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Softness of MALL proof-structures and a correctness criterion with Mix

Abstract.

We show that every MALL proof-structure [9] satisfies the property of softness, originally a categorical notion introduced by Joyal. Furthermore, we show that the notion of hereditary softness precisely captures Girard’s algebraic restriction of the technical condition on proof-structures. Relying on this characterization, we prove a MALL+Mix sequentialization theorem by a proof-theoretical method, using Girard’s notion of jump. Our MALL+Mix correctness criterion subsumes the Danos/Fleury-Retoré criterion [6] for MLL+Mix.

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Correspondence to Masahiro Hamano.

Additional information

This work was supported by Grant-in-Aid for Young Scientists of Ministry of Education, Science and Culture of Japan.

Mathematics Subject Classification (2000):03F52, 03F07, 03F03

Revised version: 9 August 2003

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Hamano, M. Softness of MALL proof-structures and a correctness criterion with Mix. Arch. Math. Logic 43, 751–794 (2004). https://doi.org/10.1007/s00153-004-0222-6

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  • DOI: https://doi.org/10.1007/s00153-004-0222-6

Key words or phrases:

  • Linear Logic
  • Multiplicative Additive Proof-Nets
  • Sequentialization