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  1. 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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  • Valuation Semantics for Intuitionic Propositional Calculus and some of its Subcalculi.Andréa Loparić - 2010 - Principia: An International Journal of Epistemology 14 (1):125-33.
    In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi. DOI:10.5007/1808-1711.2010v14n1p125.
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  • Dynamic Logics of Evidence-Based Beliefs.J. Benthem & E. Pacuit - 2011 - Studia Logica 99 (1-3):61-92.
    This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.
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  • Investigations into Logical Deduction.Gerhard Gentzen - 1964 - American Philosophical Quarterly 1 (4):288 - 306.
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  • On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
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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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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • (1 other version)On the interpretation of intuitionistic number theory.S. C. Kleene - 1945 - Journal of Symbolic Logic 10 (4):109-124.
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  • Logical pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
    Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...)
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  • Why philosophical theories of evidence are (and ought to be) ignored by scientists.Peter Achinstein - 2000 - Philosophy of Science 67 (3):180-192.
    There are two reasons, I claim, scientists do and should ignore standard philosophical theories of objective evidence: (1) Such theories propose concepts that are far too weak to give scientists what they want from evidence, viz., a good reason to believe a hypothesis; and (2) They provide concepts that make the evidential relationship a priori, whereas typically establishing an evidential claim requires empirical investigation.
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  • (1 other version)Concepts of evidence.Peter Achinstein - 1978 - Mind 87 (345):22-45.
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  • Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing. Edited by Marcelo Esteban Coniglio.
    This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...)
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  • (1 other version)Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning.Newton C. A. Da Costa & Steven French - 2003 - New York, US: Oxford University Press USA.
    In the past thirty years, two fundamental issues have emerged in the philosophy of science. One concerns the appropriate attitude we should take towards scientific theories--whether we should regard them as true or merely empirically adequate, for example. The other concerns the nature of scientific theories and models and how these might best be represented. In this ambitious book, da Costa and French bring these two issues together by arguing that theories and models should be regarded as partially rather than (...)
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  • Pluralism and Proofs.Greg Restall - 2014 - Erkenntnis 79 (S2):279-291.
    Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...)
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  • Dynamic Logics of Evidence-Based Beliefs.Johan van Benthem & Eric Pacuit - 2011 - Studia Logica 99 (1):61-92.
    This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.
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  • Dynamic dialectical logics.Diderik Batens - 1989 - In Graham Priest, Richard Routley & Jean Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 187--217.
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  • (1 other version)Evidence.Thomas Kelly - 2006 - Philosophy Compass.
    The concept of evidence is central to both epistemology and the philosophy of science. Of course, ‘evidence’ is hardly a philosopher's term of art: it is not only, or even primarily, philosophers who routinely speak of evidence, but also lawyers and judges, historians and scientists, investigative journalists and reporters, as well as the members of numerous other professions and ordinary folk in the course of everyday life. The concept of evidence would thus seem to be on firmer pre-theoretical ground than (...)
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  • (1 other version)Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning.Newton C. A. Da Costa & Steven French - 2003 - New York, US: Oup Usa.
    Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.
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  • (2 other versions)The Collected Papers of Gerhard Gentzen.K. Schütte - 1972 - Journal of Symbolic Logic 37 (4):752-753.
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  • Constructive Negations and Paraconsistency.Sergei Odintsov - 2008 - Dordrecht, Netherland: Springer.
    Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.
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  • (2 other versions)Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
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  • Propositional Calculus and Realizability.Gene F. Rose - 1954 - Journal of Symbolic Logic 19 (2):126-126.
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  • Shrieking against gluts: the solution to the 'just true' problem.Jc Beall - 2013 - Analysis 73 (3):438-445.
    This paper applies what I call the shrieking method (a refined version of an idea with roots in Priest's work) to one of – if not the – issues confronting glut-theoretic approaches to paradox (viz., the problem of ‘just true’ or, what comes to the same, ‘just false’). The paper serves as a challenge to formulate a problem of ‘just true’ that isn't solved by shrieking (as advanced in this paper), if such a problem be thought to exist.
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  • (1 other version)Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
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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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  • Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
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  • Evidence Logic: A New Look at Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-118.
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  • (1 other version)Constructible Falsity.David Nelson - 1950 - Journal of Symbolic Logic 15 (3):228-228.
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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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  • On the theory of inconsistent formal systems.Newton C. A. Costa - 1972 - Recife,: Universidade Federal de Pernambuco, Instituto de Matemática.
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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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  • (1 other version)A semantical analysis of the calculi Cn.Newton C. A. da Costa - 1977 - Notre Dame Journal of Formal Logic 18:621.
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  • Ecidence Logic: A New Look at Neighborhood Structures.Johan van Benthem, David Fernández-Duque & Eric Pacuit - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 97-118.
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  • (1 other version)A semantical Analysis of the Calculi C n.Newton C. A. Da Costa & E. H. Alves - 1977 - Notre Dame Journal Fo Formal Logic 18 (4):621-630.
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  • On the principle of the excluded middle.Andrei Kolomogorov - 1925 - In ¸ Itevanheijenoort1967. Harvard University Press. pp. 416-437.
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  • Semantics of Non-deterministic Character for LFIs.Marcelo Coniglio & Walter Carnielli - 2016 - In Walter Carnielli & Marcelo Esteban Coniglio (eds.), Paraconsistent Logic: Consistency, Contradiction and Negation. Basel, Switzerland: Springer International Publishing.
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