Dialogical Ecumenism

Abstract

Ecumenical logics are systems where two logics can coexist, sharing vocabulary and avoiding collapses between them. The literature has focused mainly on ecumenism between classical and intuitionistic logic, and several calculi of Natural Deduction and Sequents have been proposed. In this paper I contribute to this project with a dialogical ecumenical system. This Game utilizes an extension of the intuitionistic structural rules that permits to handle classical disjunctions and conditionals. I show that this is indeed an ecumenical dialogical system, where classical formulas and intuitionistic formulas can be validated without collapses between them, and provide a philosophical defense of its design.