Studia Logica

, Volume 55, Issue 2, pp 259–271 | Cite as

Undefinability of propositional quantifiers in the modal system S4

  • Silvio Ghilardi
  • Marek Zawadowski


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 □.

1980 Mathematics subject classifications

Primary 03B45, 06E25 Secondary 18C10 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Silvio Ghilardi
    • 1
  • Marek Zawadowski
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2.Instytut MatematykiUniwersytet WarszawskiWarszawaPoland

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