This book brings together contributions from philosophers interested in logic and logicians with a philosophical orientation to address a variety of logical and philosophical topics of current interest, including modal logic, intuitionistic logic, relevant logic, substructural logic, many-value logic, formal semantics, proof theory, and paradox. In particular, it provides the state of the art in three major aspects of current research in philosophical logic: negation, modality, and proof. New frameworks are proposed, e.g., meta sequent, unified inductive logic, generalized Clemens semantics, etc. The variety of topics and issues discussed in this volume is of interest to readers from a wide range of disciplines, such as logic, semantics, and computer science, philosophy, linguistics, artificial intelligence, and beyond.