Zentralblatt für Mathematik und ihre Grenzgebiete European Mathematical Society, FIZ Karlsruhe & Springer-Verlag.

This is mainly an introductory textbook on modal logic containing, apart from standard topics, some very important recent material which is not regularly included in other textbooks. Classical material concerning propositional modal logic is presented in the first three chapters, where the reader is introduced to normal modal systems, matrix semantics, possible worlds semantics (Kripke's and Carnapian style), completeness and soundness proofs of different normal modal systems with respect to sets of semantic structures as well as incompleteness results for some other normal systems, finite model property and filtrations.

Exposition of the aforementioned material is followed by one chapter on temporal logic and by another one on epistemic logic. The different logical systems characterized in these chapters and in the three initial ones are then shown, in the sixth chapter, to be just special cases of a more general theory known as multimodality, that is, the theory of logical systems having an arbitrary number of different primitive modal operators in their logical syntax. Multimodality is also taken into account with respect to quantified modal logic, which constitutes the topic of the last chapter. Some of the classical topics regarding first-order quantified modal logic are treated here, such as semantic systems with constant, nested or arbitrary domains, and formal systems of quantified modal logic with or without the Barcan formula. It is important to note that several of the different topics dealt with in the book are accompanied with philosophical remarks. [Max A. Freund (San José)]