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  1. Logical theory revision through data underdetermination: an anti-exceptionalist exercise.Sanderson Molick - 2021 - Principia: An International Journal of Epistemology 25 (1).
    The anti-exceptionalist debate brought into play the problem of what are the relevant data for logical theories and how such data affects the validities accepted by a logical theory. In the present paper, I depart from Laudan's reticulated model of science to analyze one aspect of this problem, namely of the role of logical data within the process of revision of logical theories. For this, I argue that the ubiquitous nature of logical data is responsible for the proliferation of several (...)
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  • (1 other version)Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
    A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.
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  • A logical framework for data-driven reasoning.Paolo Baldi, Esther Anna Corsi & Hykel Hosni - forthcoming - Logic Journal of the IGPL.
    We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree, and possibly by mistake, any given scientific hypothesis. There is no general agreement in science about how to do this, which motivates putting forward a logical formulation of the problem. We do so by investigating distinct definitions of ‘rejection degrees’ each yielding a consequence (...)
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  • (1 other version)Twist-Valued Models for Three-valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - 2021 - Logic and Logical Philosophy 30 (2):187-226.
    Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...)
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  • Quasi-truth and defective knowledge in science: a critical examination.Jonas R. Becker Arenhart & Décio Krause - 2023 - Manuscrito 46 (2):122-155.
    Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the formalism available does not deliver all that is promised. We examine the standard account of quasi-truth in the literature, advanced by da Costa and collaborators in many places, and argue that it (...)
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  • Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...)
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  • On formal aspects of the epistemic approach to paraconsistency.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2018 - In Marco Ruffino, Max Freund & Max Fernández de Castro (eds.), Logic and philosophy of logic. Recent trends from Latin America and Spain. College Publications. pp. 48-74.
    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 are given for (...)
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  • Combining Swap Structures: The Case of Paradefinite Ivlev-Like Modal Logics Based on $$FDE$$.Marcelo E. Coniglio - forthcoming - Studia Logica:1-52.
    The aim of this paper is to combine several Ivlev-like modal systems characterized by 4-valued non-deterministic matrices (Nmatrices) with $$\mathcal {IDM}4$$, a 4-valued expansion of Belnap–Dunn’s logic $$FDE$$ with an implication introduced by Pynko in 1999. In order to do this, we introduce a new methodology for combining logics which are characterized by means of swap structures, based on what we call superposition of snapshots. In particular, the combination of $$\mathcal {IDM}4$$ with $$Tm$$, the 4-valued Ivlev’s version of KT, will (...)
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  • On a Four-Valued Logic of Formal Inconsistency and Formal Undeterminedness.Marcelo E. Coniglio, G. T. Gomez–Pereira & Martín Figallo - forthcoming - Studia Logica:1-42.
    Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce a four-valued expansion (...)
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  • Contra o dogmatismo realista: notas sobre acordos e jogos.Marcos Silva - 2021 - Trans/Form/Ação 44 (3):287-312.
    This paper discusses the existence of rules and criteria independent of our discursive practices by using Brandom’s philosophy and Wittgenstein’s philosophical development. For that, it examines the normativity of logic, especially facing the challenge of the diversity of non-classical logics and motivates that its constitution should be based on an analogy with games. This renders a pragmatist alternative to a realist sort of dogmatism. I then defend, using this pragmatist approach inspired in the notion of games and agreements, that it (...)
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  • From Belnap-Dunn Four-Valued Logic to Six-Valued Logics of Evidence and Truth.Marcelo E. Coniglio & Abilio Rodrigues - 2024 - Studia Logica 112 (3):561-606.
    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 extends the 4 values of Belnap-Dunn logic with 2 more values (...)
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  • Contradictory Concepts = True Contradictions?Jonas Rafael Becker Arenhart - 2020 - Philosophia 49 (2):585-602.
    Dialetheism is the view that some contradictions are true. One common motivation to the view concerns cases of contradictory concepts obtaining together. Allegedly, in these cases, such concepts lead to a true contradiction. In this paper, we argue that this path is closed as a motivation for dialetheism. There are two basic difficulties to articulate the view: i) once contradictory or incompatible concepts are granted to obtain together, there is no longer any reason to claim that they were incompatible to (...)
