Semantical investigations on some weak modal logics. Part I

Abstract

In this paper, we examine weak logics similar to S0.5[\Box Φ], where Φ ⊆ S0.5. We also examine their versions (one of which is S0.5rte[\Box Φ]) that are closed under the replacement of tautological equivalents (rte). We have that: S0.5rte[\Box(K), \Box(T)]⊆ S0.9, S0.5rte[\Box(X), \Box(T)] S0.5rte[\Box(K), \Box(T)] ⊆ S1, and in general, if Φ ⊆ E1, then S0.5rte[\Box Φ] ⊆ S2. In the second part, we shall give simplified semantics for these logics, formulated by means of some Kripke-style models. We shall also prove that the logics in question are determined by some classes of these models.