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  1. Recovery Operators, Paraconsistency and Duality.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2020 - Logic Journal of the IGPL 28 (5):624-656.
    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 scenario, while LFUs recover the validity of (...)
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  • Subvaluationism and Classical Recapture.Paula Teijeiro - 2020 - Logic Journal of the IGPL 28 (5):832-844.
    Adopting a non-classical logic may not imply resigning the classical theories that have proven their worth. Nevertheless, the project of classical recapture poses some challenges, some of them specific to paraconsistent approaches. In this article, we analyse the consequences of introducing a recovery operator to subvaluationist logic. We argue that the classical recovery can indeed be carried out in a subvaluationist setting, but that doing so amounts to committing to a hierarchy of recaptures.
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  • ${LFIs}$ and Methods of Classical Recapture.Diego Tajer - 2020 - Logic Journal of the IGPL 28 (5):807-816.
    In this paper, I will argue that Logics of Formal Inconsistency $$ can be used as very sophisticated and powerful methods of classical recapture. I will compare $LFIs$ with the well-known non-monotonic logics by Batens and Priest and the ‘shrieking’ rules of Beall. I will show that these proposals can be represented in $LFIs$ and that $LFIs$ give room to more complex and varied recapturing strategies.
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  • Fraïssé’s Theorem for Logics of Formal Inconsistency.Bruno R. Mendonça & Walter A. Carnielli - 2020 - Logic Journal of the IGPL 28 (5):1060-1072.
    We prove that the minimal Logic of Formal Inconsistency $\mathsf{QmbC}$ validates a weaker version of Fraïssé’s theorem. LFIs are paraconsistent logics that relativize the Principle of Explosion only to consistent formulas. Now, despite the recent interest in LFIs, their model-theoretic properties are still not fully understood. Our aim in this paper is to investigate the situation. Our interest in FT has to do with its fruitfulness; the preservation of FT indicates that a number of other classical semantic properties can be (...)
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  • On Formal Aspects of the Epistemic Approach to Paraconsistency.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - 2018 - In Max Freund, Max Fernandez de Castro & Marco Ruffino (eds.), Logic and Philosophy of Logic: Recent Trends in Latin America and Spain. London: 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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  • 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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  • Recovery Operators, Paraconsistency and Duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - forthcoming - Logic Journal of the IGPL.
    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 paraconsistent scenario, while LFUs recover the (...)
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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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  • 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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