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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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469Erratum to “The Ricean Objection: An Analogue of Rice's Theorem for First-Order Theories” Logic Journal of the IGPL, 16: 585–590 (review)Logic Journal of the IGPL 17 (6): 803-804. 2009.This note clarifies an error in the proof of the main theorem of “The Ricean Objection: An Analogue of Rice’s Theorem for First-Order Theories”, Logic Journal of the IGPL, 16(6): 585–590(2008)
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104The Significance of the New Logic (edited book)Cambridge University Press. 2018.W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Lógica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas abo…Read more
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63MODEL-BASED REASONING IN SCIENCE AND TECHNOLOGY (edited book)Springer. 2010.This volume is based on the papers presented at the international conference Model-Based Reasoning in Science and Technology (MBR09_BRAZIL), held at the University of Campinas (UNICAMP), Campinas, Brazil, December 2009. The presentations given at the conference explored how scientific cognition, but several other kinds as well, use models, abduction, and explanatory reasoning to produce important or creative changes in theories and concepts. Some speakers addressed the problem of model-based r…Read more
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5Paraconsistency, the logical way to the inconsistent (edited book)CRC Press. 2002.Proceedings of the II World Congress on Paraconsistency held in Juquey, SP, Brazil, from May 12-19, 2000
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1Two's Company: The humbug of many logical valuesIn J. Y. Beziau (ed.), Logica Universalis, Birkhäuser Verlag. pp. 169-189. 2005.The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more than…Read more
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30Valuation Semantics for First-Order Logics of Evidence and TruthJournal of Philosophical Logic 51 (5): 1141-1173. 2022.This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows fro…Read more
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12Paraconsistency: 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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55Combining logicsStanford Encyclopedia of Philosophy. 2008.Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) a…Read more
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47Special Issue: Formal Representations in Model-based Reasoning and AbductionLogic Journal of the IGPL 20 (2): 367-369. 2012.This is the preface of the special Issue: Formal Representations in Model-based Reasoning and Abduction, published at the Logic Jnl IGPL (2012) 20 (2): 367-369. doi: 10.1093/jigpal/jzq055 First published online: December 20, 2010
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31Non-standard numbers: a semantic obstacle for modelling arithmetical reasoningLogic Journal of the IGPL 20 (2): 477-485. 2012.The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines
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54Transfers between logics and their applicationsStudia Logica 72 (3): 367-400. 2002.In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attribute…Read more
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29Society 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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725Towards a philosophical understanding of the logics of formal inconsistencyManuscrito 38 (2): 155-184. 2015.In this paper we 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 in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue …Read more
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38Special Issue on Multimodal Logics: A Preface (review)Logica Universalis 7 (1): 1-5. 2013.This is a preface for the Special Issue on Multimodal Logics published in Logica Universalis, March 2013, Volume 7, Issue 1, pp 1-5.
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14Reason 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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102New dimensions on translations between logicsLogica Universalis 3 (1): 1-18. 2009.After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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39On the way to a Wider model theory: Completeness theorems for first-order logics of formal inconsistencyReview of Symbolic Logic 7 (3): 548-578. 2014.This paper investigates the question of characterizing first-order LFIs (logics of formal inconsistency) by means of two-valued semantics. LFIs are powerful paraconsistent logics that encode classical logic and permit a finer distinction between contradictions and inconsistencies, with a deep involvement in philosophical and foundational questions. Although focused on just one particular case, namely, the quantified logic QmbC, the method proposed here is completely general for this kind of logi…Read more
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45An Event on Brazilian Logic: Proceedings of the XIII Brazilian Logic ConferenceLogic Journal of the IGPL 13 (1): 1-3. 2005.This volume corresponds to the Proceedings of the XIII Brazilian Logic Conference held at the CLE - Centre for Logic, Epistemology and the History of Science in Campinas, SP, Brazil from May 26-30, 2003 under the auspices of the SBL - Brazilian Logic Society and the ASL - Association for Symbolic Logic.
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403Book Reviews: Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, CambridgeLogic and Logical Philosophy 15 (1): 91-96. 2006.Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, Cambridge, UK, 2004, pp. 432
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122An epistemic approach to paraconsistency: a logic of evidence and truthSynthese 196 (9): 3789-3813. 2019.The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and …Read more
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113Fibring non-truth-functional logics: Completeness preservationJournal of Logic, Language and Information 12 (2): 183-211. 2003.Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that th…Read more
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5Tendencies in Logic, and Some Modest Advice to Young LogiciansFelsefe Arkivi 51 343-350. 2019.This brief note raises the question of why there is no advice in the literature for young logicians, while there is for mathematicians, musicians, and others. Trying to take advantage of what exists in other areas, some tendencies in logic, and reasons to follow – or not to follow-- trends are discussed.
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Aristóteles, paraconsistentismo e a tradição budistaO Que Nos Faz Pensar 23 163-175. 2008.This paper defends that the both the Buddhist tradition and the Aristotelian allow us to think of the distinction between to reason with contradictions and to accept them, understanding ' accept a contradiction ' by taking it as consistent. From this viewpoint, none of two would disagree with most contemporary paraconsistent views. The conclusions are, thus, that, firstly, there is no compelling reason to endorse any kind of metaphysical dialetheism, and, second, that a coherent form of reasonin…Read more
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10Computability. Computable Functions, Logic, and the Foundations of Mathematics. Second Edition of the PrecedingBulletin of Symbolic Logic 8 (1): 101. 2002.
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15On 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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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 |