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Added by: Sophie NaglerAbstract:
Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.
Comment: Suitable for a specialist class on logical pluralism (if focussed on ecumenical systems) or alethic modalities
Marin, Sonia, et al.. A Pure View of Ecumenical Modalities
2021, In Logic, Language, Information, and Computation. [Online]. Switzerland: Springer International Publishing AG. pp. 388–407
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