
396Logica 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

256La Pointure du Symbole (edited book)Petra. 2014.Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi var…Read more

204What is “Formal Logic”?Proceedings of the Xxii World Congress of Philosophy 13 922. 2008.“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…Read more

158The power of the hexagonLogica Universalis 6 (12): 143. 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 Icorner and the problem of the Ocorner. The meaning of the notion described by the Icorner does not correspond to the name used for it. In the case of the Ocorner, the problem is not a wrongname problem but a noname problem and it is not clear wha…Read more

155Professor Newton CA da Costa awarded Nicholas Copernicus University medal of meritLogic and Logical Philosophy 7 710. 1999.

139Logic and Philosophy of ReligionSophia 56 (2). 2017.This paper introduces a special issue on logic and philosophy of religion in this journal (Sophia). After discussing the role played by logic in the philosophy of religion along with classical developments, we present the basic motivation for this special issue accompanied by an exposition of its content.

133Sentence, 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

133The relativity and universality of logicSynthese 192 (7): 19391954. 2015.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 …Read more

89Relativizations of the Principle of IdentityLogic Journal of the IGPL 5 (3): 1729. 1997.We discuss some logicomathematical 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

77Manyvalued logics are standardly defined by logical matrices. They are truthfunctional. In this paper non truthfunctional manyvalued semantics are presented, in a philosophical and mathematical perspective.

68Classical negation can be expressed by one of its halvesLogic Journal of the IGPL 7 (2): 145151. 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 modeltheory 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

65In 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

55Définition, Théorie des Objets et Paraconsistance (Definition, Objects' Theory and Paraconsistance)Theoria 13 (2): 367379. 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

53Truth as a Mathematical ObjectPrincipia: An International Journal of Epistemology 14 (1): 3146. 2010.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 multivaloradas com três ou quatro valores, semântica bivalente não veritativa, semânticas dos mundos possiveis de Kripke. DOI:10.5007/1808…Read more

50of 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.

48Yaroslav Shramko and Heinrich Wansing, Truth and Falsehood  An Inquiry into Generalized Logical ValuesStudia Logica 102 (5): 10791085. 2014.

47Idempotent Full Paraconsistent Negations are not AlgebraizableNotre Dame Journal of Formal Logic 39 (1): 135139. 1998.

47Manyvalued and Kripke semanticsIn Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics, Springer. pp. 89101. 2006.

45Is the Principle of Contradiction a Consequence of $$x^{2}=x$$ x 2 = x?Logica Universalis 12 (12): 5581. 2018.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.

39Logic may be simple. Logic, congruence and algebraLogic and Logical Philosophy 5 (n/a): 129147. 1997.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 nontrivial congruence relation, like some paraconsistent logics, is called simple. The relations between simplicity, the replacement theorem and algebraization of logic are studied (including MacLaneCurry’s theorem and a discussion about Curry’s algebras). We also examine how these…Read more

36of 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.