Short Textbooks in Logic

Neighborhood models form an interesting and rich class of mathematical structures that can be fruitfully studies using modal logic. Originally, neighborhood models were introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). This book is a state-of-the-art introduction to the main techniques and results about neighborhood semantics for modal logic. An central goal of this book is to highlight both the pitfalls and key applications of neighborhood models. -size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">The book discusses a broad range of topics, including standard logical results (e.g. 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 logics of common 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 advanced 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.