Modal Logic: A Semantic Perspective
Johan van Benthem, Patrick Blackburn

Abstract:
This is a chapter in the forthcoming "Handbook of Modal Logic",
written as an introduction to the modus operandi of keeping a balance
between expressive power and complexity found in modal languages. With
this theme as a running thread, we survey the basic model theory of
modal logic over both models and frames, as well as basic results on
complexity. Against this background, we provide a uniform look at many
well-known modal formalisms, including epistemic, dynamic, temporal,
and conditional logic.  Finally, although our main emphasis is on
relational models: i.e., graphs, we also discuss the major alternative
semantics.