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  1. An Epistemic Approach to Paraconsistency: A Logic of Evidence and Truth.Walter Carnielli & Abilio Rodrigues - 2017 - Synthese 196 (9):3789-3813.
    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 Truth. The latter is a logic of (...)
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  • Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
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  • Fibring Non-Truth-Functional Logics: Completeness Preservation.C. Caleiro, W. A. Carnielli, M. E. Coniglio, A. Sernadas & C. Sernadas - 2003 - Journal of Logic, Language and Information 12 (2):183-211.
    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 thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...)
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  • Two-Valued Weak Kleene Logics.Bruno da Ré & Damian Szmuc - 2019 - Manuscrito 42 (1):1-43.
    In the literature, Weak Kleene logics are usually taken as three-valued logics. However, Suszko has challenged the main idea of many-valued logic claiming that every logic can be presented in a two-valued fashion. In this paper, we provide two-valued semantics for the Weak Kleene logics and for a number of four-valued subsystems of them. We do the same for the so-called Logics of Nonsense, which are extensions of the Weak Kleene logics with unary operators that allow looking at them as (...)
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  • Behavioral Algebraization of da Costa's C-Systems.Carlos Caleiro & Ricardo Gonçalves - 2009 - Journal of Applied Non-Classical Logics 19 (2):127-148.
    It is well-known that da Costa's C-systems of paraconsistent logic do not admit a Blok-Pigozzi algebraization. Still, an algebraic flavored semantics for them has been proposed in the literature, namely using the class of so-called da Costa algebras. However, the precise connection between these semantic structures and the C-systems was never established at the light of the theory of algebraizable logics. In this paper we propose to study the C-systems from an algebraic point of view, and to fill in this (...)
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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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  • Two-Valued Logics for Naive Truth Theory.Lucas Daniel Rosenblatt - 2015 - Australasian Journal of Logic 12 (1).
    It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical multivalued logics. In this paper I want to suggest that bivalent logic can do just as well. This is accomplished by using a non-deterministic matrix to define the negation connective. I show that the systems obtained in this way support a transparent truth predicate. The paper also contains some remarks on the conceptual interest of such (...)
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  • Paraconsistent Logical Consequence.Dale Jacquette - 1998 - Journal of Applied Non-Classical Logics 8 (4):337-351.
    ABSTRACT The concept of paraconsistent logical consequence is usually negatively defined as a validity semantics in which not every sentences is deducible or in which inferential explosion does not occur. Paraconsistency has been negatively characterized in this way because paraconsistent logics have been designed specifically to avoid the trivialization of deductive inference entailed by the classical paradoxes of material implication for applications in a system that tolerates syntactical contradictions. The effect of the negative characterization of paraconsistency has been to encourage (...)
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  • A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
    I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...)
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  • On the Way to a Wider Model Theory: Completeness Theorems for First-Order Logics of Formal Inconsistency.Walter Carnielli, Marcelo E. Coniglio, Rodrigo Podiacki & Tarcísio Rodrigues - 2014 - Review of Symbolic Logic 7 (3):548-578.
    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 logics, and can be easily extended to a large family of quantified paraconsistent (...)
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  • A Simple Approach Towards Recapturing Consistent Theories in Paraconsistent Settings.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):755-764.
    I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but (...)
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  • On Paraconsistent Deontic Logic.Newton C. A. Da Costa & Walter A. Carnielli - 1986 - Philosophia 16 (3-4):293-305.
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  • Studies in Paraconsistent Logic I: The Dialectical Principle of the Unity of Opposites.Newton C. A. Da Costa & Robert G. Wolf - 1980 - Philosophia 9 (2):189-217.
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  • Variations on da Costa C Systems and Dual-Intuitionistic Logics I. Analyses of Cω and CCω.Richard Sylvan - 1990 - Studia Logica 49 (1):47-65.
    Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC , is investigated in some detail, and dual-intuitionistic semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...)
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  • European Summer Meeting of the Association for Symbolic Logic.E. -J. Thiele - 1992 - Journal of Symbolic Logic 57 (1):282-351.
  • Studies in Paraconsistent Logic I: The Dialectical Principle of the Unity of Opposites.Newton C. A. Costa & Robert G. Wolf - 1980 - Philosophia 9 (2):189-217.
  • On Paraconsistent Deontic Logic.Newton C. A. Costa & Walter A. Carnielli - 1986 - Philosophia 16 (3-4):293-305.
    This paper develops the first deontic logic in the context of paraconsistent logics.
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