Glivenko's theorems from an ecumenical perspective
Luiz Carlos Pereira, Victor Barroso-Nascimento, Elaine Pimentel
TL;DR
This paper reexamines Glivenko's theorems, foundational to classical and intuitionistic logic, through the lens of ecumenical logical frameworks, analyzing their extensions and reinterpretations across three systems.
Contribution
It provides a new ecumenical perspective on Glivenko's theorems, exploring their adaptations within three distinct logical systems.
Findings
Analyzes Glivenko's theorems in ecumenical logical systems
Examines extensions and reinterpretations in three systems
Highlights significance within ecumenical 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systems: Prawitz's natural deduction system NE; the system NEK, closely related to one introduced by Krauss in an unpublished manuscript; and the ECI system proposed by Barroso-Nascimento.
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