Introduction to linear logic and ludics, part I

TL;DR

This paper provides an introductory survey of linear logic and ludics, focusing on their foundational principles, connectives, proof rules, and models, with a follow-up part covering proof nets and ludics.

Contribution

It offers a comprehensive first-part overview of linear logic and ludics, highlighting their core concepts, proof systems, and mathematical models.

Findings

Linear logic introduces new connectives and proof rules.

Decidability properties of linear logic are discussed.

Models of linear logic are explored.

Abstract

This two-parts paper offers a survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, respectively. Both theories revisit mathematical logic from first principles, with inspiration from and applications to computer science. The present part I covers an introduction to the connectives and proof rules of linear logic, to its decidability properties, and to its models. Part II will deal with proof nets, a graph-like representation of proofs which is one of the major innovations of linear logic, and will present an introduction to ludics.