Undefinability of propositional quantifiers in the modal system S

Studia Logica 55 (2):259 - 271 (1995)
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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DOI 10.1007/BF01061237
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Logics Containing K4. Part II.Kit Fine - 1985 - Journal of Symbolic Logic 50 (3):619-651.
Logics Containing K4. Part I.Kit Fine - 1974 - Journal of Symbolic Logic 39 (1):31-42.

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