pp. 710 - 735
Copyright
Copyright © Cambridge University Press 2016 

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