Search results for 'Paraconsistent logic' (try it on Scholar)

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  1. Maarten McKubre-Jordens & Zach Weber (2012). Real Analysis in Paraconsistent Logic. Journal of Philosophical Logic 41 (5):901-922.score: 246.0
    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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  2. Olivier Esser (2003). A Strong Model of Paraconsistent Logic. Notre Dame Journal of Formal Logic 44 (3):149-156.score: 246.0
    The purpose of this paper is mainly to give a model of paraconsistent logic satisfying the "Frege comprehension scheme" in which we can develop standard set theory (and even much more as we shall see). This is the continuation of the work of Hinnion and Libert.
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  3. Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.score: 216.0
    In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.
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  4. Newton C. A. Costa & Walter A. Carnielli (1986). On Paraconsistent Deontic Logic. Philosophia 16 (3-4):293-305.score: 206.0
    This paper develops the first deontic logic in the context of paraconsistent logics.
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  5. Sergei P. Odintsov (2010). Priestley Duality for Paraconsistent Nelson's Logic. Studia Logica 96 (1):65-93.score: 204.0
    The variety of N4┴ -lattices provides an algebraic semantics for the logic N4┴, a version of Nelson's logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of N4┴-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
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  6. Nicholas D. McGinnis (2013). The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism. [REVIEW] Foundations of Science 18 (4):625-640.score: 188.0
    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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  7. Jean-Yves Béziau (2006). The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem. Logic and Logical Philosophy 15 (2):99-111.score: 186.0
    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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  8. Arief Daynes (2006). A New Technique for Proving Realisability and Consistency Theorems Using Finite Paraconsistent Models of Cut‐Free Logic. Mathematical Logic Quarterly 52 (6):540-554.score: 186.0
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  9. Alexej P. Pynko (2002). Extensions of Hałkowska–Zajac's Three-Valued Paraconsistent Logic. Archive for Mathematical Logic 41 (3):299-307.score: 186.0
    As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we (...)
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  10. Joachim Bromand (2002). Why Paraconsistent Logic Can Only Tell Half the Truth. Mind 111 (444):741-749.score: 180.0
    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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  11. Elias H. Alves (1984). Paraconsistent Logic and Model Theory. Studia Logica 43 (1-2):17 - 32.score: 180.0
    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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  12. Newton C. A. da Costa & Décio Krause, Remarks on the Applications of Paraconsistent Logic to Physics.score: 180.0
    In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.
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  13. Arthur Buchsbaum & Tarcisio Pequeno (1993). A Reasoning Method for a Paraconsistent Logic. Studia Logica 52 (2):281 - 289.score: 180.0
    A proof method for automation of reasoning in a paraconsistent logic, the calculus C1* of da Costa, is presented. The method is analytical, using a specially designed tableau system. Actually two tableau systems were created. A first one, with a small number of rules in order to be mathematically convenient, is used to prove the soundness and the completeness of the method. The other one, which is equivalent to the former, is a system of derived rules designed to (...)
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  14. Blaise Pascal, Paraconsistent Logic! (A Reply to Slater) Jean-Yves BéziauFoot Note 1_.score: 180.0
    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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  15. Pandora Hadzidaki, Bohr's Atomic Model and Paraconsistent Logic.score: 180.0
    Bohr’s atomic model is one of the better known examples of empirically successful, albeit inconsistent, theoretical schemes in the history of physics. For this reason, many philosophers use this model to illustrate their position for the occurrence and the function of inconsistency in science. In this paper, I proceed to a critical comparison of the structure and the aims of Bohr’s research program – the starting point of which was the formulation of his model – with some of its contemporary (...)
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  16. Andrés Bobenrieth (2007). Hilbert, Trivialization and Paraconsistent Logic. The Proceedings of the Twenty-First World Congress of Philosophy 5:37-43.score: 180.0
    The origin of Paraconsistent Logic is closely related with the argument that from the assertion of two mutually contradictory statements any other statement can be deduced, which can be referred to as ex contradict!one sequitur quodlibet (ECSQ). Despite its medieval origin, only in the 1930s did it become the main reason for the unfeasibility of having contradictions in a deductive system. The purpose of this paper is to study what happened before: from Principia Mathematica to that time, when (...)
