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69Définition, Théorie des Objets et Paraconsistance (Definition, Objects' Theory and Paraconsistance)Theoria 13 (2): 367-379. 1998.Trois sortes de définitions sont présentées et discutées: les définitions nominales, les définitions contextuelles et les définitions amplificatrices. On insiste sur le fait que I’elimination des definitions n’est pas forcement un procede automatique en particulier dans le cas de la logique paraconsistante. Finalement on s’int’resse à la théorie des objets de Meinong et l’on montre comment elle peut êrre considéréecomme une théorie des descripteurs.Three kinds of definitions are presented and di…Read more
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32A sequent calculus for Lukasiewicz's three-valued logic based on Suszko's bivalent semanticsBulletin of the Section of Logic 28 (2): 89-97. 1999.
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61The paraconsistent logic Z. A possible solution to Jaśkowski's problemLogic and Logical Philosophy 15 (2): 99-111. 2006.We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem
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61Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood - An Inquiry into Generalized Logical ValuesStudia Logica 102 (5): 1079-1085. 2014.
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81Classical negation can be expressed by one of its halvesLogic Journal of the IGPL 7 (2): 145-151. 1999.We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extens…Read more
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La Critique Schopenhaurienne de l’Usage de la Logique en MathématiquesO Que Nos Faz Pensar 7 81-88. 1993.
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44Around and Beyond the Square of Opposition (edited book)Springer Verlag. 2012.Jean-Yves Béziau Abstract In this paper I relate the story about the new rising of the square of opposition: how I got in touch with it and started to develop new ideas and to organize world congresses on the topic with subsequent publications.
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Transitivity and ParadoxesThe Baltic International Yearbook of Cognition, Logic and Communication 1. 2005.
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8Preface of this special issue: The Challenge of Combining LogicsLogic Journal of the IGPL 19 (4): 543-543. 2011.
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Nouveaux résultats et nouveau regard sur la logique paraconsistante C1Logique Et Analyse 36 45-58. 1993.
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35Définition, Théorie des Objets et Paraconsistance (Definition, Objects’ Theory and Paraconsistance)Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 13 (2): 367-379. 1998.Trois sortes de définitions sont présentées et discutées: les définitions nominales, les définitions contextuelles et les définitions amplificatrices. On insiste sur le fait que I’elimination des definitions n’est pas forcement un procede automatique en particulier dans le cas de la logique paraconsistante. Finalement on s’int’resse à la théorie des objets de Meinong et l’on montre comment elle peut êrre considéréecomme une théorie des descripteurs.Three kinds of definitions are presented and di…Read more
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230The power of the hexagonLogica Universalis 6 (1-2): 1-43. 2012.The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name problem and it is not clear wha…Read more
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149Sentence, proposition and identitySynthese 154 (3). 2007.In this paper we discuss the distinction between sentence and proposition from the perspective of identity. After criticizing Quine, we discuss how objects of logical languages are constructed, explaining what is Kleene’s congruence—used by Bourbaki with his square—and Paul Halmos’s view about the difference between formulas and objects of the factor structure, the corresponding boolean algebra, in case of classical logic. Finally we present Patrick Suppes’s congruence approach to the notion of …Read more
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49Disentangling Contradiction from Contrariety via IncompatibilityLogica Universalis 10 (2-3): 157-170. 2016.Contradiction is often confused with contrariety. We propose to disentangle contrariety from contradiction using the hexagon of opposition, providing a clear and distinct characterization of three notions: contrariety, contradiction, incompatibility. At the same time, this hexagonal structure describes and explains the relations between them.
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71Idempotent Full Paraconsistent Negations are not AlgebraizableNotre Dame Journal of Formal Logic 39 (1): 135-139. 1998.Using methods of abstract logic and the theory of valuation, we prove that there is no paraconsistent negation obeying the law of double negation and such that $\neg(a\wedge\neg a)$ is a theorem which can be algebraized by a technique similar to the Tarski-Lindenbaum technique.