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Tools and concepts are provided here for those wishing to study classes of already existing logics or to design and build new ones.

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It is presented in honor of the fiftieth birthday of Jean-Yves Beziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions identity, rule, quantification and history of logic Leibniz, Peirce, Hilbert. The volume gathers personal recollections about Jean-Yves Beziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Nemeti, Henri Prade.

These essays will be of interest to all students and researchers interested in the nature and future of logic.

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The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition is a very attractive theme which has been going through centuries without evaporating.

Jean-Yves Béziau

Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists of the square from all over the world. It includes papers by leading international researchers, 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.


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The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic. Logiques classiques et non classiques : essai sur les fondements de la logique by Newton C. Handbook of paraconsistency by World Congress on Paraconsistency Book 4 editions published in in English and held by 42 WorldCat member libraries worldwide.

The square of opposition : a general framework for cognition by World Congress on the Square of Opposition Book 8 editions published in in English and held by 39 WorldCat member libraries worldwide It also includes a DVD composed of events from the first world congress on the square of opposition held in June in Montreux, featuring some of the speeches and presentations of the participants, like the professors Pascal Engel, Laurence Horn, Terence Parsons, Jan Wolenski. The movie, which was produced for this event, is a remake of the famous biblical story using the square to display the relations between the main characters.

The book and the vision behind it give logic, conceived as a scientific study of rationality, new unifying power, new perspectives, and new horizons. But while universal algebra is a long recognized field, universal logic has only recently been named as such. This is perhaps because classical logic was until relatively recently taken by many as the "one true logic".