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… 

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References

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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).

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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.

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