Modalità e multimodalità. W.A. Carnielli and C. Pizzi. Franco Angeli, Milan, 2001..

Zentralblatt für Mathematik und ihre
Grenzgebiete European Mathematical Society, FIZ Karlsruhe & SpringerVerlag.
Review number 1015.03001 Reviewer Max A.Freund (San José) Carnielli, Walter A.; Pizzi, Claudio. Modality and multimodality. (Modalità e Multimodalità). (Italian) Filosofia. Milano: Franco Angeli. 184 p. EUR 17.56 (2001). [ISBN 8846431022] 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 firstorder 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)]
