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Journal of Logic and Computation Advance Access published online on August 10, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp047
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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

From Deep Inference to Proof Nets via Cut Elimination

Lutz Strassburger

INRIA Saclay–Île-de-France, France; École Polytechnique, LIX, Rue de Saclay, 91128 Palaiseau Cedex, France.
E-mail: lutz{at}lix.polytechnique.fr

Received 11 February 2009.


  Abstract

This article shows how derivations in the deep inference system SKS for classical propositional logic can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as ‘eliminating bureaucracy’. Technically, this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS derivations and proof nets, we will see proof graphs representing derivations in ‘Formalism A’.

Keywords: Classical propositional logic; deep inference; proof nets; atomic flows; cut elimination


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