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Proof Diagrams for Multiplicative Linear Logic: Syntax and Semantics

  • Matteo AcclavioEmail author
Article

Abstract

Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative 2-dimensional syntax for multiplicative linear logic derivations. The syntax of string diagrams authorizes the definition of a framework where the sequentializability of a term, i.e.  deciding whether the term corresponds to a correct derivation, can be verified in linear time. Furthermore, we can use this syntax to define a denotational semantics for multiplicative linear logic with units by means of equivalence classes of proof diagrams modulo a terminating rewriting.

Keywords

String diagrams Liner logic Proof semantics Monoidal categories 

Mathematics Subject Classification

18D10 03b47 18C50 03B70 

Notes

Acknowledgements

I would like to thank Michele Alberti, Marianna Girlando, Giulio Guerrieri, Paolo Pistone and Lionel Vaux for the fruitful exchanges during the redaction of this work. A special acknowledgment to Yves Guiraud who wrote (and upgraded for the scope) the latex package for string diagrams representations [14] employed in the present manuscript. Thank to reviewers for carefull readings, useful remark and constructive observations.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Inria SaclayFrance
  2. 2.LIX, Ecole PolytechniquePalaiseauFrance

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