•  408
    Logica Universalis: Towards a General Theory of Logic (edited book)
    Birkhäuser Basel. 2007.
    Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there …Read more
  •  41
    CONCEPTUAL CLARIFICATIONS Tributes to Patrick Suppes (1922-2014) (edited book)
    College Publication. 2015.
    This is a volume containing papers honoring Patrick Suppes (1922-2014). All contributors have worked directly with Suppes or/and with his ideas. The book also contains one of the last papers by Suppes (co-authored by two of his collaborators). The work of Suppes touches many different areas, ranging from meteorology to physics, through logic, mathematics, psychology, neuroscience, education, painting, but he was first of all and above all a philosopher, always questioning, but not in vain. There…Read more
  •  42
    A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist …Read more
  •  67
    New Directions in Paraconsistent Logic (edited book)
    Springer, India. 2015.
    The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. 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 …Read more
  •  49
    MANY 1 - A Transversal Imaginative Journey across the Realm of Mathematics
    Journal of the Indian Council of Philosophical Research 34 (2): 259-287. 2017.
    We discuss the many aspects and qualities of the number one: the different ways it can be represented, the different things it may represent. We discuss the ordinal and cardinal natures of the one, its algebraic behaviour as a neutral element and finally its role as a truth-value in logic.
  •  70
    The paraconsistent logic Z. A possible solution to Jaśkowski's problem
    Logic 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
  •  69
    Preface
    Logica Universalis 2 (1): 1-1. 2008.
  •  51
    Sequents and bivaluations
    Logique Et Analyse 44 (176): 373-394. 2001.
  •  32
    Preface
    Logica Universalis 1 (1): 1-2. 2007.
  •  89
    Classical negation can be expressed by one of its halves
    Logic 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
  •  52
    Around and Beyond the Square of Opposition (edited book)
    with Dale Jacquette
    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.
  •  48
    The logic of confusion is a way to..
  • Transitivity and Paradoxes
    The Baltic International Yearbook of Cognition, Logic and Communication 1. 2005.
  •  133
    Identity, Structure and Logic
    Bulletin of the Section of Logic 25 89-9. 1996.
  •  36
    Définition, 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
  • Contemporary Brazilian research in logic part II
    with Arthur Buchsbaum, Tarcisio Pequeno, A. General, and Newton Ca da Costa
    Logique Et Analyse 40 3. 1997.
  •  244
    The power of the hexagon
    Logica 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
  •  60
    Preface: Is logic universal? (review)
    Logica Universalis 4 (2): 161-162. 2010.
  •  149
    Sentence, proposition and identity
    Synthese 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
  •  59
    Disentangling Contradiction from Contrariety via Incompatibility
    Logica 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.