Abstract
We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and □.
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Ghilardi, S., Zawadowski, M. Undefinability of propositional quantifiers in the modal system S4. Stud Logica 55, 259–271 (1995). https://doi.org/10.1007/BF01061237
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DOI: https://doi.org/10.1007/BF01061237