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  • (1 other version)Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter A. Carnielli & Marcelo E. Coniglio - forthcoming - Logic and Logical Philosophy:1.
    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. Finally, our (...)
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  • Measuring evidence: a probabilistic approach to an extension of Belnap–Dunn logic.Abilio Rodrigues, Juliana Bueno-Soler & Walter Carnielli - 2020 - Synthese 198 (S22):5451-5480.
    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. (...)
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  • A Four-Valued Dynamic Epistemic Logic.Yuri David Santos - 2020 - Journal of Logic, Language and Information 29 (4):451-489.
    Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information, which can be incomplete or conflicting, but not explicitly about facts. This layer of available (...)
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  • On epistemic and ontological interpretations of intuitionistic and paraconsistent paradigms.Walter Carnielli & Abilio Rodrigues - 2021 - Logic Journal of the IGPL 29 (4):569-584.
    From the technical point of view, philosophically neutral, the duality between a paraconsistent and a paracomplete logic (for example intuitionistic 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. The epistemic interpretation (...)
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  • Pragmatic logics for hypotheses and evidence.Massimiliano Carrara, Daniele Chiffi & Ciro De Florio - forthcoming - Logic Journal of the IGPL.
    The present paper is devoted to present two pragmatic logics and their corresponding intended interpretations according to which an illocutionary act of hypothesis-making is justified by a scintilla of evidence. The paper first introduces a general pragmatic frame for assertions, expanded to hypotheses, ${\mathsf{AH}}$ and a hypothetical pragmatic logic for evidence ${\mathsf{HLP}}$. Both ${\mathsf{AH}}$ and ${\mathsf{HLP}}$ are extensions of the Logic for Pragmatics, $\mathcal{L}^P$. We compare ${\mathsf{AH}}$ and $\mathsf{HLP}$. Then, we underline the expressive and inferential richness of both systems in (...)
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  • Normality operators and classical recapture in many-valued logic.Roberto Ciuni & Massimiliano Carrara - 2020 - Logic Journal of the IGPL 28 (5):657-683.
    In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and two properties that we call fixed-point negation property (...)
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  • Foreword: Consistency, Contradiction, and Consequence.Abílio Rodrigues & Federico Matías Pailos - 2018 - Principia: An International Journal of Epistemology 22 (1):01-05.
    Foreword : Consistency, Contradiction, and Consequence.
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  • Models & Proofs: LFIs Without a Canonical Interpretations.Eduardo Alejandro Barrio - 2018 - Principia: An International Journal of Epistemology 22 (1):87-112.
    In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic (...)
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  • Valuation Semantics for First-Order Logics of Evidence and Truth.H. Antunes, A. Rodrigues, W. Carnielli & M. E. Coniglio - 2022 - Journal of Philosophical Logic 51 (5):1141-1173.
    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 from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...)
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  • On Barrio, Lo Guercio, and Szmuc on Logics of Evidence and Truth.Abilio Rodrigues & Walter Carnielli - forthcoming - Logic and Logical Philosophy:1-26.
    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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  • The Liar Paradox: Between Evidence and Truth.Jonas Becker Arenhart & Ederson Safra Melo - forthcoming - Logic and Logical Philosophy:1-23.
    Systems of paraconsistent logics violate the law of explosion: from contradictory premises not every formula follows. One of the philosophical options for interpreting the contradictions allowed as premises in these cases was put forward recently by Carnielli and Rodrigues, with their epistemic approach to paraconsistent logics. In a nutshell, the plan consists in interpreting the contradictions in epistemic terms, as indicating the presence of non-conclusive evidence for both a proposition and its negation. Truth, in this approach, is consistent and is (...)
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  • Kripke-Style Models for Logics of Evidence and Truth.Henrique Antunes, Walter Carnielli, Andreas Kapsner & Abilio Rodrigues - 2020 - Axioms 9 (3).
    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 formula ∘A means that the information about (...)
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  • The Keisler–Shelah theorem for $\mathsf{QmbC}$ through semantical atomization.Thomas Macaulay Ferguson - 2020 - Logic Journal of the IGPL 28 (5):912-935.
