Modal logic: a semantic perspective

Patrick Blackburn, Johan van Benthem

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Abstract

This chapter discusses the semantic ideas underlying modern modal logic, and in particular, Kripke semantics—or relational semantics. It introduces the basic model theoretic constructions, explores links between modal logic and classical logic, both on models and on frames, and examines the extent to which the key semantic ideas transfer to richer modal logics and languages while maintaining a relatively low computational complexity. The basic modal languages and the graphs over which they are interpreted are discussed. The chapter also introduces the notion of bisimulation, based on which, modal logic as a fragment of first-order logic is characterized. The computability and computational complexity of modal logic is examined. The level of frames and the link between modal and classical logic are explored. Three alternatives to relational semantics––namely, algebraic semantics, neighborhood semantics, and topological semantics are also discussed.
Original languageEnglish
Title of host publicationHandbook of Modal Logic
EditorsPatrick Blackburn, Johan Benthem, Frank Wolter
Number of pages84
PublisherElsevier
Publication date2007
Pages1-84
ISBN (Print)9780444516909
DOIs
Publication statusPublished - 2007
Externally publishedYes
SeriesStudies in Logic and Practical Reasoning
Volume3
ISSN1570-2464

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