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  17. Valentin A. Bazhanov (2008). Heuristic Ground of Paraconsistent Logic. Proceedings of the Xxii World Congress of Philosophy 13:5-8.score: 180.0
    The paper deals with the heuristic prerequisites of paraconsistent logic in the case of imaginary logic of N.A. Vasiliev proposed in 1910.
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  18. Ayda I. Arruda (1989). Aspects of the Historical Development of Paraconsistent Logic. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 99--130.score: 180.0
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  19. Joke Meheus (2000). An Extremely Rich Paraconsistent Logic and the Adaptive Logic Based on It. In Frontiers of Paraconsistent Logic. Research Studies Press. 189-201.score: 180.0
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  20. Graham Priest & Richard Routley (1989). Systems of Paraconsistent Logic. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 142--155.score: 180.0
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  21. Arnon Avron, 5-Valued Non-Deterministic Semantics for The Basic Paraconsistent Logic mCi.score: 176.0
    One of the most important paraconsistent logics is the logic mCi, which is one of the two basic logics of formal inconsistency. In this paper we present a 5-valued characteristic nondeterministic matrix for mCi. This provides a quite non-trivial example for the utility and effectiveness of the use of non-deterministic many-valued semantics.
     
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  22. Sergei P. Odintsov (2005). The Class of Extensions of Nelson's Paraconsistent Logic. Studia Logica 80 (2-3):291 - 320.score: 174.0
    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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  23. Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. Studia Logica 54 (1):89 - 128.score: 174.0
    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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  24. Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.score: 172.0
    Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be (...)
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  25. N. Da Costa & C. De Ronde (2013). The Paraconsistent Logic of Quantum Superpositions. Foundations of Physics 43 (7):845-858.score: 168.0
    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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  26. Bryson Brown (1999). Yes, Virginia, There Really Are Paraconsistent Logics. Journal of Philosophical Logic 28 (5):489-500.score: 166.0
    B. H. Slater has argued that there cannot be any truly paraconsistent logics, because it's always more plausible to suppose whatever "negation" symbol is used in the language is not a real negation, than to accept the paraconsistent reading. In this paper I neither endorse nor dispute Slater's argument concerning negation; instead, my aim is to show that as an argument against paraconsistency, it misses (some of) the target. A important class of paraconsistent logics - the preservationist (...)
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  27. Norihiro Kamide & Heinrich Wansing (2010). Symmetric and Dual Paraconsistent Logics. Logic and Logical Philosophy 19 (1-2):7-30.score: 166.0
    Two new first-order paraconsistent logics with De Morgan-type negations and co-implication, called symmetric paraconsistent logic (SPL) and dual paraconsistent logic (DPL), are introduced as Gentzen-type sequent calculi. The logic SPL is symmetric in the sense that the rule of contraposition is admissible in cut-free SPL. By using this symmetry property, a simpler cut-free sequent calculus for SPL is obtained. The logic DPL is not symmetric, but it has the duality principle. Simple semantics for (...)
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  28. Koji Tanaka (2013). Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic. In. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 15--25.score: 164.0
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  29. Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) (2013). Paraconsistency: Logic and Applications. Springer.score: 160.0
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on (...)
