A brief guide to linear logic

Abstract

An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. 1 Overview Linear logic, introduced by Girard 45], is a reenement of classical logic. Linear logic is sometimes described as resource sensitive because it provides an intrinsic and natural accounting of resources. This is indicated by the fact that in linear logic, two assumptions of a formula A are distinguished from a single assumption of A. Informally, on the level of basic intuition, one might say that classical logic is about truth, that intuitionistic logic is about construction of proofs, and that linear logic is about process states, events, or resources, which must be carefully accounted for. A convenient way to present the syntax of linear logic is by modifying the traditional Gentzen-style sequent calculus axiomatization of classical logic,