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Summary

In classical logic, every sentence is entailed by a contradiction: A and ¬A together entail B, for any sentences A and B whatsoever. This principle is often known as ex contradictione sequitur quodlibet (from a contradiction, everything follows), or the explosion principle. In paraconsistent logic, by contrast, this principle does not hold: arbitrary contradictions do not paraconsistently entail every sentence. Accordingly, paraconsistent logics are said to be contradiction tolerant. Semantics for paraconsistent logics can be given in a number of ways, but a common theme is that a sentence is allowed to be both true and false simultaneously. This can be achieved by introducing a third truth-value, thought of as both true and false; alternatively, it can be achieved (in the propositional case) be replacing the usual valuation function with a relation between sentences and the usual truth-values, true and false, so that a sentence may be related to either or both of these. Those who think there really are true contradictions are dialethists. Not all paraconsistent logicians are dialethists: some present paraconsistent logic as a better notion of what follows from what, or as a way to reason about inconsistent data.

Key works Asenjo 1966 and Da Costa 1974 develop the Logic of Paradox (based on theor earlier work on paraconsistency in the 1950s)Priest et al 1989 is a classic early collection of papers. Priest 2006 is the classic philosophical defense of paraconsistent logic (and of dialethism). 
Introductions da Costa & Bueno 2010 and Priest 2008 are good encyclopaedia entries on paraconsistent logic. The introduction to Priest 2005 is a clear statement of the case for paraconsistent logics; chapter 7 of Priest 2001 gives basic logical details of a few paraconsistent logics.
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  1. added 2020-05-01
    D Marconi (ed.), La formalizzazione della dialettica. Hegel, Marx e la logica contemporanea. [REVIEW]Sergio Volodia Marcello Cremaschi - 1980 - Rivista di Filosofia Neo-Scolastica 72:743-748.
  2. added 2020-04-18
    Competing Ontologies and Verbal Disputes.Jakub Mácha - 2017 - Prolegomena : Časopis Za Filozofiju 16 (1):7-21.
    The notion of ontology originates in philosophy. It has been recently employed in computer science and information technology for representing knowledge. In the first part of the paper, I argue that there is a significant overlap in these notions of ontology. Utilizing this overlap, I show in the second part that ontologies can be used for developing a new powerful heuristic method for resolving verbal disputes in philosophy. Verbal disputes can be defined in terms of ontologies: A dispute over two (...)
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  3. added 2020-03-25
    Três Vezes Não: Um Estudo Sobre as Negações Clássica, Paraconsistente e Paracompleta.Kherian Gracher - 2020 - Dissertation, Federal University of Santa Catarina
    Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...)
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  4. added 2020-03-24
    Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - manuscript
    One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...)
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  5. added 2020-02-03
    Logical Argumentation by Dynamic Proof Systems.Ofer Arieli & Christian Straßer - forthcoming - Theoretical Computer Science.
    In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...)
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  6. added 2020-02-03
    Dynamic Derivations for Sequent-Based Logical Argumentation.Ofer Arieli & Christian Straßer - 2014 - In Simon Parsons, Nir Oren, Chris Reed & Federico Cerutti (eds.), Proceedings COMMA 2014. IOS Press. pp. 89--100.
  7. added 2020-02-03
    A Paraconsistent Multi-Agent Framework for Dealing with Normative Conflicts.Mathieu Beirlaen & Christian Straßer - 2011 - In Joao Leite, Paolo Torroni, Thomas Agotnes, Guido Boella & Leon van der Torre (eds.), Computational Logic in Multi-Agent Systems. CLIMA 2011. Lecture Notes in Computer Science, vol 6814. Berlin, Germany: Springer. pp. 312–329.
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  8. added 2020-01-25
    A Compatibility Relation for Sets.Luis Felipe Bartolo Alegre - manuscript
    In this paper, I generalise the logical concept of compatibility into a set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite or contrary objects. In section 1, I formalise opposition as an operation O: E→E, where E is the set of opposable elements of our universe U, and I propose some models in section 2. From this, I define in section 3 a relation C: ℘U × ℘U × ℘U^℘U, (...)
