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Journal of Logic and Computation Advance Access published online on August 25, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp044
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Intuitionistic Dual-intuitionistic Nets

Olivier Laurent

Laboratoire de l’Informatique du Parallélisme, ENS Lyon – Université de Lyon, UMR 5668 CNRS ENS-Lyon UCBL INRIA, 46, allée d’Italie, 69364 Lyon cedex 07, France. E-mail: olivier.laurent{at}ens-lyon.fr

Received 15 December 2008.


  Abstract

The intuitionistic sequent calculus (at most one formula on the right-hand side of sequents) comes with a natural dual system: the dual-intuitionistic sequent calculus (at most one formula on the left-hand side). We explain how the duality between these two systems exactly corresponds to the intensively studied duality between call-by-value systems and call-by-name systems for classical logic. Relying on the uniqueness of the computational behaviour underlying these four logics (intuitionistic, dual-intuitionistic, call-by-value classical and call-by-name classical), we define a generic syntax of nets which can be used for any of these logics.

Keywords: Classical logic; intuitionistic logic; computational duality; proof-nets


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