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  1. Assertion, denial and non-classical theories.Greg Restall - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 81--99.
    In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...)
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  • Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2012 - Dordrecht, Netherland: Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  • Paraconsistent Logic.David Ripley - 2015 - Journal of Philosophical Logic 44 (6):771-780.
    In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...)
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  • Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic.Koji Tanaka - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 15--25.
    Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...)
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  • A Non-deterministic View on Non-classical Negations.Arnon Avron - 2005 - Studia Logica 80 (2-3):159-194.
    We investigate two large families of logics, differing from each other by the treatment of negation. The logics in one of them are obtained from the positive fragment of classical logic (with or without a propositional constant ff for “the false”) by adding various standard Gentzen-type rules for negation. The logics in the other family are similarly obtained from LJ+, the positive fragment of intuitionistic logic (again, with or without ff). For all the systems, we provide simple semantics which is (...)
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  • Modulated fibring and the collapsing problem.Cristina Sernadas, João Rasga & Walter A. Carnielli - 2002 - Journal of Symbolic Logic 67 (4):1541-1569.
    Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...)
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  • Possible-translations semantics for some weak classically-based paraconsistent logics.João Marcos - 2008 - Journal of Applied Non-Classical Logics 18 (1):7-28.
    In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...)
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  • Distribution in the logic of meaning containment and in quantum mechanics.Ross T. Brady & Andrea Meinander - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 223--255.
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  • A family of genuine and non-algebraisable C-systems.Mauricio Osorio, Aldo Figallo-Orellano & Miguel Pérez-Gaspar - 2021 - Journal of Applied Non-Classical Logics 31 (1):56-84.
    In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsist...
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  • Pluralism and “Bad” Mathematical Theories: Challenging our Prejudices.Michèle Friend - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 277--307.
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  • Revisiting $\mathbb{Z}$.Mauricio Osorio, José Luis Carballido & Claudia Zepeda - 2014 - Notre Dame Journal of Formal Logic 55 (1):129-155.
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  • Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 257--276.
    I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...)
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  • On discourses addressed by infidel logicians.Walter Carnielli & Marcelo E. Coniglio - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 27--41.
    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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  • Weakening and Extending {mathbb{Z}}.Mauricio Osorio, J. L. Carballido, C. Zepeda & J. A. Castellanos - 2015 - Logica Universalis 9 (3):383-409.
    By weakening an inference rule satisfied by logic daC, we define a new paraconsistent logic, which is weaker than logic \ and G′ 3, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism. Besides, daC ' helps to understand the relationships among other logics, in particular daC, \ and PH1.
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  • A Hierarchy of Weak Double Negations.Norihiro Kamide - 2013 - Studia Logica 101 (6):1277-1297.
    In this paper, a way of constructing many-valued paraconsistent logics with weak double negation axioms is proposed. A hierarchy of weak double negation axioms is addressed in this way. The many-valued paraconsistent logics constructed are defined as Gentzen-type sequent calculi. The completeness and cut-elimination theorems for these logics are proved in a uniform way. The logics constructed are also shown to be decidable.
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  • A categorial approach to the combination of logics.Walter A. Carnielli & Marcelo E. Coniglio - 1999 - Manuscrito 22 (2):69-94.
    In this paper we propose a very general de nition 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, since they provide a new (...)
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  • Notes on inconsistent set theory.Zach Weber - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 315--328.
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  • Vague Inclosures.Graham Priest - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 367--377.
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  • On the system CB1 and a lattice of the paraconsistent calculi.Janusz Ciuciura - forthcoming - Logic and Logical Philosophy:1.
    In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB1, is an extension of systems PI, C min and B1, and a proper subsystem of Sette’s calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi.
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  • Weakening of Intuitionistic Negation for Many-valued Paraconsistent da Costa System.Zoran Majkić - 2008 - Notre Dame Journal of Formal Logic 49 (4):401-424.
    In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak negation. After that, (...)
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  • Information, Negation, and Paraconsistency.Edwin D. Mares - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 43--55.
