108 found
Order:
See also
Jean-Yves Beziau
Universidade Federal do Rio de Janeiro
  1. The Power of the Hexagon.Jean-Yves Béziau - 2012 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   24 citations  
  2.  28
    Logic and Religion.Jean-Yves Beziau & Ricardo Silvestre - 2017 - Logica Universalis 11 (1):1-12.
    We first start by describing the happening of the 1st World Congress on Logic and Religion. We then explain the motivation for developing the interaction between logic and religion. In a third part we discuss some papers presented at this event published in the present special issue.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3.  45
    Is the Principle of Contradiction a Consequence of $$X^{2}=X$$ X 2 = X?Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):55-81.
    According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  4.  15
    Paraconsistent Logic From a Modal Viewpoint.Jean-Yves Béziau - 2005 - Journal of Applied Logic 3 (1):7-14.
  5.  12
    New Directions in Paraconsistent Logic.Jean-Yves Beziau (ed.) - 2015 - New Delhi, India: Springer, India.
    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 constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  6.  30
    Universal Logic: Evolution of a Project.Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):1-8.
    We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created for promoting the universal logic project, with a school, a congress, a secret speaker and a contest. We explain how the contest has evolved into a session of logic prizes.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  7.  48
    A New Four-Valued Approach to Modal Logic.Jean-Yves Béziau - 2011 - Logique Et Analyse 54 (213):109.
  8.  19
    Trivial Dialetheism and the Logic of Paradox.Jean-Yves Beziau - 2016 - Logic and Logical Philosophy 25 (1):51-56.
    In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  24
    Disentangling Contradiction From Contrariety Via Incompatibility.Jean-Yves Beziau - 2016 - 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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  10.  33
    The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem.Jean-Yves Béziau - 2006 - 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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  11.  68
    Classical Negation Can Be Expressed by One of its Halves.Jean-Yves Beziau - 1999 - 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  12. The Relativity and Universality of Logic.Jean-Yves Beziau - 2015 - Synthese 192 (7):1939-1954.
    After recalling the distinction between logic as reasoning and logic as theory of reasoning, we first examine the question of relativity of logic arguing that the theory of reasoning as any other science is relative. In a second part we discuss the emergence of universal logic as a general theory of logical systems, making comparison with universal algebra and the project of mathesis universalis. In a third part we critically present three lines of research connected to universal logic: logical pluralism, (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  13.  11
    Self-Extensional Three-Valued Paraconsistent Logics Have No Implications.Arnon Avron & Jean-Yves Beziau - 2017 - Logic Journal of the IGPL 25 (2):183-194.
    A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  14.  35
    The Vatican Square.Jean-Yves Beziau & Raffaela Giovagnoli - 2016 - 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  15.  25
    From Consequence Operator to Universal Logic: A Survey of General Abstract Logic.Jean-Yves Beziau - 2005 - In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlog. pp. 3--17.
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  16. New Dimensions of the Square of Opposition.Jean-Yves Beziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  35
    Preface.Jean-Yves Beziau & Gillman Payette - 2008 - Logica Universalis 2 (1):1-1.
  18.  8
    Logic Prizes Et Cætera.Jean-Yves Beziau - 2018 - Logica Universalis 12 (3-4):271-296.
    I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG in Vichy in June 2018 with the participation of 9 logic (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  19.  26
    Sequents and Bivaluations.Jean-Yves Béziau - 2001 - Logique Et Analyse 44 (176):373-394.
  20.  29
    Square of Opposition: A Diagram and a Theory in Historical Perspective.Jean-Yves Beziau & Stephen Read - 2014 - History and Philosophy of Logic 35 (4):315-316.
  21.  22
    The Square of Opposition: A Cornerstone of Thought.Jean-Yves Beziau & Gianfranco Basti (eds.) - 2016 - Basel, Switzerland: Birkhäuser.
    This is a collection of new investigations and discoveries on the theory of opposition (square, hexagon, octagon, polyhedra of opposition) by the best specialists from all over the world. The papers range from historical considerations to new mathematical developments of the theory of opposition including applications to theology, theory of argumentation and metalogic.
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  22.  77
    Non Truth-Functional Many-Valuedness.Jean-Yves Beziau - manuscript
    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.
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  23.  34
    13 Questions About Universal Logic.Jean-Yves Béziau - 2006 - Bulletin of the Section of Logic 35 (2/3):133-150.
  24.  39
    Logic May Be Simple. Logic, Congruence and Algebra.Jean-Yves Béziau - 1997 - 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  25.  23
    The New Rising of the Square of Opposition.Jean-Yves Béziau - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 3--19.
  26.  53
    Truth as a Mathematical Object.Jean-Yves Béziau - 2010 - Principia: An International Journal of Epistemology 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.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  27.  1
    A Chromatic Hexagon of Psychic Dispositions.Jean-Yves Beziau - 2017 - In Marcos Silva (ed.), How Colours Matter to Philosophy. Springer.
    Colors can be understood in a logical way through the theory of opposition. This approach was recently developed by Dany Jaspers, giving a new and fresh approach to the theory of colors, in particular with a hexagon of colors close to Goethe’s intuitions. On the other hand colors can also be used at a metalogical level to understand and characterize the relations of opposition, including the relations of opposition between colors themselves. In this paper we furthermore develop a theory of (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  28. What is Semantics? A Brief Note on a Huge Question.Newton da Costa, Otávio Bueno & Jean-Yves Béziau - 1995 - 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.
     
