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On formal aspects of the epistemic approach to paraconsistency

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 (2018)

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  1. Algebraizable Logics.W. J. Blok & Don Pigozzi - 1989 - Advanced Reasoning Forum.
    W. J. Blok and Don Pigozzi set out to try to answer the question of what it means for a logic to have algebraic semantics. In this seminal book they transformed the study of algebraic logic by giving a general framework for the study of logics by algebraic means. The Dutch mathematician W. J. Blok (1947-2003) received his doctorate from the University of Amsterdam in 1979 and was Professor of Mathematics at the University of Illinois, Chicago until his death in (...)
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  • Justification Logic.Sergei Artemov - forthcoming - Stanford Encyclopedia of Philosophy.
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  • The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
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  • Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
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  • An Epistemic Approach to Paraconsistency: A Logic of Evidence and Truth.Walter Carnielli & Abilio Rodrigues - 2019 - 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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  • Towards a Philosophical Understanding of the Logics of Formal Inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    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 that in order to philosophically justify (...)
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  • Nearly Every Normal Modal Logic is Paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.
    An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...)
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  • Modal Logics, Justification Logics, and Realization.Melvin Fitting - 2016 - Annals of Pure and Applied Logic 167 (8):615-648.
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  • Paraconsistent Logic, Evidence, and Justification.Melvin Fitting - 2017 - Studia Logica 105 (6):1149-1166.
    In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as asserting (...)
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  • The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
    We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...)
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  • Notes on N-Lattices and Constructive Logic with Strong Negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
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  • On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
    N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...)
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  • Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
    In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...)
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  • Investigations Into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
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