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

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

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. Rely...

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Bibliographic Details
Published in:Archive for mathematical logic 2004-08, Vol.43 (6), p.751-794
Main Author: Hamano, Masahiro
Format: Article
Language:eng
Subjects:
Logic
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:0933-5846
1432-0665