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The structure of multiplicatives

# The structure of multiplicatives,10.1007/BF01622878,Archive for Mathematical Logic,Vincent Danos,Laurent Regnier

The structure of multiplicatives
Investigating Girard's new propositionnal calculus which aims at a large scale study of computation, we stumble quickly on that question: What is a multiplicative connective? We give here a detailed answer together with our motivations and expectations.
Journal: Archive for Mathematical Logic - Arch. Math. Log. , vol. 28, no. 3, pp. 181-203, 1989
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## Citation Context (85)

• ...A correctness criterion is a test that, given a proof structure N, answers yes when N is a proof net and no when there is no sequentialization of N. The Danos-Regnier switching condition is the most known correctness criterion: let a switch of N be the graph obtained by disconnecting one of the premises of each O-link; then N is a proof net i every switch of N is a tree [3]...

### Stefano Guerrini. A linear algorithm for MLL proof net correctness and sequentialization

• ...Another important new feature of linear logic was the fact that it had a manifestly geometrical aspect to it, which translated in purely diagrammatic characterisations of linear logic proofs and of proof transformations 18...

### Bob Coecke. Quantum picturalism

• ...Due to their “graphical nature”, atomic flows can be seen as relatives of Girard’s proof nets [8, 6] and Buss’ logical flow graphs [5]...

### Alessio Guglielmi, et al. Breaking Paths in Atomic Flows for Classical Logic

• ...For example, the switching criterion [17]: A (well-formed) proof net is the translation of a sequent proof if and only if each of its switchings is a connected and acyclic graph, where a switching of a proof net π is a graph that is obtained from π by removing for each ∨-node and each cont-node one of the two edges connecting it to its children...

### Lutz Straßburger. What Is the Problem with Proof Nets for Classical Logic?

• ...condition for multiplicative proof structures, and how it leads to a proof of sequentialization for MLL − + Mix proof nets [5,6]...

## References (3)

### Linear logic(Citations: 2031)

Journal: Theoretical Computer Science - TCS , vol. 50, no. 1, pp. 1-102, 1987

### Towards a geometry of interaction(Citations: 102)

Conference: Computer Science Logic - CSL , 1989

### Quantifiers in linear logic(Citations: 26)

Published in 1987.
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