On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2

This is the second, out of two papers, in which we identify all logics between  C1  and  S5  having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following 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 [1], where he proved that all modal logics between  S1  and  S5  have the same theses which does not involve iterated modalities (i.e., the same first-degree theses).