Geodesic
From Intuitionism to Brouwer's Modal Logic
Bulletin of the Section of Logic, Tome 49 (2020) no. 4, pp. 343-358

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We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.
Keywords: intuitionistic logic, Kripke frames, Brouwer's modal logic 
Kostrzycka, Zofia. From Intuitionism to Brouwer's Modal Logic. Bulletin of the Section of Logic, Tome 49 (2020) no. 4, pp. 343-358. http://geodesic.mathdoc.fr/item/BSL_2020_49_4_a1/
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