TY - CHAP

T1 - Modal logic

T2 - a semantic perspective

AU - Blackburn, Patrick

AU - van Benthem, Johan

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

U2 - 10.1016/S1570-2464(07)80004-8

DO - 10.1016/S1570-2464(07)80004-8

M3 - Book chapter

AN - SCOPUS:40849096248

SN - 9780444516909

T3 - Studies in Logic and Practical Reasoning

SP - 1

EP - 84

BT - Handbook of Modal Logic

A2 - Blackburn, Patrick

A2 - Benthem, Johan

A2 - Wolter, Frank

PB - Elsevier

ER -