Results for 'paraconsistent logic'

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  1. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a (...) is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)
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  2.  19
    Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing.
  3. Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
  4. Paraconsistent Logic: Essays on the Inconsistent.G. Priest, R. Routley & J. Norman (eds.) - 1989 - Philosophia Verlag.
     
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  5.  25
    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 (...)
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  6. The Paraconsistent Logic of Quantum Superpositions.Newton C. A. da Costa & Christian de Ronde - 2013 - Foundations of Physics 43 (7):845-858.
    Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...)
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  7.  71
    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 (...)
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  8. Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic.Koji Tanaka - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. 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 (...)
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  9.  33
    The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem.Jean-Yves Béziau - 2006 - Logic and Logical Philosophy 15 (2):99-111.
    We present a paraconsistent logic, called Z, based on an intuitive possible worlds semantics, in which the replacement theorem holds. We show how to axiomatize this logic and prove the completeness theorem.
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  10.  55
    Frontiers of Paraconsistent Logic.Diderik Batens - 2000
  11.  73
    Real Analysis in Paraconsistent Logic.Maarten McKubre-Jordens & Zach Weber - 2012 - Journal of Philosophical Logic 41 (5):901-922.
    This paper begins an analysis of the real line using an inconsistency-tolerant (paraconsistent) logic. We show that basic field and compactness properties hold, by way of novel proofs that make no use of consistency-reliant inferences; some techniques from constructive analysis are used instead. While no inconsistencies are found in the algebraic operations on the real number field, prospects for other non-trivializing contradictions are left open.
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  12.  15
    Paraconsistent Logic From a Modal Viewpoint.Jean-Yves Béziau - 2005 - Journal of Applied Logic 3 (1):7-14.
  13.  77
    Why Paraconsistent Logic Can Only Tell Half the Truth.Joachim Bromand - 2002 - Mind 111 (444):741-749.
    The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into (...) logic in order to avoid strengthened liar paradoxes. (shrink)
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  14.  13
    New Directions in Paraconsistent Logic.Jean-Yves Beziau (ed.) - 2015 - New Delhi, India: Springer, India.
    The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. (...)
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  15.  71
    Paraconsistent Logic and Model Theory.Elias H. Alves - 1984 - Studia Logica 43 (1-2):17 - 32.
    The object of this paper is to show how one is able to construct a paraconsistent theory of models that reflects much of the classical one. In other words the aim is to demonstrate that there is a very smooth and natural transition from the model theory of classical logic to that of certain categories of paraconsistent logic. To this end we take an extension of da Costa''sC 1 = (obtained by adding the axiom A A) (...)
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  16.  20
    Paraconsistent Logic: Essays on the Inconsistent.L. R. S., Graham Priest, Richard Sylvan & Jean Norman - 1991 - Philosophical Quarterly 41 (165):515.
  17. Systems of Paraconsistent Logic.Graham Priest & Richard Routley - 1989 - In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 142--155.
     
