Polytopological models equipped with closure or derivative operators, subject to regularity conditions, are sound and strongly complete for constructive, intuitionistic, and Gödel-Dummett variants of K4 and S4.
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Polytopological Semantics for Intuitionistic Modal Logics
Polytopological models equipped with closure or derivative operators, subject to regularity conditions, are sound and strongly complete for constructive, intuitionistic, and Gödel-Dummett variants of K4 and S4.