Abstract

The aim of this paper is to investigate the expressibility of classical propositional monomodal logics. To this end, a notion of embedding of one logic into another is introduced, which is a translation preserving theoremhood. Each translation trF is induced by a formula F of one variable p; it respects boolean connectives and translates a formula of a form □A into F). This notion enables to measure the expressibility of a logic by a number of logics embeddable into it. This measure is calculated here for a large family of modal logics including K, K4, KB, K5, GL, GL.3, T, S4, B, S5, Grz, Grz.3, and provability logics. It is also shown that some of these logics are not embeddable into some others