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LFIs Based on Other LogicsIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
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Contradiction and ConsistencyIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
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Semantics of Non-deterministic Character for LFIsIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
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Some Extensions of mbCIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
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Paraconsistent Set TheoryIn Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation, Springer International Publishing. 2016.
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673In 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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402A categorial approach to the combination of logicsManuscrito 22 (2): 69-94. 1999.In this paper we propose a very general denition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, sin…Read more
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36On discourses addressed by infidel logiciansIn Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications, Springer. pp. 27--41. 2013.We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.
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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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474Erratum 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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87The 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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64MODEL-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 Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic, Birkhäuser Verlog. 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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32Valuation 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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746Towards 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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16Reason 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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71New 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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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 |