Normal monomodal logics can simulate all others

This paper shows that non–normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic. Normal monomodal logics can simulate all others 1 This paper is dedicated to our teacher, Wolfgang Rautenberg §1. Introduction. A simulation of a logic Λ by a logic Θ is a translation of the expressions of the language for Λ into the language of Θ such that the consequence relation defined by Λ is reflected under the translation by the consequence relation of Θ. A well–known case is provided by the Gödel translation, which simulate