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Undefinability of propositional quantifiers in the modal system S4. (English) Zbl 0831.03008
Summary: We show that (contrary to the parallel case of intuitionistic logic) there does not exist a translation from \(\text{S}4^2\) (the propositional modal system S4 enriched with propositional quantifiers) into S4 that preserves provability and reduces to identity for Boolean connectives and \(\square\).

03B45 Modal logic (including the logic of norms)
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
18C10 Theories (e.g., algebraic theories), structure, and semantics
Full Text: DOI
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