Abstract
The discussion about how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system is back in fashion. Indeed, recently Prawitz and others have been discussing the so called ecumenical Systems, where connectives from these logics can co-exist in peace. In Prawitz’ system, 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. In this work we extend Prawitz’ ecumenical idea to alethic \(\mathsf {K}\)-modalities.
This work was partially financed by CNPq and CAPES (Finance Code 001).
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Notes
- 1.
We have presented a proof with \(\mathsf {cut}\) for clarity, remember that \(\mathsf {labEK}\) has the cut-elimination property (see Appendix 4.1).
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Marin, S., Pereira, L.C., Pimentel, E., Sales, E. (2020). Ecumenical Modal Logic. In: Martins, M.A., Sedlár, I. (eds) Dynamic Logic. New Trends and Applications. DaLi 2020. Lecture Notes in Computer Science(), vol 12569. Springer, Cham. https://doi.org/10.1007/978-3-030-65840-3_12
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