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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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511Recovery 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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700The 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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196th Workshop on Logic, Language, Information and Computation (Wollic'99)Bulletin of Symbolic Logic 5 (3): 424-425. 1999.
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39The 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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86The dialogical approach to paraconsistencySynthese 125 (1-2): 201-232. 2000.Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, s…Read more
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68Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil (review)American Mathematical Soc.. 1999.This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were select…Read more
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216The tyranny of knowledgeManuscrito 31 (1): 511-518. 2008.EN In his “Logic, Language, and Knowledge” Chateaubriand denounces the tyranny of belief , but takes some positions on knowledge and justification which seem to be too exacting. The fact that Chateaubriand derives constraints on the notion of justification by a close parallel to the notion of proof makes it unnecessarily loaded with the individual, rather than with the collective perspective. His position seems to leave little room for common knowledge, collective knowledge and usual common-sen…Read more
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107Surviving AbductionLogic Journal of the IGPL 14 (2): 237-256. 2006.Abduction or retroduction, as introduced by C.S. Peirce in the double sense of searching for explanatory instances and providing an explanation is a kind of complement for usual argumentation. There is, however, an inferential step from the explanandum to the abductive explanans . Whether this inferential step can be captured by logical machinery depends upon a number of assumptions, but in any case it suffers in principle from the triviality objection: any time a singular contradictory explanan…Read more
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35Meeting of the Association for Symbolic Logic, Campinas, Brazil, 1985Journal of Symbolic Logic 51 (4). 1986.This is the ASL report on the 7th Latin American Symposium on Mathematical Logic held in Campinas, SP, Brazil, from July 29- August 02, 1985.
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28This is a review of Yves Nievergelt, Foundations of Logic and Mathematics: Applications to Computer Science and Cryptography, Birkäuser Verlag, Boston, 2002, €90, pp. 480, ISBN 0-8176-4249-8, hardcover
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64Limits for Paraconsistent CalculiNotre Dame Journal of Formal Logic 40 (3): 375-390. 1999.This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 year…Read more
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338Tableaux sin refutaciónMatemáticas: Enseñanza Universitaria 13 (2): 81-99. 2005.Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of cla…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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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 |