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408Logica 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
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41CONCEPTUAL 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
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42Universal Logic: An Anthology From Paul Hertz to Dov Gabbay (edited book)Birkhäuser. 2012.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
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67New 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
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49MANY 1 - A Transversal Imaginative Journey across the Realm of MathematicsJournal 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.
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10Ruth Barcan Marcus est-elle la mère du fils de Wittgenstein?(Considerations existencialistes sur la formule de Barcan)Manuscrito: Revista Internacional de Filosofía 22 (2): 11-27. 1999.
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106Many-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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33O Suicídio segundo Arthur SchopenhauerDiscurso 28 127-144. 1997.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
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94In 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. A de…Read more
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Définition, 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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19Truth as a Mathematical Object DOI:10.5007/1808-1711.2010v14n1p31Principia: An International Journal of Epistemology 14 (1): 31-46. 2010.In this paper we discuss in which sense truth is considered as a mathematical object in propositional logic. After clarifying how this concept is used in classical logic, through the notions of truth-table, truth-function and bivaluation, we examine some generalizations of it in non-classical logics: many-valued matrix semantics with three and four values, non-truth-functional bivalent semantics, Kripke possible world semantics. • DOI:10.5007/1808-1711.2010v14n1p31.
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108Relativizations of the Principle of IdentityLogic Journal of the IGPL 5 (3): 17-29. 1997.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 a formulatio…Read more
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40of 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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39A 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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70Définition, 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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64Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood - An Inquiry into Generalized Logical ValuesStudia Logica 102 (5): 1079-1085. 2014.
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70The 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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89Classical 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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52Around 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.