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Keywords:

  • Gödel-Gentzen negative translation;
  • Girard translation;
  • embedding theorem;
  • linear-time temporal logic;
  • sequent calculus;
  • MSC (2010);
  • 03B44

Abstract

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.