Normalization, Soundness and Completeness for the Propositional Fragment of Prawitz’ Ecumenical System

Revista Portuguesa de Filosofia 73 (3-4):1153-1168 (2017)

Ricardo Oscar Rodriguez
Universidad de Buenos Aires (UBA)
In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. The aim of the present paper is [1] to prove the normalization theorem for the propositional fragment NEp of Prawitz’ ecumenical system, and [2] to show that NEp is sound and complete with respect to a Kripke-style semantics for the language of NEp.
Keywords classical logic,  ecumenical logic,  intuitionistic logic
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DOI 10.17990/RPF/2017_73_3_1153
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