    In this paper, we consider some contributions to the model theory of the logic of formal inconsistency $\mathsf{QmbC}$ as a reply to Walter Carnielli, Marcelo Coniglio, Rodrigo Podiacki and Tarcísio Rodrigues’ call for a ‘wider model theory.’ This call demands that we align the practices and techniques of model theory for logics of formal inconsistency as closely as possible with those employed in classical model theory. The key result is a proof that the Keisler–Shelah isomorphism theorem holds for $\mathsf{QmbC}$, i.e. (...)
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  • (1 other version)Dialetheism.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
    A dialetheia is a sentence, A, such that both it and its negation, A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and (...)
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  • First-order Logics of Evidence and Truth with Constant and Variable Domains.Abilio Rodrigues & Henrique Antunes - 2022 - Logica Universalis 16 (3):419-449.
    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 and truth combine them in a very natural way.
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  • Varieties of entailment: introduction to the special issue.Heinrich Wansing & Marco Ruffino - 2020 - Synthese 198 (S22):5207-5211.
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  • Logical Pluralism and Interpretations of Logical Systems.Diego Tajer & Camillo Fiore - 2022 - Logic and Logical Philosophy 31:1-26.
    Logical pluralism is a general idea that there is more than one correct logic. Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence. The authors appeal to this epistemic interpretation to briefly motivate a kind of logical pluralism: “different accounts of logical consequence may preserve different properties of propositions”. The aim of this paper is to study the prospect of (...)
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  • Semantical investigations on non-classical logics with recovery operators: negation.David Fuenmayor - forthcoming - Logic Journal of the IGPL.
    We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to ‘recover’ the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean algebras extended with additional operations subject to specific conditions of a topological nature. In this study, we focus on the paradigmatic case of negation. We demonstrate how these algebras are well-suited to provide a (...)
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  • Interpreting philosophical interpretations of paraconsistency.Jonas R. Becker Arenhart - 2022 - Synthese 200 (6):1-21.
    In this paper, we critically discuss the idea of a ‘philosophical interpretation’ of paraconsistent logics. We do so by considering the epistemic approach to paraconsistency, by Carnielli and Rodrigues, according to which paraconsistent logics should be interpreted exclusively in terms of non-conclusive evidence, and also, by considering counter-arguments by Barrio and Barrio and Da Re, according to whom paraconsistent logics are not specially tied to any specific interpretation. We begin by presenting the positions involved, and by arguing that the debate (...)
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  • Volume I: Recovery operators in logics of formal inconsistency.Eduardo Alejandro Barrio & Walter Carnielli - 2020 - Logic Journal of the IGPL 28 (5):615-623.
    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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  • The evidence approach to paraconsistency versus the paraconsistent approach to evidence.Jonas Rafael Becker Arenhart - 2020 - Synthese 198 (12):11537-11559.
    In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions, it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: interpreting paraconsistency in general through the notion (...)
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  • Deeply Disagreeing with Myself: Synchronic Intrapersonal Deep Disagreements.Patrick Bondy - 2020 - Topoi 40 (5):1225-1236.
    Interpersonal disagreement happens all the time. How to properly characterize interpersonal disagreement and how to respond to it are important problems, but the existence of such disagreements at least is obvious. The existence of intrapersonal disagreement, however, is another matter. On the one hand, we do change our minds sometimes, especially when new evidence comes in, and so there is a clear enough sense in which we can be characterized as having disagreements with our past selves. But what about synchronic (...)
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  • Paraconsistent and Paracomplete Logics Based on k-Cyclic Modal Pseudocomplemented De Morgan Algebras.Aldo Figallo-Orellano, Miguel Peréz-Gaspar & Juan Manuel Ramírez-Contreras - 2022 - Studia Logica 110 (5):1291-1325.
    The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in papers [20] and [21]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by a k-periodic automorphism -algebras). We denote by \ the automorphism where k is a positive integer. For \, the class coincides with the one studied in [20] where the automorphism works as a new unary operator which can be considered as a negation. In (...)
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  • A Brief Note on Béziau’s “Rather Trivial Theorem” About LP.Luis Estrada-González - forthcoming - Logic and Logical Philosophy:1.
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  • Time-stamped claim logic.João Rasga, Cristina Sernadas, Erisa Karafili & Luca Viganò - 2021 - Logic Journal of the IGPL 29 (3):303-332.
    The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...)
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