On the Relations between S. Kripke's Simplified Semantics for the Systems of Modal Logic and an Algebraical Approach to the Syntax of these Systems and their Semantics

Abstract

The first part of this paper presents the syntax of several most important systems of contemporary modal propositional logic. The presentation is given in two versions: typical and algebraical. The second part deals with the semantics of the systems in question. Here one highlights especially this semantics which is often regarded in texts as philosophically crucial. The paper seeks to give, as it seems, exhaustive metalogical and strictly logical analyses, which show the relations between the models of set theory, which occur in S. Kripke's semantics, and appropriate algebraic models. The formalization of the algebraic theorems which deal with the completeness of the systems under analysis is the central aim of the third part of this paper.