This book offers a state-of-the-art introduction to the basic techniques
and results of neighborhood semantics for modal logic. In addition to
presenting the relevant technical background, it highlights both the
pitfalls and potential uses of neighborhood models - an interesting
class of mathematical structures that were originally introduced to
provide a semantics for weak systems of modal logic (the so-called
non-normal modal logics).
In addition, the book discusses a broad range of topics, including
standard modal logic results (i.e., completeness, decidability and
definability); bisimulations for neighborhood models and other
model-theoretic constructions; comparisons with other semantics for
modal logic (e.g., relational models, topological models, plausibility
models); neighborhood semantics for first-order modal logic,
applications in game theory (coalitional logic and game logic);
applications in epistemic logic (logics of evidence and belief); and
non-normal modal logics with dynamic modalities.
The book can be used as the primary text for seminars on philosophical
logic focused on non-normal modal logics; as a supplemental text for
courses on modal logic, logic in AI, or philosophical logic (either at
the undergraduate or graduate level); or as the primary source for
researchers interested in learning about the uses of neighborhood
semantics in philosophical logic and game theory.