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  18.  21
    Paraconsistent Logic in a Historical Perspective.Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno - 1995 - Logique Et Analyse 38:111-125.
  19.  38
    The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism. [REVIEW]Nicholas D. McGinnis - 2013 - Foundations of Science 18 (4):625-640.
    Paraconsistent logics are characterized by rejection of ex falso quodlibet, the principle of explosion, which states that from a contradiction, anything can be derived. Strikingly these logics have found a wide range of application, despite the misgivings of philosophers as prominent as Lewis and Putnam. Such applications, I will argue, are of significant philosophical interest. They suggest ways to employ these logics in philosophical and scientific theories. To this end I will sketch out a ‘naturalized semantic dialetheism’ following Priest’s (...)
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  20.  28
    Paraconsistent Logic: The View From the Right.Peter K. Schotch - 1992 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:421 - 429.
    "The best known approaches to "reasoning with inconsistent data" require a logical framework which is decidedly non-classical. An alternative is presented here, beginning with some motivation which has been surprised in the work of C.I. Lewis, which does not require ripping great swatches from the fabric of classical logic. In effect, the position taken in this essay is representative of an approach in which one assumes the correctness of classical methods excepting only the cases in which the premise set (...)
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  21.  11
    A System of Paraconsistent Logic Equipped with Classical Negation.Toshiharu Waragai & Hitoshi Omori - 2009 - Journal of the Japan Association for Philosophy of Science 36 (1):9-18.
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  22. Paraconsistent Logic.Newton C. A. Costa & Otávio Bueno - 2010 - In Susana Nuccetelli, Ofelia Schutte & Otávio Bueno (eds.), A Companion to Latin American Philosophy. Wiley-Blackwell.
  23. Paraconsistent Logic.Newton da Costa & Otávio Bueno - 2010 - In Susana Nuccetelli, Ofelia Schutte & Otávio Bueno (eds.), A Companion to Latin American Philosophy. Wiley-Blackwell.
  24.  27
    Opening Address: Paraconsistent Logic.Newton C. A. Da Costa - 1999 - Logic and Logical Philosophy 7:25.
    I am honoured with and touched by the invitation of delivering the opening address of this Congress. Firstly, to see paraconsistent logic flourishing and growing, as we can readily see by simply glacing over the programme of this conference, is among one of my greatest joys. Secondly, and equally important, because this congress takes place in the University of Toruń.I am honoured for having lectured here, a most congenial and stimulating place, and could not think of a better (...)
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  25.  67
    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.
  26.  24
    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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  27.  5
    Introduction to Paraconsistent Logic.Graham Priest & Richard Routley - 1984 - Studia Logica 43 (1-2):3-16.
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  28.  14
    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 (...)
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  29.  38
    Paraconsistent Logic! (A Reply to Slater) Jean-Yves BéziauFoot Note 1_.Blaise Pascal - unknown
    Paraconsistent logic is the study of logics in which there are some theories embodying contradictions but which are not trivial, in particular in a paraconsistent logic, the ex contradictione sequitur quod libet, which can be formalized as Cn(T, a,¬a)=F is not valid. Since nearly half a century various systems of paraconsistent logic have been proposed and studied. This field of research is classified under a special section (B53) in the Mathematical Reviews and watching this (...)
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  30.  14
    Aspects of Paraconsistent Logic.Newton C. A. da Costa, Jean-Yves Béziau & Otávio A. S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  31.  10
    Aspects of Paraconsistent Logic.Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno - 1995 - Logic Journal of the IGPL 3 (4):597-614.
  32.  62
    Remarks on the Epistemic Interpretation of Paraconsistent Logic.Nicolás Lo Guercio & Damian Szmuc - 2018 - Principia: An International Journal of Epistemology 22 (1):153-170.
    In a recent work, Walter Carnielli and Abilio Rodrigues present an epistemically motivated interpretation of paraconsistent logic. In their view, when there is conflicting evidence with regard to a proposition A (i.e. when there is both evidence in favor of A and evidence in favor of ¬A) both A and ¬A should be accepted without thereby accepting any proposition B whatsoever. Hence, reasoning within their system intends to mirror, and thus, should be constrained by, the way in which (...)
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  33.  21
    Relations Between Paraconsistent Logic and Many-Valued Logic.Newton Ca da Costa & Elias H. Alves - 1981 - Bulletin of the Section of Logic 10 (4):185-191.
  34. If Logic Meets Paraconsistent Logic.Jaakko Hintikka - unknown
    particular alternative logic could be relevant to another one? The most important part of a response to this question is to remind the reader of the fact that independence friendly (IF) logic is not an alternative or “nonclassical” logic. (See here especially Hintikka, “There is only one logic”, forthcoming.) It is not calculated to capture some particular kind of reasoning that cannot be handled in the “classical” logic that should rather be called the received or (...)
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  35.  10
    Laws of Form and Paraconsistent Logic[REVIEW]Jean Paul Van Bendegem - 2017 - Constructivist Foundations 13 (1):21-22.
    The aim of this commentary is to show that a new development in formal logic, namely paraconsistent logic, should be connected with the laws of form. This note also includes some personal history to serve as background.
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  36. From Paraconsistent Logic to Universal Logic.Jean-Yves Béziau - 2001 - Sorites 12:5-32.
    For several years I have been developing a general theory of logics that I have called Universal Logic. In this article I will try to describe how I was led to this theory and how I have progressively conceived it, starting my researches about ten years ago in Paris in paraconsistent logic and the broadening my horizons, pursuing my researches in Brazil, Poland and the USA.
     
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  37. Paraconsistent Logic!Jean-Yves Béziau - 2006 - Sorites 17:17-25.
    We answer Slater's argument according to which paraconsistent logic is a result of a verbal confusion between «contradictories» and «subcontraries». We show that if such notions are understood within classical logic, the argument is invalid, due to the fact that most paraconsistent logics cannot be translated into classical logic. However we prove that if such notions are understood from the point of view of a particular logic, a contradictory forming function in this logic (...)
     
