Ecumenism : a new perspective on the relation between logics

RICARDO O. RODRIGUEZ; LUIZ CARLOS PEREIRA

Cerisy-la Salle

Workshop; Beyond Logic Conference; 2017

Universidad de Cerisy-la Salle

In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The proponents of these logics would share conjunction and disjunction, but they would each have their own disjunction and implication with different meanings. The main idea is that these different meanings are given by a semantical framework accepted by both parties. The aim of the present paper is twofold: [1] to prove the normalization theorem for Prawitz´ Ecumenical system and [2] to propose a truth-theoretical semantics for which Prawitz´ system is sound and complete.