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Deep inference and expansion trees for second-order multiplicative linear logic

Published online by Cambridge University Press:  02 November 2018

LUTZ STRAßBURGER
LUTZ STRAßBURGER*
Affiliation:
Inria Saclay – Île-de-France, 1 rue Honoré d’Estienne d’Orves, Bâtiment Alan Turing, Campus de l’École Polytechnique, 91120 Palaiseau, France Email: lutz@lix.polytechnique.fr
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Abstract

In this paper, we introduce the notion of expansion tree for linear logic. As in Miller's original work, we have a shallow reading of an expansion tree that corresponds to the conclusion of the proof, and a deep reading which is a formula that can be proved by propositional rules. We focus our attention to MLL2, and we also present a deep inference system for that logic. This allows us to give a syntactic proof to a version of Herbrand's theorem.

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