- October 12, Sonia Marin (University College London)
Ecumenical modal logic
Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion of proof systems for combining logics, called Ecumenical systems by Prawitz and others.
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.
We extended this discussion to alethic K-modalities: using Simpson’s meta-logical characterization, necessity is shown to be independent of the viewer, while possibility can be either intuitionistic or classical.
We furthermore proposed an internal and pure calculus for ecumenical modalities, where every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic.
(joint work with Elaine Pimentel, Luiz Carlos Pereira, and Emerson Sales, partially published in the proceedings of Dali’20 and WoLLiC’21)
Time: 16.00 – 17.30
Location: This is an online meeting. The platform for our meetings is Microsoft Teams. If you would like to join the meeting, please contact the organizers for details.