From Intuitionism to Brouwer's Modal Logic
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...