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20From Belnap-Dunn Four-Valued Logic to Six-Valued Logics of Evidence and TruthStudia Logica 112 (3): 561-606. 2024.The main aim of this paper is to introduce the logics of evidence and truth $$LET_{K}^+$$ and $$LET_{F}^+$$ together with sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics $$LET_{K}$$ and $$LET_{F}^-$$ with rules of propagation of classicality, which are inferences that express how the classicality operator $${\circ }$$ is transmitted from less complex to more complex sentences, and vice-versa. The six-valued semantics here proposed extend…Read more
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102Definability and InvarianceStudia Logica 86 (1): 1-30. 2007.In his thesis Para uma Teoria Geral dos Homomorfismos (1944), the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we tried…Read more
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44Definability and InvarianceStudia Logica 86 (1): 1-30. 2007.In his thesis 'Para uma Teoria Geral dos Homomorfismos' (1944) the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we trie…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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34First-order Logics of Evidence and Truth with Constant and Variable DomainsLogica Universalis 16 (3): 419-449. 2022.The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over time. The paper also discusses the connections between Belnap-Dunn’s and da Costa’s approaches to paraconsistency, and argues that the logics of evidence…Read more
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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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20Paraconsistent Logic: Consistency, Contradiction and Negation: Walter Carnielli and Marcelo E. Coniglio, New York, Springer International Publishing, 2016, xxiv + 398 pp., US$109.99 (pbk) ISBN-13: 978-3319814537 (review)History and Philosophy of Logic 42 (3): 300-306. 2021.The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...
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48Kripke-Style Models for Logics of Evidence and TruthAxioms 9 (3). 2020.In this paper, we propose Kripke-style models for the logics of evidence and truth LETJ and LETF. These logics extend, respectively, Nelson’s logic N4 and the logic of first-degree entailment with a classicality operator ∘ that recovers classical logic for formulas in its scope. According to the intended interpretation here proposed, these models represent a database that receives information as time passes, and such information can be positive, negative, non-reliable, or reliable, while a formu…Read more
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39Paraconsistent Logic: Consistency, Contradiction and NegationHistory and Philosophy of Logic 42 (3): 300-306. 2021.The book Paraconsistent Logic: Consistency, Contradiction and Negation by Walter Carnielli and Marcelo Coniglio is the most thorough study of Logics of Formal Inconsistency...
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18Inferential 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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32Measuring evidence: a probabilistic approach to an extension of Belnap–Dunn logicSynthese 198 (S22): 5451-5480. 2020.This paper introduces the logic of evidence and truth \ as an extension of the Belnap–Dunn four-valued logic \. \ is a slightly modified version of the logic \, presented in Carnielli and Rodrigues. While \ is equipped only with a classicality operator \, \ is equipped with a non-classicality operator \ as well, dual to \. Both \ and \ are logics of formal inconsistency and undeterminedness in which the operator \ recovers classical logic for propositions in its scope. Evidence is a notion weake…Read more
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38On epistemic and ontological interpretations of intuitionistic and paraconsistent paradigmsLogic Journal of the IGPL. forthcoming.From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic lies in the fact that explosion does not hold in the former and excluded middle does not hold in the latter. From the point of view of the motivations for rejecting explosion and excluded middle, this duality can be interpreted either ontologically or epistemically. An ontological interpretation of intuitionistic logic is Brouwer’s idealism; of paraconsistency is dialetheism. …Read more
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24Recovery 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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329On formal aspects of the epistemic approach to paraconsistencyIn Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain, College Publications. pp. 48-74. 2018.This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability a…Read more
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21Foreword: Consistency, Contradiction, and ConsequencePrincipia: An International Journal of Epistemology 22 (1): 01-05. 2018.Foreword : Consistency, Contradiction, and Consequence.
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717Towards 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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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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17Fazedores-de-verdade, a tese da disjunção eo princípio do terceiro excluídoPhilósophos - Revista de Filosofia 12 (2). 2007.
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455Recovery 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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640In 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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31Fazedores-de-verdadeDois Pontos 6 (2). 2009.This papers’ goal is to present a survey of the contemporary discussions regarding truthmakers. The emphasis will be on the characterization of the truthmaking relation and on the problems involved in universal propositions and negations
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Logic and Philosophy of Logic |
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Logic and Philosophy of Logic |