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  9. added 2019-12-24
    First-Order Swap Structures Semantics for Some Logics of Formal Inconsistency.Marcelo E. Coniglio - forthcoming - Journal of Logic and Computation.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  10. added 2019-12-20
    Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
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  11. added 2019-12-05
    Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - manuscript
    Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...)
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  12. added 2019-11-28
    Para além das Colunas de Hércules, uma história da paraconsistência.Evandro Luis Gomes & Itala Maria Loffredo D'Ottaviano - 2017 - Campinas, Brazil: Editora da Unicamp.
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  13. added 2019-09-12
    Sylvan's Jungle Volume 1: Exploring Meinong's Jungle and Beyond.Maureen Eckert - 2018 - International: Synthese Library.
    In this first volume of The Sylvan Jungle, the editors present a scholarly edition of the first chapter, "Exploring Meinong's Jungle," of Richard Routley's 1000-plus page book, Exploring Meinong's Jungle and Beyond. Going against the Quinean orthodoxy, Routley’s aim was to support Meinong’s idea that we can truthfully refer to non-existent and even impossible objects, like Superman, unicorns and the (infamous) round-square cupola on Berkeley College. The tools of non-classical logic at Routley’s disposal enabled him to update Meinong’s project for (...)
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  14. added 2019-06-06
    The Origins of the Use of the Argument of Trivialization in the Twentieth Century.M. Andrés Bobenrieth - 2010 - History and Philosophy of Logic 31 (2):111-121.
    The origin of paraconsistent logic is closely related with the argument, 'from the assertion of two mutually contradictory statements any other statement can be deduced'; this can be referred to as ex contradictione sequitur quodlibet. Despite its medieval origin, only by the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this article is to study what happened earlier: from Principia Mathematica to that time, when it became well established. (...)
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  15. added 2019-06-06
    Kripke-Type Semantics for Da Costa's Paraconsistent Logic "C" W.Matthias Baaz - 1986 - Notre Dame Journal of Formal Logic 27:523-527.
  16. added 2019-06-06
    Hegenberg Leonidas H. B.. Tabela Das Propriedades Do Símbolo ├ . Anuário da Sociedade Paranaense de Matemática, Vol. 4 , Pp. 29–33. [REVIEW]Hugo Ribeiro - 1959 - Journal of Symbolic Logic 24 (3):273-273.
  17. added 2019-06-06
    Review: Olivier Costa de Beauregard, Extension d'Une Theorie de M. J. De Neumann au Cas des Projecteurs Non Commutables. [REVIEW]A. Borel & E. Specker - 1949 - Journal of Symbolic Logic 14 (3):192-193.
  18. added 2019-06-06
    Leeuwen and Costa's Odyssey, Vol. II. [REVIEW]Arthur Platt - 1893 - The Classical Review 7 (1-2):31-32.
  19. added 2019-06-05
    Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox.Yaroslav Petrukhin & Vasily Shangin - 2017 - Review of Symbolic Logic 10 (4):756-781.
    B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.
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  20. added 2019-06-05
    The Relevant Fragment of First Order Logic.Guillermo Badia - 2016 - Review of Symbolic Logic 9 (1):143-166.
    Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.
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  21. added 2019-05-21
    G. Priest and R. Routley. First Historical Introduction. A Preliminary History of Paraconsistent and Dialethic Approaches. Paraconsistent Logic, Essays on the Inconsistent, Edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, Pp. 3–75. - Ayda I. Arruda. Aspects of the Historical Development of Paraconsistent Logic. Paraconsistent Logic, Essays on the Inconsistent, Edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, Pp. 99–130. - G. Priest and R. Routley. Systems of Paraconsistent Logic. Paraconsistent Logic, Essays on the Inconsistent, Edited by Graham Priest, Richard Routley, and Jean Norman, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, Pp. 151–186. - G. Priest and R. Routley. Applications of Paraconsistent Logic. Paraconsistent Logic, Essays on the Inconsistent, Edited by Graham Priest, Richard Routley, and Jean Norman, Ana. [REVIEW]F. G. Asenjo - 1991 - Journal of Symbolic Logic 56 (4):1503-1504.
