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 □.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Fine K., ‘Logics containing K4, Part I’,Journal of Symbolic Logic 34 31–42 (1974);
Fine K., ‘Logics containing K4, Part II’,Journal of Symbolic Logic 50 619–651 (1985);
Ghilardi S., ‘An algebraic theory of normal forms’,Annals of Pure and Applied Logic 71 (3 189–245 (1995);
Ghilardi S., Zawadowski M., ‘A sheaf representation and duality for finitely presented Heyting algebras’, to appear inJournal of Symbolic Logic;
Hughes G.E., Cresswell M.J.,A companion to modal logic, Methuen, London (1984);
McLane S.,Categories for the working mathematician, Springer, Berlin (1971);
Pitts A.M., ‘On an interpretation of second order quantification in first order intuitionistic propositional logic’,Journal of Symbolic Logic 57, 1 33–52 (1992);
Shavrukov V.Yu.,Subalgebras of diagonalizable algebras of theories containing arithmetic, Dissertationes Mathematicae, CCCXXIII, Polska Akademia Nauk, Instytut Matematyczny, Warsaw (1993).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01061237