Modalities and Multimodalities

This book is intended to provide a philosophically, and historically-based introduction to modal logic, offering to every reader, even those with little specific background, a conceptually clear path through the labyrinth of contemporary modal logic. This is done by emphasizing the notion of multimodality while delineating the formal side of the semantics and proof theory behind the topics in a smooth and gentle pace. The conceptual thread which ties the book together passes through topics like the development of modal logic from standard logic; the syntax and semantics of normal modal systems; the seminal ideas behind completeness, incompleteness, canonicity and finite models; the temporal logics, the logics of knowledge and belief; the generalized syntactical and semantical treatment of multimodalities and finally the pleasures and difficulties of quantified modal logic. – Multimodality is the notion which stands behind the most fertile investigations in modal logic, such as temporal logics, epistemic logics, dynamic logics and so on. By focusing on multimodal logic this book provides common ground for philosophers, logicians, linguists, mathematicians and computer scientists. The book is also designed to provide a repertoire of ideas and techniques for students interested in progressive inquiry in modal and multimodal logic. Each chapter is relatively independent, complemented with exercises and followed by a short bibliographical commentary intended for historically-minded readers. – Table of contents : Preface. - 1. Modal logic and standard logic. - 2. The syntax of normal modal systems. - 3. The semantics of normal modal systems. - 4. Completeness and canonicity. - 5. Incompleteness and finite models. - 6. Temporal logics. - 7. Epistemic logic: knowledge and belief. - 8. Multimodal logics. - 9. Towards quantified modal logic. M.-M. V.