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<p>Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are: (1) to consider extensions of intuitionistic linear logic corresponding to each of these systems, and (2) using this common logical basis, to develop a uniform approach to devising and simplifying proof translations. Through this process of “simplification” we recover most of the well-known translations in the literature.</p>

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On Various Translations Between Classical, Intuitionistic, and Linear Logic

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月21日

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  • Gilda Ferreira,
  • Paulo Oliva,
  • Clarence Lewis Protin

摘要

Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are: (1) to consider extensions of intuitionistic linear logic corresponding to each of these systems, and (2) using this common logical basis, to develop a uniform approach to devising and simplifying proof translations. Through this process of “simplification” we recover most of the well-known translations in the literature.