# Locus Solum: From the rules of logic to the logic of rules

@article{Girard2001LocusSF, title={Locus Solum: From the rules of logic to the logic of rules}, author={Jean-Yves Girard}, journal={Mathematical Structures in Computer Science}, year={2001}, volume={11}, pages={301 - 506} }

Go back to An-fang, the Peace Square at An-Fang, the Beginning Place at An-Fang, where all things start (…) An-Fang was near a city, the only living city with a pre-atomic name (…) The headquarters of the People Programmer was at An-Fang, and there the mistake happened: A ruby trembled. Two tourmaline nets failed to rectify the laser beam. A diamond noted the error. Both the error and the correction went into the general computer. Cordwainer SmithThe Dead Lady of Clown Town, 1964.

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## References

SHOWING 1-10 OF 115 REFERENCES

### A new constructive logic: classic logic

- Computer Science, PhilosophyMathematical Structures in Computer Science
- 1991

This work follows the order of discovery of the concepts, which (as expected) starts with the semantics and ends with the syntex; it is hoped that this orthogonal look at the same object will help to apprehend the concepts.

### Linear logic: its syntax and semantics

- Philosophy
- 1995

The first objection to that view is that there are in mathematics, in real life, cases where reaction does not exist or can be neglected : think of a lemma which is forever true, or of a Mr. Soros, who has almost an infinite amount of dollars.

### Geometry of interaction III: accommodating the additives

- Computer Science
- 1995

The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants, as well as a slight modification of familiar sequent calculus in the case of exponential-free conclusions.

### Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory

- Computer Science
- 1981

### PROOF-NETS : THE PARALLEL SYNTAX FOR PROOF-THEORY

- Computer Science
- 1996

The paper is mainly concerned with the extension of proof-nets to additives, for which the best known solution is presented, which is shown to be compatible with quantifiers, and the structural rules of exponentials are also accommodated.

### A Theory of Objects

- Computer ScienceMonographs in Computer Science
- 1996

This book takes a novel approach to the understanding of object-oriented languages by introducing object calculi and developing a theory of objects around them, which covers both the semantics of objects and their typing rules.

### The Mathematics of Sentence Structure

- Computer Science, Linguistics
- 1958

An effective rule (or algorithm) for distinguishing sentences from nonsentences is obtained, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or at least for fragments of such languages.

### Light affine logic

- Computer ScienceProceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226)
- 1998

This paper introduces a slight variation of LLL, by adding full weakening, which is called light affine logic, and reduces the logical system from 21 to just 11 rules, and with simpler, traditional sequents.