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1Kantian and non-Kantian logicsLogique Et Analyse 31 (121/122): 3-9. 1988.In a previous work [the second and the third author, “On paraconsistent deontic logic”, Philosophia 16, 293-303 (1986)] investigated certain systems of paraconsistent deontic in order to investigate the problem of contradiction in the domain of ethics. This paper continues this line of research, studying some paraconsistent systems containing alethic and deontic modalities. This approach allows us to treat the principles of Kant (OA→ \diamond A) and Hintikka (\square A → OA) from the classica…Read more
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17The problem Of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3‐Valued LogicsMathematical Logic Quarterly 33 (1): 19-29. 1987.This paper introduces the notions of perfect quantifiers in general many-valued logics and investigates the problem of quantificational completeness for such logics as well as the problem of characterizing all perfect quantifiers in 3-valued logics using techniques of combinatorial group theory.
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205Resenha de 'Logiques classiques et non classiques. essai sur les fondements de la logique' (Newton C.A. da Costa)Manuscrito 23 (1): 235-241. 2000.This is a review of: Newton C.A. da Costa, Logiques Classiques et Non Classiques. Essai sur les Fondements de la Logique. Translated from the Portuguese by Jean-Yves Béziau (with two appendices by the translator) Culture Scientifique, Masson, Paris, 1997, 276p. ISBN 2-225-85247-2
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363Modulated logics and flexible reasoningLogic and Logical Philosophy 17 (3): 211-249. 2008.This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. This approach offers a new regard to what we call flexible reasoning. A uniform treatment of modulated logics is given here, obtaining some general results in model theory. Besides reviewing the “Logic of Ultrafilters”, which formalizes inductive assertions of the kind “almost all”, two new …Read more
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442Book Reviews: Ernst Schröder, Parafrasi Schröderiane. Ovvero: Ernst Schröder, Leoperazioni del Calcolo LogicoLogic and Logical Philosophy 20 (3): 267-272. 2011.Ernst Schröder, Parafrasi Schröderiane. Ovvero: Ernst Schröder, Leoperazioni del Calcolo Logico. Original German text with Italian translation, commentary and annotations by Davide Bondoni, LED Edizioni, Milan, 2010, pp. 208, 15,5 × 22 cm, ISBN 978-88-7916-474-0
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100Modulated fibring and the collapsing problemJournal of Symbolic Logic 67 (4): 1541-1569. 2002.Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the s…Read more
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167On paraconsistent deontic logicPhilosophia 16 (3-4): 293-305. 1986.This paper develops the first deontic logic in the context of paraconsistent logics.
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750Translations between logical systems: a manifestoLogique Et Analyse 157 67-81. 1997.The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, log…Read more
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998We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically …Read more
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530Formal inconsistency and evolutionary databasesLogic and Logical Philosophy 8 (2): 115-152. 2000.This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems a…Read more
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116th Workshop on Logic, Language, Information and ComputationBulletin of Symbolic Logic 5 (3): 424-425. 1999.
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39The Single-minded Pursuit of Consistency and its WeaknessStudia Logica 97 (1). 2011.I argue that a compulsive seeking for just one sense of consistency is hazardous to rationality, and that observing the subtle distinctions of reasonableness between individual and groups may suggest wider, structuralistic notions of consistency, even relevant to re-assessing Gödei's Second Incompleteness Theorem and to science as a whole
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427Razão e irracionalidade na representação do conhecimentoTrans/Form/Ação 14 165-177. 1991.How is it possible that beginning from the negation of rational thoughts one comes to produce knowledge? This problem, besides its intrinsic interest, acquires a great relevance when the representation of a knowledge is settled, for example, on data and automatic reasoning. Many treatment ways have been tried, as in the case of the non-monotonic logics; logics that intend to formalize an idea of reasoning by default, etc. These attempts are incomplete and are subject to failure. A possible solut…Read more
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227Seventh Latin American on Mathematical Logic- Meeting of the association for symbolic logic: Campinas, Brazil, 1985Journal of Symbolic Logic 51 (4): 1093-1103. 1986.This publication refers to the proceedings of the Seventh Latin American on Mathematical Logic held in Campinas, SP, Brazil, from July 29 to August 2, 1985. The event, dedicated to the memory of Ayda I. Arruda, was sponsored as an official Meeting of the Association for Symbolic Logic. Walter Carnielli. The Journal of Symbolic Logic Vol. 51, No. 4 (Dec., 1986), pp. 1093-1103
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60Book review r A. (2004). "Book review: Yves nievergelt, foundations of ...
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55Maximal weakly-intuitionistic logicsStudia Logica 55 (1). 1995.This article introduces the three-valuedweakly-intuitionistic logicI 1 as a counterpart of theparaconsistent calculusP 1 studied in [11].I 1 is shown to be complete with respect to certainthree-valued matrices. We also show that in the sense that any proper extension ofI 1 collapses to classical logic.The second part shows thatI 1 is algebraizable in the sense of Block and Pigozzi (cf. [2]) in a way very similar to the algebraization ofP 1 given in [8].
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196th Workshop on Logic, Language, Information and Computation (Wollic'99)Bulletin of Symbolic Logic 5 (3): 424-425. 1999.
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36The problem of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3-Valued LogicsZeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1): 19-29. 1987.This paper investigates a problem related to quantifiers which has some analogies to that of propositional completeness I give a definition of quantifier in many-valued logics generalizing the cases which already occur in first order many- valued logics. Though other definitions are possible, this particular one, which I call distribution quantifiers, generalizes the classical quantifiers in a very natural way, and occurs in finite numbers in every m-valued logic. We …Read more
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33Polynomizing: Logic inference in polynomial format and the legacy of BooleIn L. Magnani & P. Li (eds.), Model-Based Reasoning in Science, Technology, and Medicine, Springer. pp. 349--364. 2007.Polynomizing is a term that intends to describe the uses of polynomial-like representations as a reasoning strategy and as a tool for scientific heuristics. I show how proof-theory and semantics for classical and several non-classical logics can be approached from this perspective, and discuss the assessment of this prospect, in particular to recover certain ideas of George Boole in unifying logic, algebra and the differential calculus.
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5Logic, sets and information: proceedings of the tenth Brazilian Conference on Mathematical Logic (edited book)Centro de Lógica, Epistemologia e História da Ciência, UNICAMP. 1995.Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.
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University of CampinasCentre For Logic, Epistemology And The History Of ScienceDistinguished Professor
Campinas, São Paulo, Brazil
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |