Bulletin of the Section of Logic Volume 42:1/2 (2013), pp. 43–52 Krystyna Mruczek-Nasieniewska and Marek Nasieniewski A SEGERBERG-LIKE CONNECTION BETWEEN CERTAIN CLASSES OF PROPOSITIONAL LOGICS Abstract In [5, 6] and [7] two classes of logics called K and R were considered. The idea is to treat the negation as “it is possible that not”. Equivalently, such a negation is understood as “it is not necessary” and comes from [2]. The use of the modal language force us to choose some modal logic. In [1] a logic called Z was formulated with the help of S5, the class K is obtained by the use of normal modal logics, while R is obtained by applying the idea to regular logics. In the present paper we will indicate connections between classes K and R, that mainly refer to a Segerberg theorem expressing a connection between normal and regular modal logics. Introduction In [1] the propositional logic Z is formulated. Negation is understood there as “it is possible that not”. Other connectives are treated classically. The logic Z is obtained by using the respective translation of theses of the modal logic S5. In [5, 6] and [7] the same idea was applied to classes of normal and regular modal logics. In this way the classes K and R are respectively obtained. By the definition K⊆R and it is easy to see that K̸ = R. In the case of logics obtained by translation of thesis of normal logics, i.e. in the case of logics from the set K we have (see [5, 6]) a general way of characterizing them syntactically and semantically. Up to our knowledge, for the case of the broader class R only some particular results of this kind are known (see [7]). Thus, a natural question arises, whether there