Glivenko's theorems from an ecumenical perspective
For logicians, this work offers a comparative analysis of ecumenical systems, but it is incremental as it primarily reviews and reinterprets existing results without introducing new theorems or empirical findings.
The paper revisits Glivenko's theorems linking classical and intuitionistic logic, analyzing their reinterpretation within three ecumenical logical frameworks (NE, NEK, ECI). It provides a historical context and examines extensions of these foundational results.
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systems: Prawitz's natural deduction system NE; the system NEK, closely related to one introduced by Krauss in an unpublished manuscript; and the ECI system proposed by Barroso-Nascimento.