Abstract

There are two approaches to logic, semantic and axiomatic. In 1910's, when C.I. Lewis wrote his first papers on modal logic, he adopted the axiomatic approach, the sole one apparently available. The situation remained identical during about forty years, until Kanger, Kripke, and Hintikka discovered the so-called possible worlds semantics. A new flourishing “paradigmatic” period began, and it became possible to define soundness and completeness in modal logic. Unfortunately , however, this period did not go on for more than twenty years. “Strange” systems appeared, which were impossible to be defined semantically and so soundness and completeness were lost again