The§present book discusses all aspects of paraconsistent logic, including the§latest findings, and its various systems. It includes papers by leading§international researchers, presented at the 5th World Congress on Paraconsistency,§held in Kolkata, India, during 13-17 February 2014, which address the subject§in many different ways: development of abstract paraconsistent systems and new§theorems about them; studies of the connections between these systems and other§non-classical logics, such as non-monotonic, many-valued, relevant,§paracomplete and fuzzy logics; philosophical interpretations of these§constructions; and applications to other sciences, in particular quantum§physics and mathematics. Reasoning with contradictions is the challenge of§paraconsistent logic. The book will be of interest to graduate students and§researchers working in mathematical logic, computer science, philosophical§logic, linguistics and physics.§