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  38.  51
    The Class of Extensions of Nelson's Paraconsistent Logic.Sergei P. Odintsov - 2005 - Studia Logica 80 (2-3):291-320.
    The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
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  39.  34
    On a “Most Telling” Argument for Paraconsistent Logic.Michaelis Michael - 2016 - Synthese 193 (10).
    Priest and others have presented their “most telling” argument for paraconsistent logic: that only paraconsistent logics allow non-trivial inconsistent theories. This is a very prevalent argument; occurring as it does in the work of many relevant and more generally paraconsistent logicians. However this argument can be shown to be unsuccessful. There is a crucial ambiguity in the notion of non-triviality. Disambiguated the most telling reason for paraconsistent logics is either question-begging or mistaken. This highlights an (...)
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  40. Aspects of the Historical Development of Paraconsistent Logic.Ayda I. Arruda - 1989 - In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. pp. 99--130.
  41.  10
    On Recent Applications of Paraconsistent Logic: An Exploratory Literature Review.A. Zamansky - 2019 - Journal of Applied Non-Classical Logics 29 (4):382-391.
    This paper aims to empirically explore the state of practical applications of paraconsistent logics. To this end, we performed an exploratory literature review, analysing papers published between the years 2015 and 2018. Paraconsistent formalisms based on annotated logics are practically the sole type of approach we found to be applied in engineering applications. The engineering problems solved by paraconsistent approaches were mainly in the fields of signal and image processing and decision support. The results of our exploratory (...)
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  42.  8
    An Encompassing Framework for Paraconsistent Logic Programs.João Alcântara, Carlos Viegas Damásio & Luís Moniz Pereira - 2005 - Journal of Applied Logic 3 (1):67-95.
  43.  58
    Paraconsistent Logic in The Office.Morgan Luck - 2008 - The Philosophers' Magazine 42 (42):100-104.
    Normally, we would accuse anyone who holds inconsistent beliefs of irrationality. However, Keenan apologists may claim that in some circumstances it does seem perfectly rational to hold inconsistent beliefs. And we are not alone in this assertion. A small band of philosophers, led most notably by Graham Priest, have also championed this cause, the cause of paraconsistency.
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    Paraconsistent Logic in The Office.Morgan Luck - 2008 - The Philosophers' Magazine 42:100-104.
    Normally, we would accuse anyone who holds inconsistent beliefs of irrationality. However, Keenan apologists may claim that in some circumstances it does seem perfectly rational to hold inconsistent beliefs. And we are not alone in this assertion. A small band of philosophers, led most notably by Graham Priest, have also championed this cause, the cause of paraconsistency.
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  45. Paraconsistent Logic: A Proof-Theoretical Approach.Hubert Marraud - 2006 - Teorema: International Journal of Philosophy 25 (2):5-24.
     
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  46. Paraconsistent Logic Essays on the Inconsistent.Graham Priest, Richard Routley & Jean Norman - 1993 - British Journal for the Philosophy of Science 44 (1):167-170.
     
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  47. Paraconsistent Logic Essays on the Inconsistent.Graham Priest, Richard Routley & Jean Normann - 1992 - Studia Logica 51 (2):344-346.
     
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  48.  34
    Algebraic Study of Sette's Maximal Paraconsistent Logic.Alexej P. Pynko - 1995 - Studia Logica 54 (1):89 - 128.
    The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to (...)
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  49.  19
    Opening Address: Paraconsistent Logic.Newton C. A. Da Costa - 1999 - Logic and Logical Philosophy 7:25-34.
  50.  19
    Heaps and Gluts: Paraconsistent Logic Applied to Vagueness.Joanna Odrowąż-Sypniewska - 1999 - Logic and Logical Philosophy 7:179.
    This paper is an attempt to show that the subvaluation theory isnot a good theory of vagueness. It begins with a short review of supervaluation and subvaluation theories and procedes to evaluate the subvaluation theory. Subvaluationism shares all the main short-comings of supervaluationism.Moreover, the solution to the sorites paradox proposed by subvaluationists isnot satisfactory. There is another solution which subvaluationists could availthemselves of, but it destroys the whole motivation for using a paraconsistentlogic and is not different from the one offered (...)
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