Paraconsistent logics are logics which allow solid deductivereasoning under contradictions by offering a mathematical andphilosophical support to contradictory yet non-trivial theories.Due to its role in models of scientific reasoning and to itsphilosophical implications, as well as to its connections totopics such as abduction, automated reasoning, logic programming,and belief revision, paraconsistency has becoming a fast growingarea.During the III World Congress onParaconsistency (WCP3) held in Toulouse, France, in July, 2003, it became apparent that there is a need for a Handbook covering the most recent results on several aspects of paraconsistent logic, including philosophical debates onparaconsistency and its connections to philosophy of language,argumentation theory, computer science, information theory, andartificial intelligence.This book is a basic tool for those who want to know more about paraconsistent logic, its history and philosophy, the various systems of paraconsistent logic and their applications.The present volume is edited by Jean-Yves Beziau, Walter Carnielli and Dov Gabbay, expert logicians versed in a variety of logics.