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

Andrzej Pietruszczak

doi:10.18778/0138-0680.46.1.2.09

Authors

Andrzej Pietruszczak Nicolaus Copernicus University in Toruń, Department of Logic, ul. Moniuszki 16, 87–100 Toruń, Poland

DOI:

https://doi.org/10.18778/0138-0680.46.1.2.09

Keywords:

first-degree theses of modal logics, theses without iterated modalities, Pollack’s theory of Basic Modal Logic, basic theories for modal logics between C1 and S5

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: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (alt_n)⌝, where (T) has not the atom ‘q’, and(T) and (alt_n) 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 (i.e., the same first-degree theses).

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