Paraconsistency -- Introduction -- Part I Logic -- 1. Making Sense of paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic: Koji Tanaka -- 2. On Discourse Addressed by Infidel Logicians: Walter Carnielli and Marcelo E. Coniglio -- 3. Information, Negation and paraconsistency: Edwin D. Mares -- 4. Noisy vs. merely equivocal logics: Patrick Allo -- 5. Assertion, Denial and Non-Classical Theories: Greg Restall -- 6. New Arguments for adaptive Logics as Unifying Frame for the Defeasible Handling of Inconsistency: Diederik Batens -- 7. Consequence as preservation: Some Refinements: Bryson Brown -- 8. On Modal Logics defining Jaskowski's D2-consequence: Marek Nasieniewski and Andrzej Pietruszczak -- 9. FDE: A Logic of Clutters: R.E. Jennings and Y. Chen -- 10. A paraconsistent and Substructural Conditional Logic -- Part II Applications: Francesco Paoli -- 11. An approach to Human-level commonsense reasoning: Michael L. Anderson, Walid Gomaa, John Grant and Don Perlis -- 12. Distribution in the Logic of Meaning Containment and in Quantum Mechanics: Ross T. Brady and Andrea Meinander -- 13. Wittgenstein on Incompleteness Makes Paraconsistent sense: Francesco Berto -- 14. Pluralism and "Bad" Mathematical theories: Challenging our prejudices: Michele Friend -- 15. Arithmetic Starred: Chris Mortensen -- 16. Notes on inconsistent set theory: Zach Weber -- 17. Sorting out the Sorites: David Ripley -- 18. Are the sorites and liar paradox of a Kind?: Dominic Hyde -- 19. Vague Inclosures: Graham Priest.-.

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation.   The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.