Variants into minimal logic of the Kuroda negative translation

TL;DR

This paper introduces eight variants of the Kuroda negative translation that successfully translate classical logic into minimal logic, expanding the applicability of the translation with diverse proof methods.

Contribution

The paper presents new variants of the Kuroda negative translation capable of translating classical logic into minimal logic, along with novel proof techniques for their soundness.

Findings

Eight variants of the Kuroda negative translation into minimal logic

Four different proof methods demonstrated for soundness

Enhanced understanding of translation techniques between classical and minimal logic

Abstract

The Kuroda negative translation translates classical logic only into intuitionistic logic, not into minimal logic. We present eight variants of the Kuroda negative translation that translate classical logic even into minimal logic. The proofs of their soundness theorems are interesting because they illustrate four different methods of proof.