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  30. Jaakko Hintikka, If Logic Meets Paraconsistent Logic.score: 156.0
    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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  31. Matthias Baaz (1986). Kripke-Type Semantics for da Costa's Paraconsistent Logic ${\Rm C}_\Omega$. Notre Dame Journal of Formal Logic 27 (4):523-527.score: 156.0
  32. Peter K. Schotch (1992). Paraconsistent Logic: The View From the Right. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992:421 - 429.score: 156.0
    "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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  33. Newton C. A. Da Costa (2014). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25.score: 156.0
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  34. F. G. Asenjo (1991). Priest G. And Routley R.. First Historical Introduction. A Preliminary History of Paraconsistent and Dialethic Approaches. Paraconsistent Logic, Essays on the Inconsistent, Edited by Priest Graham, Routley Richard, and Norman Jean, Analytica, Philosophia Verlag, Munich, Hamden, and Vienna, 1989, Pp. 3–75. Arruda Ayda I.. Aspects of the Historical Development of Paraconsistent Logic. Paraconsistent Logic, Essays on the Inconsistent, Edited by Priest Graham, Routley Richard, and Norman Jean, Analytica ... [REVIEW] Journal of Symbolic Logic 56 (4):1503-1504.score: 156.0
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  35. Soma Dutta & Mihir K. Chakraborty (2011). Negation and Paraconsistent Logics. Logica Universalis 5 (1):165-176.score: 156.0
    Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation ( ${\neg}$ ) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent (...)
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  36. Yu V. Ivlev (2004). Quasi-Matrix Logic as a Paraconsistent Logic for Dubitable Information. Logic and Logical Philosophy 8:91.score: 156.0
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  37. Joanna Odrowąż-Sypniewska (2014). Heaps and Gluts: Paraconsistent Logic Applied to Vagueness. Logic and Logical Philosophy 7:179.score: 156.0
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  38. Newton C. A. Da Costa (2004). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25-34.score: 156.0
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  39. Newton Ca da Costa & Elias H. Alves (1981). Relations Between Paraconsistent Logic and Many-Valued Logic. Bulletin of the Section of Logic 10 (4):185-191.score: 156.0
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  40. Norihiro Kamide (2010). An Embedding-Based Completeness Proof for Nelson's Paraconsistent Logic. Bulletin of the Section of Logic 39 (3/4):205-214.score: 156.0
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  41. J. Odrowaz-Sypneiwska (1999). Heaps and Gluts: Paraconsistent Logic Applied to Vagueness. Logic and Logical Philosophy 7:179-193.score: 156.0
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  42. Morgan Luck (2008). Paraconsistent Logic in The Office. The Philosophers' Magazine 42 (42):100-104.score: 152.0
    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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  43. Antonino Drago (2001). Vasiliev's Paraconsistent Logic Interpreted by Means of the Dual Role Played by the Double Negation Law. Journal of Applied Non-Classical Logics 11 (3-4):281-294.score: 152.0
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  44. Norihiro Kamide (2005). Natural Deduction Systems for Nelson's Paraconsistent Logic and its Neighbors. Journal of Applied Non-Classical Logics 15 (4):405-435.score: 152.0
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  45. Gerson Zaverucha (1992). Relevant Logic as a Basis for Paraconsistent Epistemic Logics. Journal of Applied Non-Classical Logics 2 (2):225-241.score: 152.0
    ABSTRACT In this work we argue for relevant logics as a basis for paraconsistent epistemic logics. In order to do so, a paraconsistent nonmonotonic multi-agent epistemic logic, MDR (for Modal Defeasible Relevant), is briefly introduced. In MDR each agent has two kinds of belief: an absolute belief that P, represented by AiP, and a defeasible belief that P, represented by DiP. Therefore, an agent can reason with his own absolute and defeasible beliefs about the world and also (...)
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  46. Graham Priest, Paraconsistent Logic. Stanford Encyclopedia of Philosophy.score: 150.0
  47. Diego Marconi (1984). Wittgenstein on Contradiction and the Philosophy of Paraconsistent Logic. History of Philosophy Quarterly 1 (3):333 - 352.score: 150.0
  48. Manuel Bremer (2008). The Logic of Truth in Paraconsistent Internal Realism. Studia Philosophica Estonica 1 (1):76-83.score: 150.0
    The paper discusses which modal principles should hold for a truth operator answering to the truth theory of internal realism. It turns out that the logic of truth in internal realism is isomorphic to the modal system S4.
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  49. Diderik Batens, Christian Edward Mortensen, Graham Priest & Jean-Paul Van Bendegem, Frontiers of Paraconsistent Logic.score: 150.0
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