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

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  1.  42
    Maarten McKubre-Jordens & Zach Weber (2012). Real Analysis in Paraconsistent Logic. 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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  2.  12
    Newton C. A. Da Costa (1999). Opening Address: Paraconsistent Logic. 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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  3.  11
    Olivier Esser (2003). A Strong Model of Paraconsistent Logic. Notre Dame Journal of Formal Logic 44 (3):149-156.
    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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  4.  32
    David Ripley (forthcoming). Paraconsistent Logic. Journal of Philosophical Logic:1-10.
    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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  5.  11
    Pandora Hadzidaki, Bohr's Atomic Model and Paraconsistent Logic.
    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 (...)
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  6.  22
    Torben Braüner (2006). Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic. Journal of Logic, Language and Information 15 (3):179-194.
    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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  7.  3
    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.
    A new technique for proving realisability results is presented, and is illustrated in detail for the simple case of arithmetic minus induction. CL is a Gentzen formulation of classical logic. CPQ is CL minus the Cut Rule. The basic proof theory and model theory of CPQ and CL is developed. For the semantics presented CPQ is a paraconsistent logic, i.e. there are non-trivial CPQ models in which some sentences are both true and false. Two systems of arithmetic (...)
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  8.  62
    Newton C. A. Costa & Walter A. Carnielli (1986). On Paraconsistent Deontic Logic. Philosophia 16 (3-4):293-305.
    This paper develops the first deontic logic in the context of paraconsistent logics.
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  9.  1
    Michaelis Michael (forthcoming). On a “Most Telling” Argument for Paraconsistent Logic. Synthese:1-16.
    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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  10. Seiki Akama, Tetsuya Murai & Yasuo Kudo (forthcoming). Partial and Paraconsistent Approaches to Future Contingents in Tense Logic. Synthese:1-11.
    The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These approaches theoretically meet (...)
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  11.  8
    Sergei P. Odintsov (2005). The Class of Extensions of Nelson's Paraconsistent Logic. 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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  12.  26
    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.
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  13.  9
    Jean-Yves Béziau (2006). The Paraconsistent Logic Z. A Possible Solution to Jaśkowski's Problem. 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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  14.  2
    Alexej P. Pynko (2002). Extensions of Hałkowska–Zajac's Three-Valued Paraconsistent Logic. Archive for Mathematical Logic 41 (3):299-307.
    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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  15.  19
    Nicholas D. McGinnis (2013). The Unexpected Applicability of Paraconsistent Logic: A Chomskyan Route to Dialetheism. [REVIEW] 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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  16.  49
    Joachim Bromand (2002). Why Paraconsistent Logic Can Only Tell Half the Truth. 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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  17. 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.
     
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  18.  19
    Arthur Buchsbaum & Tarcisio Pequeno (1993). A Reasoning Method for a Paraconsistent Logic. Studia Logica 52 (2):281 - 289.
    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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  19.  38
    Elias H. Alves (1984). Paraconsistent Logic and Model Theory. 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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  20.  48
    Newton C. A. da Costa & Décio Krause, Remarks on the Applications of Paraconsistent Logic to Physics.
    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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  21. Jean-Yves Béziau (2001). From Paraconsistent Logic to Universal Logic. 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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  22. 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.
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  23.  17
    Blaise Pascal, Paraconsistent Logic! (A Reply to Slater) Jean-Yves BéziauFoot Note 1_.
    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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  24.  5
    Valentin A. Bazhanov (2008). Heuristic Ground of Paraconsistent Logic. Proceedings of the Xxii World Congress of Philosophy 13:5-8.
    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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  25.  10
    Andrés Bobenrieth (2007). Hilbert, Trivialization and Paraconsistent Logic. The Proceedings of the Twenty-First World Congress of Philosophy 5:37-43.
    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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  26. Jean-Yves Béziau (2006). Paraconsistent Logic! 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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  27.  12
    Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. 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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  28. Arnon Avron, 5-Valued Non-Deterministic Semantics for The Basic Paraconsistent Logic mCi.
    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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  29.  46
    N. Da Costa & C. De Ronde (2013). The Paraconsistent Logic of Quantum Superpositions. 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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  30.  1
    L. R. S., Graham Priest, Richard Sylvan & Jean Norman (1991). Paraconsistent Logic: Essays on the Inconsistent. Philosophical Quarterly 41 (165):515.
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  31.  61
    Graham Priest, Paraconsistent Logic. Stanford Encyclopedia of Philosophy.
  32. G. Priest, R. Routley & J. Norman (eds.) (1989). Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag.
     
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  33.  18
    Norihiro Kamide (2010). An Embedding-Based Completeness Proof for Nelson's Paraconsistent Logic. Bulletin of the Section of Logic 39 (3/4):205-214.
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  34.  9
    Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.
    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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  35. Jaakko Hintikka, If Logic Meets Paraconsistent Logic.
    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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  36.  3
    Newton C. A. Da Costa (2004). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25-34.
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  37.  6
    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.
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  38. Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno (1995). Aspects of Paraconsistent Logic. Logic Journal of the Igpl 3 (4):597-614.
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  39.  7
    Koji Tanaka (2013). Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer 15--25.
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  40.  21
    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.
  41.  6
    Yury V. Ivlev (2004). Quasi-Matrix Logic as a Paraconsistent Logic for Dubitable Information. Logic and Logical Philosophy 8:91.
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  42.  6
    Joanna Odrowąż-Sypniewska (2014). Heaps and Gluts: Paraconsistent Logic Applied to Vagueness. 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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  43. J. Odrowaz-Sypneiwska (1999). Heaps and Gluts: Paraconsistent Logic Applied to Vagueness. Logic and Logical Philosophy 7:179-193.
     
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  44.  14
    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.
    "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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  45.  6
    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.
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  46.  30
    Diderik Batens (2000). Frontiers of Paraconsistent Logic.
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  47.  1
    Sergei Odintsov & Vladimir Rybakov (2013). Unification and Admissible Rules for Paraconsistent Minimal Johanssonsʼ Logic J and Positive Intuitionistic Logic. Annals of Pure and Applied Logic 164 (7-8):771-784.
    We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any (...)
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  48.  51
    Fred Johnson & Peter Woodruff (2002). Categorical Consequence for Paraconsistent Logic. In Walter Carnielli (ed.), Paraconsistency:the logical way to the inconsistent. 141-150.
    Consequence rleations over sets of "judgments" are defined by using "overdetermined" as well as "underdetermined" valuations. Some of these relations are shown to be categorical. And generalized soundness and completeness results are given for both multiple and single conclusion consequence relations.
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  49. Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.) (2000). Frontiers in Paraconsistent Logic. Research Studies Press.
     
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  50.  9
    Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno (1995). Paraconsistent Logic in a Historical Perspective. Logique Et Analyse 38:111-125.
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