Abstract
This Chapter provides a necessary background for studying applications of ND in modal logics. It is a collection of basic facts needed for understanding of the remaining chapters. Section 5.1. introduces propositional languages of multimodal logics and establishes notational conventions. After a presentation of general taxonomy of modal logics in Section 5.2. we characterize them axiomatically in the next section. Section 5.4. introduces relational semantics for different families of modal logics. Except standard Krikpe’s semantics it contains the basics of neighborhood semantics for weak modal logics. Some attention is paid to correspondence theory and some general schemata investigated later. After short section on completeness and decidability matters we finally present various kinds of first-order modal logic in Section 5.6.
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