    Export citation  
     
    Bookmark   4 citations  
  29.  14
    Aspects of Paraconsistent Logic.Newton C. A. da Costa, Jean-Yves Béziau & Otávio A. S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  30.  17
    Semantic Computations of Truth Based on Associations Already Learned.Patrick Suppes & Jean-Yves Béziau - 2004 - Journal of Applied Logic 2 (4):457-467.
  31.  10
    Aspects of Paraconsistent Logic.Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  32.  47
    Idempotent Full Paraconsistent Negations Are Not Algebraizable.Jean-Yves Béziau - 1998 - Notre Dame Journal of Formal Logic 39 (1):135-139.
  33.  19
    A Sequent Calculus for Lukasiewicz's Three-Valued Logic Based on Suszko's Bivalent Semantics.Jean-Yves Béziau - 1999 - Bulletin of the Section of Logic 28 (2):89-97.
  34.  21
    Paraconsistent Logic in a Historical Perspective.Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno - 1995 - Logique Et Analyse 38:111-125.
  35.  20
    Around and Beyond the Square of Opposition.Jean-Yves Béziau & Dale Jacquette (eds.) - 2012 - Springer Verlag.
    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.
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  36.  19
    Non Truth-Functional Many-Valuedness.Buchsbaum Arthur & Jean-Yves Béziau - unknown
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  37.  41
    BookReview.Jean-Yves Beziau - 2012 - Studia Logica 100 (3):653-657.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  38. What is “Formal Logic”?Jean-Yves Béziau - 2008 - 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  39.  50
    Introduction of Implication and Generalization in Axiomatic Calculi.Arthur Buchsbaum & Jean-Yves Beziau - unknown
    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.
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  40.  30
    Théorie Legislative de la Négation Pure.Jean-Yves Béziau - 1994 - Logique Et Analyse 147 (148):209-225.
    Direct download  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  41.  65
    Combining Conjunction with Disjunction.Jean-Yves Beziau - manuscript
    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. (...)
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  42.  12
    To Distribute or Not to Distribute?Jean-Yves Béziau & Marcelo E. Coniglio - 2011 - 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. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  43.  6
    Preface of This Special Issue: The Challenge of Combining Logics.Jean-Yves Béziau - 2011 - Logic Journal of the IGPL 19 (4):543-543.
  44.  31
    Preface.Jean-Yves Béziau - 2007 - Logica Universalis 1 (1):1-2.
  45.  89
    Relativizations of the Principle of Identity.Décio Krause & Jean-Yves Béziau - 1997 - 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  46.  14
    O Suicídio segundo Arthur Schopenhauer.Jean-Yves Béziau - 1997 - Discurso 28:127-144.
    Neste artigo examinamos a concepção filosófica do suicídio em Schopenhauer. Mostramos que a razão fundamental pela qual Schopenhauer rejeita o suicídio está intimamente ligada ao fundamento da sua metafísica. Explicamos suas diferenças face às rejeições tradicionais do suicídio, visto que Schopenhauer considera o suicídio um erro mas não um crime, e quais são os casos nos quais o suicídio pode ser aceito.
    Direct download (8 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  47.  16
    Introduction of Implication and Generalization in Axiomatic Calculi.Buchsbaum Arthur & Jean-Yves Béziau - unknown
    Direct download  
     
    Export citation  
     
    Bookmark  
  48. Aftermath of the Logical Paradise.Jean-Yves Beziau, Alexandre Costa-Leite & Itala M. Loffredo D’Ottaviano (eds.) - 2017
    No categories
     
    Export citation  
     
    Bookmark  
  49. Being Aware of Rational Animals.Jean-Yves Beziau - 2017 - In Gordana Dodig-Crnkovic & Raffaela Giovagnoli (eds.), Representation of Reality: Humans, Other Living Organism and Intelligent Machines. Springer.
    Modern science has qualified human beings as homo sapiens. Is there a serious scientific theory backing this nomenclature? And can we proclaim ourselves as wise? The classical rational animals characterization has apparently the same syntactic form but it is not working exactly in the same way. Moreover the semantics behind is more appropriate, encompassing a pivotal ambiguity. In the second part of the paper, we further delve into this ambiguity, relating rationality with three fundamental features of these creatures: ability to (...)
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark  
  50. Logica Universalis: Towards a General Theory of Logic.Jean-Yves Béziau (ed.) - 2007 - Birkhäuser Basel.
    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 (...)
    Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
1 — 50 / 108