Section: New Results

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

Participant : Lutz Straßburger.

In this work, 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. This has been published in an special issue of MSCS [12].