Technical Reports (CIS)

Document Type

Technical Report

Date of this Version

2-27-2014

Comments

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-14-03.

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 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.

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Date Posted: 23 June 2014