Search results for 'Many-valued logic' (try it on Scholar)

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  1. in Lukasiewicz'S. Infinitely Valued Logic (1992). Arithmetic and Truth in Lukasiewicz's Infinitely Valued Logic. Logique Et Analyse 35 (140):303-312.score: 540.0
     
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  2. Many-Valued Logic (forthcoming). DM72. Fact and Existence. By Joseph Margolis. University of Toronto Press. 1969. Pp. V, 144, $4.50. Principles of Logic. By Alex C. Michalos. Englewood Cliffs, New Jersey, Prentice-Hall. 1969. Pp. Xiii, 433. [REVIEW] Filosofia.score: 380.0
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  3. J. C. Beall (2003). Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. Oxford University Press.score: 180.0
    Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.
     
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  4. Merrie Bergmann (2008). An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press.score: 176.0
    This volume is an accessible introduction to the subject of many-valued and fuzzy logic suitable for use in relevant advanced undergraduate and graduate courses. The text opens with a discussion of the philosophical issues that give rise to fuzzy logic – problems arising from vague language – and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind (...)
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  5. Grzegorz Malinowski (1993). Many-Valued Logics. Oxford University Press.score: 151.0
    This book provides an incisive, basic introduction to many-valued logics and to the constructions that are "many-valued" at their origin. Using the matrix method, the author sheds light on the profound problems of many-valuedness criteria and its classical characterizations. The book also includes information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many-valuedness. With its selective bibliography and many useful historical references, this book provides logicians, computer scientists, philosophers, and mathematicians (...)
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  6. Nicholas Rescher (1969). Many-Valued Logic. New York, Mcgraw-Hill.score: 150.0
     
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  7. Richard DeWitt (2005). On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics. Journal of Philosophical Logic 34 (5/6):545 - 560.score: 149.3
    In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This (...)
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  8. Marcelo Tsuji (1998). Many-Valued Logics and Suszko's Thesis Revisited. Studia Logica 60 (2):299-309.score: 146.0
    Suszko's Thesis maintains that many-valued logics do not exist at all. In order to support it, R. Suszko offered a method for providing any structural abstract logic with a complete set of bivaluations. G. Malinowski challenged Suszko's Thesis by constructing a new class of logics (called q-logics by him) for which Suszko's method fails. He argued that the key for logical two-valuedness was the "bivalent" partition of the Lindenbaum bundle associated with all structural abstract logics, while his q-logics (...)
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  9. Alexej P. Pynko (2010). Many-Place Sequent Calculi for Finitely-Valued Logics. Logica Universalis 4 (1):41-66.score: 140.0
    In this paper, we study multiplicative extensions of propositional many-place sequent calculi for finitely-valued logics arising from those introduced in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) through their translation by means of singularity determinants for logics and restriction of the original many-place sequent language. Our generalized approach, first of all, covers, on a uniform formal basis, both the one developed in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) for singular (...)
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  10. Gemma Robles, Francisco Salto & José M. Méndez (2013). Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz's 3-Valued Logic Ł3. Journal of Philosophical Logic:1-30.score: 134.3
    Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension (...)
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  11. Franco Montagna (2012). Partially Undetermined Many-Valued Events and Their Conditional Probability. Journal of Philosophical Logic 41 (3):563-593.score: 134.0
    A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti. Finally, we show that the whole investigation can be carried out in a logical and (...)
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  12. Zoran Majkić (2008). Weakening of Intuitionistic Negation for Many-Valued Paraconsistent da Costa System. Notre Dame Journal of Formal Logic 49 (4):401-424.score: 134.0
    In this paper we propose substructural propositional logic obtained by da Costa weakening of the intuitionistic negation. We show that the positive fragment of the da Costa system is distributive lattice logic, and we apply a kind of da Costa weakening of negation, by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion, and additivity for distributive lattices. The other stronger paraconsistent logic with constructive negation is obtained by adding an axiom for multiplicative property of weak (...)
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  13. Roberto Cignoli (1999). Algebraic Foundations of Many-Valued Reasoning. Kluwer Academic Publishers.score: 132.0
    This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material (...)
     
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  14. Reiner Hähnle (1998). Commodious Axiomatization of Quantifiers in Multiple-Valued Logic. Studia Logica 61 (1):101-121.score: 132.0
    We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem (...)
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  15. Jarosław Pykacz (2010). Unification of Two Approaches to Quantum Logic: Every Birkhoff -von Neumann Quantum Logic is a Partial Infinite-Valued Łukasiewicz Logic. Studia Logica 95 (1/2):5 - 20.score: 125.0
    In the paper it is shown that every physically sound Birkhoff - von Neumann quantum logic, i.e., an orthomodular partially ordered set with an ordering set of probability measures can be treated as partial infini te-valued Lukasiewicz logic, which unifies two competing approaches: the many-valued, and the two-valued but non-distributive, which have co-existed in the quantum logic theory since its very beginning.
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  16. Petr Hájek, Lluis Godo & Francesc Esteva (1996). A Complete Many-Valued Logic with Product-Conjunction. Archive for Mathematical Logic 35 (3):191-208.score: 122.0
    A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.
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  17. Dan Butnariu, Erich Peter Klement, Radko Mesiar & Mirko Navara (2005). Sufficient Triangular Norms in Many-Valued Logics with Standard Negation. Archive for Mathematical Logic 44 (7):829-849.score: 121.0
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  18. F. Montagna & L. Sacchetti (2004). Corrigendum to "Kripke-Style Semantics for Many-Valued Logics". Mathematical Logic Quarterly 50 (1):104.score: 121.0
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  19. F. Montagna & L. Sacchetti (2003). Kripke-Style Semantics for Many-Valued Logics. Mathematical Logic Quarterly 49 (6):629.score: 121.0
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  20. Stan J. Surma (1995). An Axiomatisation of the Conditionals of Post's Many Valued Logics. Mathematical Logic Quarterly 41 (3):369-372.score: 121.0
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  21. Robert John Ackermann (1967). An Introduction to Many-Valued Logics. New York, Dover Publications.score: 118.0
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  22. J. Barkley Rosser (1977). Many-Valued Logics. Greenwood Press.score: 118.0
  23. Ivan Stojmenović (1987). Some Combinatorial and Algorithmic Problems in Many-Valued Logics. University of Novi Sad, Faculty of Science, Institute of Mathematics.score: 118.0
     
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  24. Simone Bova (2012). Lewis Dichotomies in Many-Valued Logics. Studia Logica 100 (6):1271-1290.score: 115.7
    In 1979, H. Lewis shows that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise [21]. Recently, an investigation in the same spirit has been extended to nonclassical propositional logics, modal logics in particular [2, 3]. In this note, we pursue this line in the realm of many-valued propositional logics, and obtain complexity classifications for the parameterized satisfiability (...)
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  25. Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú (2006). On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth. Archive for Mathematical Logic 45 (7):839-868.score: 113.0
    Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully (...)
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  26. Stefano Aguzzoli & Agata Ciabattoni (2000). Finiteness in Infinite-Valued Łukasiewicz Logic. Journal of Logic, Language and Information 9 (1):5-29.score: 111.0
    In this paper we deepen Mundici's analysis on reducibility of the decision problem from infinite-valued ukasiewicz logic to a suitable m-valued ukasiewicz logic m , where m only depends on the length of the formulas to be proved. Using geometrical arguments we find a better upper bound for the least integer m such that a formula is valid in if and only if it is also valid in m. We also reduce the notion of logical consequence in to (...)
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  27. Josep Maria Font & Petr Hájek (2002). On Łukasiewicz's Four-Valued Modal Logic. