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Profile: Jean-Yves Beziau (Universidade Federal do Rio de Janeiro)
  1. Newton C. A. da Costa, Jean-Yves Béziau & Otávio Bueno (1999). Professor Newton CA da Costa Awarded Nicholas Copernicus University Medal of Merit. Logic and Logical Philosophy 7:7-10.
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  2.  10
    Jean-Yves Beziau (2016). Disentangling Contradiction From Contrariety Via Incompatibility. Logica Universalis 10 (2-3):157-170.
    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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  3.  32
    Jean-Yves Béziau (2011). A New Four-Valued Approach to Modal Logic. Logique Et Analyse 54 (213):109.
  4.  7
    Jean-Yves Beziau & Raffaela Giovagnoli (2016). The Vatican Square. Logica Universalis 10 (2-3):135-141.
    After explaining the interdisciplinary aspect of the series of events organized around the square of opposition since 2007, we discuss papers related to the 4th World Congress on the Square of Opposition which was organized in the Vatican at the Pontifical Lateran University in 2014. We distinguish three categories of work: those dealing with the evolution and development of the theory of opposition, those using the square as a metalogical tool to give a better understanding of various systems of logic (...)
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  5.  92
    Jean-Yves Beziau (2015). The Relativity and Universality of Logic. Synthese 192 (7):1939-1954.
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  6.  64
    Jean-Yves Béziau (2012). The Power of the Hexagon. Logica Universalis 6 (1-2):1-43.
    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 (...)
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  7. Jean-Yves Beziau (2008). What is “Formal Logic”? Proceedings of the Xxii World Congress of Philosophy 13:9-22.
    “Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal (...)
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  8.  16
    Jean-Yves Béziau & Dale Jacquette (eds.) (2012). Around and Beyond the Square of Opposition. Springer Science & Business Media.
    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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  9.  51
    Jean-Yves Beziau, Non Truth-Functional Many-Valuedness.
    Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.
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  10.  52
    Jean-Yves Beziau (1999). Classical Negation Can Be Expressed by One of its Halves. Logic Journal of the Igpl 7 (2):145-151.
    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 extension of (...)
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  11. Newton da Costa, Jean-Yves Béziau & Otávio Bueno (1996). Malinowski and Suszko on Many-Valued Logics: On the Reduction of Many-Valuedness to Two-Valuedness. Modern Logic 6 (1):272--299.
  12.  36
    Arthur Buchsbaum & Jean-Yves Beziau, Introduction of Implication and Generalization in Axiomatic Calculi.
    of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.
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  13. Newton Ca da Costa & Jean-Yves Béziau (1994). Théorie de la Valuation. Logique Et Analyse 146 (146):95-117.
     
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  14.  14
    Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno (1995). Paraconsistent Logic in a Historical Perspective. Logique Et Analyse 38:111-125.
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  15.  21
    Jean-Yves Béziau (2006). 13 Questions About Universal Logic. Bulletin of the Section of Logic 35 (2/3):133-150.
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  16.  14
    Jean-Yves Béziau (2001). Sequents and Bivaluations. Logique Et Analyse 44 (176):373-394.
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  17.  2
    Jean-Yves Béziau (2011). Preface of This Special Issue: The Challenge of Combining Logics. Logic Journal of the IGPL 19 (4):543-543.
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  18.  12
    Jean-Yves Béziau (1999). A Sequent Calculus for Lukasiewicz's Three-Valued Logic Based on Suszko's Bivalent Semantics. Bulletin of the Section of Logic 28 (2):89-97.
  19.  87
    Jean-Yves Beziau (1996). Identity, Structure and Logic. Bulletin of the Section of Logic 25:89-9.
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  20.  13
    Jean-Yves Béziau (2006). The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem. Logic and Logical Philosophy 15 (2):99-111.
    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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  21.  11
    Jean-Yves Béziau (2003). Logic May Be Simple. Logic, Congruence and Algebra. Logic and Logical Philosophy 5:129-147.
    This paper is an attempt to clear some philosophical questions about the nature of logic by setting up a mathematical framework. The notion of congruence in logic is defined. A logical structure in which there is no non-trivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLane-Curry’s theorem and a discussion about Curry’s algebras). We also examine how these concepts are related to such notions as (...)
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  22.  71
    Jean-Yves Béziau (2007). Sentence, Proposition and Identity. Synthese 154 (3):371 - 382.
    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 proposition, according to which a whole hierarchy of congruences (...)
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  23.  21
    Jean-Yves Beziau & Stephen Read (2015). Square of Opposition: A Diagram and a Theory in Historical Perspective. History and Philosophy of Logic 35 (4):315-316.
  24. Newton da Costa, Otávio Bueno & Jean-Yves Béziau (1995). What is Semantics? A Brief Note on a Huge Question. Sorites 3:43-47.
    After mentioning the cogent connection between pure semantics and the particular set theoretical framework in which it is formulated, some issues regarding the conceptual status of semantics itself, as well as its relationship to logic, are concisely raised.
     
