Work

A Linear/Producer/Consumer Model of Classical Linear Logic

Year: 2015

Type: article

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.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.176.2

Authors: Jennifer Paykin, Steve Zdancewic

Institution: University of Pennsylvania

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Graduate Research Fellowship Program (GRFP), SHF: SMALL: NONSTANDARD COMPUTATIONAL MODELS OF LINEAR LOGIC