Linear logic

@article{Lincoln1992LinearL,
  title={Linear logic},
  author={Patrick Lincoln},
  journal={SIGACT News},
  year={1992},
  volume={23},
  pages={29-37}
}
  • P. Lincoln
  • Published 1 May 1992
  • Computer Science, Philosophy
  • SIGACT News
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… 

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  • 2004
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Application of linear logic to simulation

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  • Computer Science
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  • 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

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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.

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References

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From Petri nets to linear logic

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?

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.

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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.

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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.

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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.