On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1

Bulletin of the Section of Logic 46 (1/2) (2017)
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Abstract

This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group:,,, ⌜∨ ☐q⌝,and for any n > 0 a formula ⌜ ∨ ⌝, where has not the atom ‘q’, and and have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities.

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Andrzej Pietruszczak
Nicolaus Copernicus University

References found in this work

New foundations for Lewis modal systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.
Modal Logics in the Vicinity of S.Brian F. Chellas & Krister Segerberg - 1996 - Notre Dame Journal of Formal Logic 37 (1):1-24.

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