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  • FDE: A Logic of Clutters.Ray E. Jennings & Yue Chen - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 163--172.
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  • Noisy vs. Merely Equivocal Logics.Patrick Allo - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 57--79.
    Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...)
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  • A Paraconsistentist Approach to Chisholm's Paradox.Marcelo Esteban Coniglio & Newton Marques Peron - 2009 - Principia: An International Journal of Epistemology 13 (3):299-326.
    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 well-known Chisholm's paradox, taking profit of the fact that, besides contradictory obligations do (...)
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  • An Infinite Family of Finite-Valued Paraconsistent Algebraizable Logics.Hugo Albuquerque & Carlos Caleiro - forthcoming - Studia Logica:1-28.
    We present a new infinite family of finite-valued paraconsistent logics—whose _n_-th member we call _Sette’s logic of order_ _n_ and denote by \({\mathscr {S}}_n\) —all of which extending da Costa’s logic \({\mathscr {C}}_1\) and extended by classical logic \(\mathcal {C\!\hspace{0.0pt}L}\). We classify the family \(\{ {\mathscr {S}}_n: n \ge 2 \}\) within the Leibniz hierarchy by proving that all its members are finitely algebraizable. We also prove a completeness theorem for each logic \({\mathscr {S}}_n\) wrt. a single logical matrix and (...)
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  • Some new results on PCL1 and its related systems.Toshiharu Waragai & Hitoshi Omori - 2010 - Logic and Logical Philosophy 19 (1-2):129-158.
    In [Waragai & Shidori, 2007], a system of paraconsistent logic called PCL1, which takes a similar approach to that of da Costa, is proposed. The present paper gives further results on this system and its related systems. Those results include the concrete condition to enrich the system PCL1 with the classical negation, a comparison of the concrete notion of “behaving classically” given by da Costa and by Waragai and Shidori, and a characterisation of the notion of “behaving classically” given by (...)
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  • New arguments for adaptive logics as unifying frame for the defeasible handling of inconsistency.Diderik Batens - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 101--122.
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  • Consequence as Preservation: Some Refinements.Bryson Brown - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 123--139.
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  • Proof theory and mathematical meaning of paraconsistent C-systems.Paolo Gentilini - 2011 - Journal of Applied Logic 9 (3):171-202.
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  • Are the Sorites and Liar Paradox of a Kind?Dominic Hyde - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 349--366.
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  • Arithmetic Starred.Chris Mortensen - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 309--314.
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  • On Modal Logics Defining Jaśkowski's D2-Consequence.Marek Nasieniewski & Andrzej Pietruszczak - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 141--161.
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  • A Paraconsistent and Substructural Conditional Logic.Francesco Paoli - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 173--198.
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  • Paraconsistent conjectural deduction based on logical entropy measures I: C-systems as non-standard inference framework.Paola Forcheri & Paolo Gentilini - 2005 - Journal of Applied Non-Classical Logics 15 (3):285-319.
    A conjectural inference is proposed, aimed at producing conjectural theorems from formal conjectures assumed as axioms, as well as admitting contradictory statements as conjectural theorems. To this end, we employ Paraconsistent Informational Logic, which provides a formal setting where the notion of conjecture formulated by an epistemic agent can be defined. The paraconsistent systems on which conjectural deduction is based are sequent formulations of the C-systems presented in Carnielli-Marcos [CAR 02b]. Thus, conjectural deduction may also be considered to be a (...)
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  • Paraconsistent Logic and Weakening of Intuitionistic Negation.Zoran Majkić - 2012 - Journal of Intelligent Systems 21 (3):255-270.
    . A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. In an earlier paper [Notre Dame J. Form. Log. 49, 401–424], we developed the systems of weakening of intuitionistic negation logic, called and, in the spirit of da Costa's approach by preserving, differently from da Costa, the fundamental properties of negation: antitonicity, inversion and additivity for distributive lattices. Taking into account these results, we make some observations on the modified systems of and, (...)
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