Temporal Gödel-Gentzen and Girard translations

Mathematical Logic Quarterly 59 (1-2):66-83 (2013)

A theorem for embedding a first-order linear- time temporal logic LTL into its intuitionistic counterpart ILTL is proved using Baratella-Masini's temporal extension of the Gödel-Gentzen negative translation of classical logic into intuitionistic logic. A substructural counterpart LLTL of ILTL is introduced, and a theorem for embedding ILTL into LLTL is proved using a temporal extension of the Girard translation of intuitionistic logic into intuitionistic linear logic. These embedding theorems are proved syntactically based on Gentzen-type sequent calculi.
Keywords MSC  linear‐time temporal logic  sequent calculus  Gödel‐Gentzen negative translation  embedding theorem  03B44  Girard translation
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DOI 10.1002/malq.201100083
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References found in this work BETA

A Proof-Theoretic Investigation of a Logic of Positions.Stefano Baratella & Andrea Masini - 2003 - Annals of Pure and Applied Logic 123 (1-3):135-162.
2-Sequent Calculus: A Proof Theory of Modalities.Andrea Masini - 1992 - Annals of Pure and Applied Logic 58 (3):229-246.
An Approach to Infinitary Temporal Proof Theory.Stefano Baratella & Andrea Masini - 2004 - Archive for Mathematical Logic 43 (8):965-990.
Phase Semantics for Linear-Time Formalism.Norihiro Kamide - 2011 - Logic Journal of the IGPL 19 (1):121-143.

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