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Paraconsistency: The Logical Way to the InconsistentBulletin of Symbolic Logic 9 (3): 410-412. 2003.
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25Computability. Computable Functions, Logic, and the Foundations of MathematicsBulletin of Symbolic Logic 8 (1): 101-104. 2002.
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4The Many Sides of Logic. (edited book)College Publications. 2009.The ``Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the Stat…Read more
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1An algorithm for axiomatizing and theorem proving in finite many - valued propositional logicsLogique Et Analyse 28 (12): 363. 1985.
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11Paraconsistent AlgebrasStudia Logica 43 (1): 79-88. 1984.The propositional calculi $C_{n}$ , $1\leq n\leq \omega $ introduced by N.C.A. da Costa consitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum's algebra for $C_{n}$ . C. Mortensen settled the problem, proving that no equivalence relation for $C_{n}$ determines a non-trivial quotient algebra. The concept of da Costa algebra, which reflects most of the logical properties of $C_{n}$ , as well as the con…Read more
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22Some results on polarized partion relations of higher dimensionMathematical Logic Quarterly 39 (1): 461-474. 1993.Several types of polarized partition relations are considered. In particular we deal with partitions defined on cartesian products of more than two factors. MSC: 03E05
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31Possible-translations algebraization for paraconsistent logicsBulletin of the Section of Logic 34 (2): 77-92. 2005.
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51Paraconsistent algebrasStudia Logica 43 (1-2). 1984.The prepositional calculiC n , 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum''s algebra forC n . C. Mortensen settled the problem, proving that no equivalence relation forC n . determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC n , as well as the concept of paraconsistent closure syst…Read more
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455Recovery operators, paraconsistency and dualityLogic Journal of the IGPL 28 (5): 624-656. 2020.There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a parac…Read more
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691The Wonder of Colors and the Principle of AriadneIn Walter Carnielli & Carlos di Prisco (eds.), The Wonder of Colors and the Principle of Ariadne, Springer. pp. 309-317. 2017.The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne and proposes the Ariadne Game, showing that the Principle of Ariadne, corresponds precisely to a winning strategy for the Ariadne Ga…Read more
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10The proceedings of the XVI ebl--16th Brazilian logic conference, 2011: A prefaceLogic Journal of the IGPL 22 (2): 181-185. 2014.
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13Paraconsistency: The Logical Way to the Inconsistent (edited book)CRC Press. 2002.The Logical Way to the Inconsistent Walter Alexandr Carnielli, Marcelo Coniglio, Itala Maria Lof D'ottaviano. Beyond Truth(-Preservation) R.E. JENNINGS Laboratory for Logic and Experimental Philosophy, Simon Fraser University, Burnaby, ...
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385Meeting Hintikka's Challenge to ParaconsistentismPrincipia: An International Journal of Epistemology 13 (3): 283-297. 2009.Jaakko Hintikka, in a series of talks in Brazil in 2008, defended that IF logic and paraconsistent logic are, in a sense, very similar. Having sketched the proposal of a new paraconsistent system, he maintains that several achievements of IF logic could be reproducible in paraconsistent logic. One of the major difficulties, left as a challenge, would be to formulate some truth conditions for this new paraconsistent first-order language in order to make IF logic and paraconsistent logic more inte…Read more
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394Book Reviews: Claude P. Bruter (editor), Mathematics in Art: Mathematical Visualization in Art and EducationLogic and Logical Philosophy 13 (n/a): 163-166. 2004.Claude P. Bruter (editor), Mathematics in Art: Mathematical Visualization in Art and Education, Springer-Verlag, New York, 2002, pp. X + 337, ISBN 3-540-43422-4
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41Interpolation via translationsMathematical Logic Quarterly 55 (5): 515-534. 2009.A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear lo…Read more
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184XVI Brazilian Logic Conference (EBL 2011)Bulletin of Symbolic Logic 18 (1): 150-151. 2012.This is the report on the XVI BRAZILIAN LOGIC CONFERENCE (EBL 2011) held in Petrópolis, Rio de Janeiro, Brazil between May 9–13, 2011 published in The Bulletin of Symbolic Logic Volume 18, Number 1, March 2012. The 16th Brazilian Logic Conference (EBL 2011) was held in Petro ́polis, from May 9th to 13th, 2011, at the Laboratório Nacional de Computação o Científica (LNCC). It was the sixteenth in a series of conferences that started in 1977 with the aim of congregating logicians from Brazil an…Read more
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97Systematization of finite many-valued logics through the method of tableauxJournal of Symbolic Logic 52 (2): 473-493. 1987.his paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way. We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Lowenheim-Skolem theorem. The paper is comp…Read more
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15On a Theoretical Analysis of Deceiving: How to Resist a Bullshit AttackIn & C. Pizzi W. Carnielli L. Magnani (ed.), Model-Based Reasoning in Science and Technology, . pp. 291--299. 2010.This paper intends to open a discussion on how certain dangerous kinds of deceptive reasoning can be defined, in which way it is achieved in a discussion, and which would be the strategies for defense against such deceptive attacks on the light of some principles accepted as fundamental for rationality and logic.
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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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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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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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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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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 |