Constructive Negations and Paraconsistency [Hardcover]

Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

Reductio ad Absurdum.- Minimal Logic. Preliminary Remarks.- Logic of Classical Refutability.- The Class of Extensions of Minimal Logic.- Adequate Algebraic Semantics for Extensions of Minimal Logic.- Negatively Equivalent Logics.- Absurdity as Unary Operator.- Strong Negation.- Semantical Study of Paraconsistent Nelson's Logic.- N4?-Lattices.- The Class of N4?-Extensions.- Conclusion.

From the reviews:

This book is much more than a collection of papers, everything has been organized very smoothly and it forms a coherent whole about the study of a big class of logics. The presentation of this systematic work in a book is a very good point. It will turn research on paraconsistent logic and negation more accessible. This kind of book can easily be used as a textbook for advanced courses. It is clearly written, gathering a variety of scattered concepts and results. (Jean-Yves Beziau, Studia Logica, Vol. 100, 2012)

This is the first book-length algebraic study of constructive paraconsistent logics. & The monograph under review has a very clear structure. & This monograph is indispensable for anybody interested in the algebraic study of constructive paraconsistent logics in particular, but it is also most rewarding for anyone interested in non-classical logics in general. (Heinrich Wansing, Zentralblatt MATH, Vol. 1161, 2009)

This book presents the authors recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic.lœ