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360Non-deterministic algebraization of logics by swap structures1Logic Journal of the IGPL 28 (5): 1021-1059. 2020.Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization …Read more
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488AGM-Like Paraconsistent Belief ChangeLogic Journal of the IGPL 25 (4): 632-672. 2017.Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical …Read more
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38Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’Journal of Applied Non-Classical Logics 26 (4): 336-345. 2016.In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally point…Read more
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Paraconsistency: The Logical Way to the InconsistentBulletin of Symbolic Logic 9 (3): 410-412. 2003.
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25Xlth Latin American Symposium on Mathematical Logic Merida, Venezuela, 6-1 0 July, 1998Annals of Pure and Applied Logic 108 (1-3): 79-101. 2001.
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27Modules in the category of sheaves over quantalesAnnals of Pure and Applied Logic 108 (1-3): 103-136. 2001.In this paper we develop the elementary theory of modules in the category Sh of sheaves over right-sided idempotent quantales. The main ingredient is the construction of a logic sound for Sh . As an application we prove that in Sh , a finitely generated projective module is free , a result that is relevant to the study of representation of non-commutative C ∗ -algebras
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53Transfers 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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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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445Recovery 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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406A model-theoretic analysis of Fidel-structures for mbCIn Can Başkent & Thomas Macaulay Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer Verlag. pp. 189-216. 2019.In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theo…Read more
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331Maximality in finite-valued Lukasiewicz logics defined by order filtersJournal of Logic and Computation 29 (1): 125-156. 2019.In this paper we consider the logics
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50Paraconsistent Logic: Consistency, Contradiction and NegationSpringer International Publishing. 2016.This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Para…Read more
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417Modal logic S4 as a paraconsistent logic with a topological semanticsIn Caleiro Carlos, Dionisio Francisco, Gouveia Paula, Mateus Paulo & Rasga João (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas, College Publications. pp. 171-196. 2017.In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This c…Read more
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54Recovering a logic from its fragments by meta-fibringLogica Universalis 1 (2): 377-416. 2007.. In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main fea…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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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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14A Formal Framework for Hypersequent Calculi and Their FibringIn Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I, Springer. pp. 73-93. 2014.Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are intro…Read more
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214Some results on ordered structures in toposesReports on Mathematical Logic 181-198. 2006.A topos version of Cantor’s back and forth theorem is established and used to prove that the ordered structure of the rational numbers (Q,
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50Hilbert-style Presentations of Two Logics Associated to Tetravalent Modal AlgebrasStudia Logica 102 (3): 525-539. 2014.We analyze the variety of A. Monteiro’s tetravalent modal algebras under the perspective of two logic systems naturally associated to it. Taking profit of the contrapositive implication introduced by A. Figallo and P. Landini, sound and complete Hilbert-style calculi for these logics are presented
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101New 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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8Towards an hyperalgebraic theory of non-algebraizable logicsCLE E-Prints 16 (4): 1-27. 2016.Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. …Read more
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233Some investigations on mbC and mCiIn Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas, Nel/ufsc. pp. 11-70. 2014.
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90A Paraconsistentist Approach to Chisholm's ParadoxPrincipia: An International Journal of Epistemology 13 (3): 299-326. 2009.The Logics of Deontic (In)Consistency (LDI's) can be considered as the deontic counterpart of the paraconsistent logics known as Logics of Formal (In)Consistency. This paper introduces and studies new LDI's and other paraconsistent deontic logics with different properties: systems tolerant to contradictory obligations; systems in which contradictory obligations trivialize; and a bimodal paraconsistent deontic logic combining the features of previous systems. These logics are used to analyze the …Read more
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384A 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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42Logics of formal inconsistency arising from systems of fuzzy logicLogic Journal of the IGPL 22 (6): 880-904. 2014.This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of…Read more
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207On graph-theoretic fibring of logicsJournal of Logic and Computation 19 (6): 1321-1357. 2009.A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive syste…Read more
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51Non-commutative topology and quantalesStudia Logica 65 (2): 223-236. 2000.The relationship between q-spaces (c.f. [9]) and quantum spaces (c.f. [5]) is studied, proving that both models coincide in the case of Spec A, the spectrum of a non-commutative C*-algebra A. It is shown that a sober T 1 quantum space is a classical topological space. This difficulty is circumvented through a new definition of point in a quantale. With this new definition, it is proved that Lid A has enough points. A notion of orthogonality in quantum spaces is introduced, which permits us to ex…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.
University of São Paulo
Department of Philosophy, Languages and Literature, and Human Sciences
PhD, 1997
Campinas, São Paulo, Brazil
Areas of Specialization
Logic and Philosophy of Logic |
Areas of Interest
Logic and Philosophy of Logic |