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  25.  9
    Jean-Yves Béziau & Marcelo E. Coniglio (2011). To Distribute or Not to Distribute? Logic Journal of the IGPL 19 (4):466-583.
    In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...)
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  26.  11
    Buchsbaum Arthur & Jean-Yves Béziau, Non Truth-Functional Many-Valuedness.
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  27.  25
    Jean-Yves Béziau, Alexandre Costa Leite & A. Facchini, Aspects of Universal Logic.
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  28.  41
    Jean-Yves Béziau (2006). Many-Valued and Kripke Semantics. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer 89--101.
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  29.  10
    Jean-Yves Béziau (1994). Théorie Legislative de la Négation Pure. Logique Et Analyse 147 (148):209-225.
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  30.  2
    Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno (1995). Aspects of Paraconsistent Logic. Logic Journal of the Igpl 3 (4):597-614.
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  31.  13
    Jean-Yves Beziau (2014). Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood - An Inquiry Into Generalized Logical Values. Studia Logica 102 (5):1079-1085.
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  32.  14
    Jean-Yves Béziau (2012). The New Rising of the Square of Opposition. In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser 3--19.
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  33.  18
    Jean-Yves Beziau (2005). From Consequence Operator to Universal Logic: A Survey of General Abstract Logic. In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlog 3--17.
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  34.  40
    Jean-Yves Beziau (2010). Preface: Is Logic Universal? [REVIEW] Logica Universalis 4 (2):161-162.
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  35.  28
    Jean-Yves Beziau (2012). BookReview. Studia Logica 100 (3):653-657.
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  36.  49
    Décio Krause & Jean-Yves Béziau (1997). Relativizations of the Principle of Identity. Logic Journal of the IGPL 5 (3):17-29.
    We discuss some logico-mathematical systems which deviate from classical logic and mathematics with respect to the concept of identity. In the first part of the paper we present very general formulations of the principle of identity and show how they can be ‘relativized’ to objects and to properties. Then, as an application, we study the particular cases of physics and logic . In the last part of the paper, we discuss the alphabar logics, that is, those logical systems which violate (...)
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  37.  46
    Jean-Yves Béziau & Décio Krause (2007). New Trends in the Foundations of Science. Synthese 154 (3):345 - 347.
  38.  28
    Newton C. A. da Costa & Jean-Yves Béziau (1998). Définition, Théorie des Objets et Paraconsistance (Definition, Objects' Theory and Paraconsistance). Theoria 13 (2):367-379.
    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 discussed: nominal definitions, contextual definitions, amplifying definitions. It is emphasized that (...)
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  39.  8
    Newton Ca da Costa & Jean-Yves Béziau (1993). Carnot's Logic. Bulletin of the Section of Logic 22 (3):98-105.
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  40.  38
    Jean-Yves Beziau, Combining Conjunction with Disjunction.
    In this paper we address some central problems of combination of logics through the study of a very simple but highly informative case, the combination of the logics of disjunction and conjunction. At first it seems that it would be very easy to combine such logics, but the following problem arises: if we combine these logics in a straightforward way, distributivity holds. On the other hand, distributivity does not arise if we use the usual notion of extension between consequence relations. (...)
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  41.  9
    Jean-Yves Beziau (2014). Preface: Scope of Logic Theorems In Memoriam Adolf Lindenbaum. Logica Universalis 8 (3-4):283-284.
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  42.  32
    Jean-Yves Beziau, The Logic of Confusion.
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  43.  17
    Jean-Yves Béziau (2011). Truth as a Mathematical Object. Principia 14 (1):31-46.
    Neste artigo, discutimos em que sentido a verdade é considerada como um objeto matemático na lógica proposicional. Depois de esclarecer como este conceito é usado na lógica clássica, através das noções de tabela de verdade, de função de verdade, de bivaloração, examinamos algumas generalizações desse conceito nas lógicas não clássicas: semânticas matriciais multi-valoradas com três ou quatro valores, semântica bivalente não veritativa, semânticas dos mundos possiveis de Kripke. DOI:10.5007/1808-1711.2010v14n1p31.
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  44.  15
    Buchsbaum Arthur & Jean-Yves Béziau, Introduction of Implication and Generalization in Axiomatic Calculi.
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  45.  28
    Jean-Yves Béziau (1998). Idempotent Full Paraconsistent Negations Are Not Algebraizable. Notre Dame Journal of Formal Logic 39 (1):135-139.
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  46.  31
    Jean-Yves Beziau, Introduction of Implication and Generalization in Axiomatic Calculi.
    of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.
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  47.  1
    Newton C. A. da Costa, Jean-Yves Béziau & Otávio A. S. Bueno (1995). Aspects of Paraconsistent Logic. Logic Journal of the IGPL 3 (4):597-614.
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  48. Jean-Yves Béziau (2001). From Paraconsistent Logic to Universal Logic. Sorites 12:5-32.
    For several years I have been developing a general theory of logics that I have called Universal Logic. In this article I will try to describe how I was led to this theory and how I have progressively conceived it, starting my researches about ten years ago in Paris in paraconsistent logic and the broadening my horizons, pursuing my researches in Brazil, Poland and the USA.
     
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  49.  10
    Jean-Yves Béziau & Alexandre Costa-Leite (2012). Foreword. Journal of Applied Non-Classical Logics 22 (1-2):1-1.
    (2012). Foreword. Journal of Applied Non-Classical Logics: Vol. 22, SPECIAL ISSUE 1: Uses of Non-Classical Logic: Foundational Issues; SPECIAL ISSUE 2: Formal Models of Norm Change, pp. 1-1. doi: 10.1080/11663081.2012.682433.
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  50.  8
    Jean-Yves Béziau (2003). Quine on Identity. Principia 7 (1-2):1-15.
    In a first section, we discuss Quine’s claim according to which identity\nis a logical notion. We point out that Quine mixes up various types\nof identities: trivial (or diagonal) identity, Leibniz identity,\netc.; and this leads him to commit several mistakes. In a second\nsection, we review Quine’s criticisms to various philosophers (Wittgenstein,\nWhitehead, Leibniz, etc.), who ac-cording to him made confusion between\nnames and objects in defining iden-tity. We show that in fact only\nKorzybski can be accused of such confusion. In a third section, we\nanalyze (...)
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