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28Twist-Valued Models for Three-Valued Paraconsistent Set TheoryLogic and Logical Philosophy 1. forthcoming.We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. F…Read more
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27This 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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26Finite 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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25Society semantics and the logic way to collective intelligenceJournal of Applied Non-Classical Logics 27 (3-4): 255-268. 2017.The so-called phenomenon of collective intelligence is now a burgeoning movement, with several guises and examples in many areas. We briefly survey some relevant aspects of collective intelligence in several formats, such as social software, crowdfunding and convergence, and show that a formal version of this paradigm can also be posed to logic systems, by employing the notion of logic societies. The paradigm of logical societies has lead to a new notion of distributed semantics, the society sem…Read more
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24Computability. Computable Functions, Logic, and the Foundations of MathematicsBulletin of Symbolic Logic 8 (1): 101-104. 2002.
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22Recovery 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 metalogical 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 and by the logics of formal undeterminedness. LFIs recover the validity of the principle of explosion in a paraconsistent scena…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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19Reduction Techniques for Proving Decidability in Logics and Their Meet–CombinationBulletin of Symbolic Logic 27 (1): 39-66. 2021.Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity pro…Read more
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18Some 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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18Volume II: New advances in Logics of Formal InconsistencyLogic Journal of the IGPL 28 (5): 845-850. 2020.
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17Inferential Semantics, Paraconsistency, and Preservation of EvidenceIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 165-187. 2019.Proof-theoretic semantics provides meanings to the connectives of intuitionistic logic without the need for a semantics in the standard sense of an attribution of semantic values to formulas. Meanings are given by the inference rules that, in this case, do not express preservation of truth but rather preservation of availability of a constructive proof. Elsewhere we presented two paraconsistent systems of natural deduction: the Basic Logic of Evidence and the Logic of Evidence and Truth. The rul…Read more
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16The 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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15Volume I: Recovery operators in logics of formal inconsistencyLogic Journal of the IGPL 28 (5): 615-623. 2020.There are a considerable number of logics that do not seem to share the same inferential principles. Intuitionistic logics do not include the law of the exclude.
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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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14Fraïssé’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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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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13Reason and irrationality in the representation of knowledgeTrans/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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13On Barrio, Lo Guercio, and Szmuc on Logics of Evidence and TruthLogic and Logical Philosophy 1-26. forthcoming.The aim of this text is to reply to criticisms of the logics of evidence and truth and the epistemic approach to paraconsistency advanced by Barrio [2018], and Lo Guercio and Szmuc [2018]. We also clarify the notion of evidence that underlies the intended interpretation of these logics and is a central point of Barrio’s and Lo Guercio & Szmuc’s criticisms.
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11The Ricean Objection: An Analogue of Rice's Theorem for First-order TheoriesLogic Journal of the IGPL 16 (6): 585-590. 2008.We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order theories and P is non-trivial over the set of finitely axiomatizable theories , then P is undecidable. This not only means that the problem of deciding properties of first-order theories is as hard as the problem of deciding properties about languages accepted by Turing machines, but also offers a general setting for proving …Read more
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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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11Paraconsistency: The Logical Way to the InconsistentMarcel Dekker. 2002.This impressive compilation of the material presented at the Second World Congress on Paraconsistency held in Juquehy-Sao Sebastião, São Paulo, Brazil, represents an integrated discussion of all major topics in the area of paraconsistent logic---highlighting philosophical and historical aspects, major developments and real-world applications.
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10Modalities and MultimodalitiesSpringer. 2008.In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancie…Read more
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106th Workshop on Logic, Language, Information and ComputationBulletin of Symbolic Logic 5 (3): 424-425. 1999.
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9The 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 |