Logical Consequence in Modal Logic: Alternative Semantic Systems for Normal Modal Logics

Abstract

This chapter discusses the alternative semantic systems of normal modal logics. The novelty of the approach discussed in the chapter is twofold: first, to treat modal logics as consequence systems rather than logistic systems; and second, to view modal logics as extensions of non-modal ones. This second feature leads to the realization that certain usually desired properties of modal logics (e.g., compactness, weak completeness, and strong completeness) are at least in part determined by properties of the semantic systems of their non-modal “base.”