# Linear logic

@article{Lincoln1992LinearL, title={Linear logic}, author={Patrick Lincoln}, journal={SIGACT News}, year={1992}, volume={23}, pages={29-37} }

Linear logic was introduced by Girard in 1987 [11] . Since then many results have supported Girard' s statement, "Linear logic is a resource conscious logic," and related slogans . Increasingly, computer scientists have come to recognize linear logic as an expressive and powerful logic with connection s to a variety of topics in computer science . This column presents a.n intuitive overview of linear logic, some recent theoretical results, an d summarizes several applications of linear logic to…

## 3,219 Citations

### A brief guide to linear logic

- PhilosophyBull. EATCS
- 1990

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…

### Natural Deduction for Linear Logic

- Philosophy

Linear logic, proposed by Girard [Gir1987], has shown to be extremely valuable for the formalization of typical problems in Computer Science. This is due to the fact that, in linear logic, sentences…

### Proof strategies in linear logic

- Computer ScienceJournal of Automated Reasoning
- 2004

Methods for automated theorem proving in propositional linear logic are investigated, both the “bottom-up” (tableaux) and "top-down" (resolution) proof strategies are analyzed.

### Proof Strategies in Linear Logic Proof Strategies in Linear Logic

- Computer Science
- 1994

Methods for automated theorem proving in propositional linear logic are investigated and various modiications of sequent rules and eecient search strategies are presented along with the experiments performed with the implemented theorem provers.

### Application of linear logic to simulation

- Computer ScienceDefense, Security, and Sensing
- 1998

This paper discuses the application of linear logic to simulation and proposes a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups.

### From Petri nets to linear logic

- Computer Science, PhilosophyMathematical Structures in Computer Science
- 1991

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.

### The syntax of Linear logic

- Computer Science
- 2012

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.

### Linear Objects in a Logic Processes with Built-in Inheritance

- Computer ScienceICLP
- 1990

This exciting advance in logic provides new ways of embracing aspects of computation directly in a rich logical framework and provides new insights into the many computational systems built on those two logics.

### Introduction to linear logic and ludics, part I

- Computer ScienceArXiv
- 2005

A survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, are offered, which covers an introduction to the connectives and proof rules oflinear logic, to its decidability properties, and to its models.

### Programming in Lygon: An Overview

- Computer ScienceAMAST
- 1996

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

## References

SHOWING 1-10 OF 36 REFERENCES

### A brief guide to linear logic

- PhilosophyBull. EATCS
- 1990

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…

### From Petri nets to linear logic

- Computer Science, PhilosophyMathematical Structures in Computer Science
- 1991

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.

### Is there a use for linear logic?

- Computer SciencePEPM '91
- 1991

This paper defines a sequence of languages based on linear logic that span the gap between theory and practice that can derive information about sharing in a linear type system.

### Logic programming in a fragment of intuitionistic linear logic

- Computer Science[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
- 1991

The intuitionistic notion of context is refined by using a fragment of J.-Y. Girard's (Theor. Comput. Sci., vol.50, p.1-102, 1987) linear logic that includes additive and multiplicative conjunction,…

### Horn programming in linear logic is NP-complete

- Computer Science[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science
- 1992

The question of developing a computational interpretation of J. Girard's (1987) linear logic and obtaining efficient decision algorithms for this logic, based on the bottom-up approach, is addressed and it is proved that this fragment is NP-complete.

### Lilac: a functional programming language based on linear logic

- Computer ScienceJournal of Functional Programming
- 1994

A type reconstruction algorithm is given for Abramsky's term assignment for Intuitionistic Linear Logic as the basis of a functional programming language where the programmer must embed explicitly the resource and control information of an algorithm.

### A linear semantics for allowed logic programs

- Computer Science, Philosophy[1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science
- 1990

It is proven that the computational notion of success of an allowed query Q for an allowed program P corresponds to the Provability of an instantiation of Q in the linear completion of P, and the notion of failure to the provability of the (linear) negation of QIn the linearpletion of P.

### There's No Substitute for Linear Logic

- Linguistics
- 1991

An alternative syntax is proposed, that has striking parallels to Moggi's language for monads, that eliminates some terms look like the identity that should not, and vice versa; the new syntax eliminates this awkwardness.

### Bounded Linear Logic: A Modular Approach to Polynomial-Time Computability

- Computer ScienceTheor. Comput. Sci.
- 1992