2025-02-24: Robert Atkey (MSP)

Thu, 20 Feb 2025 09:32:09 +0000

Robert Atkey (MSP)

Semantic proofs of Cut-elimination for Deep Infererence

Abstract

Deep Inference systems are a kind of proof calculus that allow inference rules to be applied anywhere in a formula. Cut-elimination for these systems is similar to that for Sequent calculi: rules that introduce intermediate formulas can be removed from proofs. Prior proofs of cut-elimination relied on intricate syntactic method. I'll talk about a semantic approach that builds a model of the whole calculus from cut-free proofs, such that every proof constructed in this model can be read back as a cut-free proof. This is a similar technique to the one used in Normalisation by Evaluation (NbE). The technique is very flexible and extends to many extensions of Multiplicative Linear Logic, including BV's self-dual non-commutative before connective, additives, and exponentials.
This is joint work with Wen Kokke and was published at MFPS last year: https://bentnib.org/sem-cut-elim-mfps.html

2025-02-24 15:00:00 UTC
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