# A brief guide to linear logic

```@article{Scedrov1990ABG,
title={A brief guide to linear logic},
author={Andre Scedrov},
journal={Bull. EATCS},
year={1990},
volume={41},
pages={154-165}
}```
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…
75 Citations

### Linear Logic: A Survey

This introduction to linear logic is organised in four chapters: The formal system is introduced, with a special emphasis on the treatment of structural rules, and from the experience gathered in linear logic, it seems possible to put all (decent) logical systems together.

### The syntax of Linear logic

This paper deals only with syntax aspect of linear logic in order to arouse interest in the subject, leaving semantics and proof nets for future studies.

### Simulating Linear Logic in 1-Only Linear Logic

This paper focuses on the study of the simplest fragments of Linear Logic, such as the one-literal and constant-only fragments (the latter contains no literals at all).

### Some Applications of the Linear Logic Programming

This paper describes and discusses the applications of a logic programming language called Lygon, which is based on linear logic, a logic designed with bounded resources in mind, and contains various features which do not exist in Prolog, whilst maintaining all the features of (pure) Prolog.

### A linear logical framework

• Computer Science
Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
• 1996
The linear type theory LLF is presented as the formal basis for a conservative extension of the LF logical framework and can be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination.

### Linear logic

This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.

### Some Applications of the Linear Logic Programming Language Lygon

This paper describes and discusses the applications of a logic programming language called Lygon, which is based on linear logic, a logic designed with bounded resources in mind, and contains various features which do not exist in Prolog, whilst maintaining all the features of (pure) Prolog.

### Programming in Lygon: An Overview

• Computer Science
AMAST
• 1996
It appears that Lygon can be considered to be the largest possible first-order linear logic programming language derivable in this way.

### Appeared in SIGACT 1992 Linear Logic

This note presents an intuitive overview oflinear logic, some recent theoretical results, and some interesting applications of linear logic to computer science.

### Some Applications of the Linear Logic Programming Language Lygon

This paper describes and discusses the applications of a logic programming language called Lygon, which is based on linear logic, a logic designed with bounded resources in mind, and contains various features which do not exist in Prolog, whilst maintaining all the features of (pure) Prolog.

## References

SHOWING 1-10 OF 93 REFERENCES

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This thesis augments the proof theoretic framework of linear logic by providing theorems such as permutability, impermutability, and cut-normalization with non-logical theories, and points out that linear logic is not about "Truth"; it is about computation.

### Lectures on linear logic

1. Introduction 2. Sequent calculus for linear logic 3. Some elementary syntactic results 4. The calculus of two implications: a digression 5. Embeddings and approximations 6. Natural deduction

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The aim of the investigations underlying this paper was to see, first, what happens when the exchange rule is removed from the sequent calculus for the linear propositional logic at all, and how to recover the strength of the exchangeRule by means of exponential connectives.

### Linear Lambda-Calculus and Categorial Models Revisited

• Mathematics
CSL
• 1992
In this paper, multiplicative exponential linear logic (MELL) is considered, i.e. the fragment which has multiplicative conjunction or tensor, , linear implication,, and the logical operator, `!', which allows a formula to be used as many times as required (including zero).

### Logic Programming with Focusing Proofs in Linear Logic

It is shown that the syntactic restriction induced by LinLog is not performed at the cost of any expressive power: a mapping from full linear logic to LinLog, preserving focusing proofs, and analogous to the normalization to clausal form for classical logic, is presented.

### The pi-Calculus as a Theory in Linear Logic: Preliminary Results

Using ideas from proof-theory, co-agents are introduced and it is shown that they can specify some testing equivalences for πo, the “propositional” fragment of the π-calculus, which lacks restriction and value passing.

### Linear logic

This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.

### From Petri Nets to Linear Logic

• Computer Science, Philosophy
Math. Struct. Comput. Sci.
• 1989
A systematic correspondence between Petri nets, linear logic theories, and linear categories is established, which sheds new light on the relationships between linear logic and concurrency, and on how both areas are related to category theory.