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Undefinability of Propositional Quantifiers in the Modal System S4

Silvio Ghilardi and Marek Zawadowski
Studia Logica: An International Journal for Symbolic Logic
Vol. 55, No. 2 (Sep., 1995), pp. 259-271
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015818
Page Count: 13
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Undefinability of Propositional Quantifiers in the Modal System S4
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Abstract

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation from $S4^{2}$ (the propositional modal system S4 enriched with propositional quantifiers) into S4 that preserves provability and reduces to identity for Boolean connectives and □.

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