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  22. added 2019-05-17
    Arnon Avron. Relevance and Paraconsistency—a New Approach. The Journal of Symbolic Logic, Vol. 55 , Pp. 707–732. - Arnon Avron. Relevance and Paraconsistency—a New Approach. Part II: The Formal Systems. Notre Dame Journal of Formal Logic, Vol. 31 , Pp. 169–202. - Arnon Avron. Relevance and Paraconsistency—a New Approach. Part III: Cut-Free Gentzen-Type Systems. Notre Dame Journal of Formal Logic, Vol. 32 , Pp. 147–160. [REVIEW]Alasdair Urquhart - 1992 - Journal of Symbolic Logic 57 (4):1481-1482.
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  23. added 2019-05-06
    Manuel Bremer. An Introduction to Paraconsistent Logics. Peter Lang, Frankfurt, 2005, 249 Pp. [REVIEW]Casey McGinnis - 2005 - Bulletin of Symbolic Logic 11 (3):447-451.
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  24. added 2019-04-08
    A Hierarchy of Classical and Paraconsistent Logics.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Journal of Philosophical Logic 49 (1):93-120.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to (...)
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  25. added 2019-03-25
    Curry's Paradox.Lionel Shapiro & Jc Beall - 2017 - Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. CSLI Publications.
    “Curry’s paradox”, as the term is used by philosophers today, refers to a wide variety of paradoxes of self-reference or circularity that trace their modern ancestry to Curry (1942b) and Löb (1955). The common characteristic of these so-called Curry paradoxes is the way they exploit a notion of implication, entailment or consequence, either in the form of a connective or in the form of a predicate. Curry’s paradox arises in a number of different domains. Like Russell’s paradox, it can take (...)
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  26. added 2019-03-11
    Hegel and the Sciences. [REVIEW]Sergio Cremaschi - 1989 - The Owl of Minerva 20 (2):224-228.
    I discuss this collection of essays on Hegel and the sciences while stressing the interest of Hegel's philosophy of nature in the light of later non-mainstream developments in the life-sciences and medicine. I compare then the chapters dedicated to Hegel's logic with recent literature on para-consistent logic and re-interpretations of Hegel's own logic.
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  27. added 2019-03-09
    A Plea for Epistemic Truth: Jaina Logic From a Many-Valued Perspective.Fabien Schang - 2009 - In A. Schuman (ed.), Logic in Religious Discourse. Ontos Verlag. pp. 54--83.
    We present the Jaina theory of sevenfold predication as a 7-valued logic, in which every logical value consists in a 3-tuple of opinions. A question-answer semantics is used in order to give an intuitive characterization of these logical values in terms of opinion polls. Two different interpretations are plausible for the latest sort of opinion, depending upon whether "non-assertability" refers to incompleteness or inconsistency. It is shown hat the incomplete version of JL_{G} is equivalent to Kleene's logic K3, whereas the (...)
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  28. added 2019-02-26
    Contradictoriness, Paraconsistent Negation and Non-Intended Models of Classical Logic.Carlos A. Oller - 2016 - In Holger Andreas & Peter Verdee (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Trends In Logic. Dordrecht: Springer. pp. 103-110.
    It is usually accepted in the literature that negation is a contradictory-forming operator and that two statements are contradictories if and only if it is logically impossible for both to be true and logically impossible for both to be false. These two premises have been used by Hartley Slater [Slater, 1995] to argue that paraconsistent negation is not a “real” negation because a sentence and its paraconsistent negation can be true together. In this paper we claim that a counterpart of (...)
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  29. added 2019-02-22
    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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  30. added 2019-02-12
    Logical Revision by Counterexamples: A Case Study of the Paraconsistent Counterexample to Ex Contradictione Quodlibet.Seungrak Choi - 2019 - In Proceedings of the 14th and 15th Asian Logic Conferences. pp. 141-167.
