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17Fraïssé’s theorem for logics of formal inconsistencyLogic Journal of the IGPL 28 (5): 1060-1072. 2020.We prove that the minimal Logic of Formal Inconsistency $\mathsf{QmbC}$ validates a weaker version of Fraïssé’s theorem. LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classi…Read more
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32Contradictions, from Consistency to Inconsistency (edited book)Springer. 2018.This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and tr…Read more
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340On formal aspects of the epistemic approach to paraconsistencyIn Marco Ruffino, Max Freund & Max Fernández de Castro (eds.), Logic and philosophy of logic. Recent trends from Latin America and Spain, College Publications. pp. 48-74. 2018.This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability a…Read more
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Contradictions, from Consistency to InconsistencyIn Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency, Springer. 2018.
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Making The ‘Hardest Logic Puzzle Ever’ a Bit HarderIn Brian Rayman & Melvin Fitting (eds.), Raymond Smullyan on Self Reference, Springer Verlag. 2017.
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Experimenting with ConsistencyIn Dmitry Zaitsev & Vladimir Markin (eds.), The Logical Legacy of Nikolai Vasiliev and Modern Logic, Springer Verlag. pp. 199-221. 2017.This paper discusses logical accounts of the notions of consistency and negation, and in particular explores some potential means of defining consistency and negation when expressed in modal terms. Although this can be done with interesting consequences when starting from classical normal modal logics, some intriguing cases arise when starting from paraconsistent modalities and negations, as in the hierarchy of the so-called cathodic modal paraconsistent systems (cf. Bueno-Soler, Log Univers 4(1…Read more
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19Finite and infinite-valued logics: inference, algebra and geometry: PrefaceJournal of Applied Non-Classical Logics 9 (1): 7-8. 1999.This is the preface for a special volume published by the Journal of Applied Non-Classical Logics Volume 9, Issue 1, 1999.
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The Wonder of Colors and the Principle of AriadneIn Marcos Silva (ed.), How Colours Matter to Philosophy, Springer. 2017.
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Paraconsistency: The Logical Way to the InconsistentBulletin of Symbolic Logic 9 (3): 410-412. 2003.
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22Computability. 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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32Possible-translations algebraization for paraconsistent logicsBulletin of the Section of Logic 34 (2): 77-92. 2005.
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52Paraconsistent 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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520Recovery 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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707The 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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219Resenha 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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376Modulated 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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101Modulated 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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456Book 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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150On 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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772Translations 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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1030We 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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549Formal 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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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 |