Glivenko's theorems from an ecumenical perspective
Logic in Computer Science
2026-05-05 v1 Logic
Abstract
In this paper, we revisit Glivenko's theorems, foundational results relating classical and intuitionistic logic, from an ecumenical perspective. We begin by discussing the historical context and significance of Glivenko's original contributions, and then examine their extensions and reinterpretations within ecumenical logical frameworks. Our analysis focuses on three ecumenical systems: Prawitz's natural deduction system NE; the system NEK, closely related to one introduced by Krauss in an unpublished manuscript; and the ECI system proposed by Barroso-Nascimento.
Cite
@article{arxiv.2605.02450,
title = {Glivenko's theorems from an ecumenical perspective},
author = {Luiz Carlos Pereira and Victor Barroso-Nascimento and Elaine Pimentel},
journal= {arXiv preprint arXiv:2605.02450},
year = {2026}
}