    It is often said that a correct logical system should have no counterexample to its logical rules and the system must be revised if its rules have a counterexample. If a logical system (or theory) has a counterexample to its logical rules, do we have to revise the system? In this paper, focussing on the role of counterexamples to logical rules, we deal with the question. -/- We investigate two mutually exclusive theories of arithmetic - intuitionistic and paraconsistent theories. The (...)
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  31. added 2019-02-07
    Relevant Logics Obeying Component Homogeneity.Roberto Ciuni, Damian Szmuc & Thomas Macaulay Ferguson - 2018 - Australasian Journal of Logic 15 (2):301-361.
    This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...)
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  32. added 2019-02-07
    A Note on Goddard and Routley's Significance Logic.Damian Szmuc & Hitoshi Omori - 2018 - Australasian Journal of Logic 15 (2):431-448.
    The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this (...)
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  33. added 2019-02-04
    Recapture, Transparency, Negation and a Logic for the Catuskoti.Adrian Kreutz - 2019 - Comparative Philosophy 10 (1):67-92.
    The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. (...)
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  34. added 2019-01-31
    Review of 'Inconsistent Geometry', by Chris Mortensen. [REVIEW]Zach Weber - 2012 - Australasian Journal of Philosophy 90 (3):611-614.
    Australasian Journal of Philosophy, Volume 90, Issue 3, Page 611-614, September 2012.
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  35. added 2019-01-29
    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 logic is (...)
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  36. added 2019-01-09
    A Graph-Theoretic Account of Logics.A. Sernadas, C. Sernadas, J. Rasga & Marcelo E. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1281-1320.
    A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...)
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  37. added 2019-01-09
    On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...)
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  38. added 2019-01-08
    Non-Deterministic Algebraization of Logics by Swap Structures.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - forthcoming - Logic Journal of the IGPL.
    Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of (...)
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  39. added 2018-11-29
    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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  40. added 2018-10-03
    Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Synthese:1-17.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...)
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  41. added 2018-10-03
    A Recovery Operator for Nontransitive Approaches.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Review of Symbolic Logic 13 (1):80-104.
    In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...)
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  42. added 2018-10-03
    Track-Down Operations on Bilattices.Damian Szmuc - 2018 - In Robert Wille & Martin Lukac (eds.), Proceedings of the 48th IEEE International Symposium on Multiple-Valued Logic. Los Alamitos, California, EE. UU.: pp. 74-79.
    This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and track-down (...)
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  43. added 2018-08-09
    Logic for Exact Entailment.Kit Fine & Mark Jago - 2018 - Review of Symbolic Logic:1-21.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...)
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  44. added 2018-04-28
    In Contradiction. A Study of the Transconsistent. [REVIEW]Jan Woleński - 1989 - Studia Logica 48 (2):259-260.
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  45. added 2018-04-07
    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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  46. added 2018-04-07
    A Model-Theoretic Analysis of Fidel-Structures for mbC.Marcelo E. Coniglio - 2020 - In Can Baskent and Thomas Ferguson (ed.), Graham Priest on Dialetheism and Paraconsistency. Springer. pp. 189-216.
    In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...)
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  47. added 2018-04-07
    Maximality in Finite-Valued Lukasiewicz Logics Defined by Order Filters.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2019 - Journal of Logic and Computation 29 (1):125-156.
  48. added 2018-04-06
    Negation And Contradiction.Richard Routley Val Routley, Richard Sylvan & Richard Routley - 1985 - Revista Columbiana de Mathematicas:201 - 231.
    The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. The question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modelings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which (...)
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  49. added 2018-03-01
    Can Gödel's Incompleteness Theorem Be a Ground for Dialetheism?Seungrak Choi - 2017 - Korean Journal of Logic 20 (2):241-271.
    Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest’s argument for Dialetheism from Gödel’s theorem is unconvincing as the lesson of Gödel’s proof (or Rosser’s proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest’s inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying Gödel sentence to the inconsistent and complete theory of arithmetic. We argue, (...)
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  50. added 2018-02-18
    Dualising Intuitionictic Negation.Graham Priest - 2009 - Principia: An International Journal of Epistemology 13 (2):165-184.
    One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper (...)
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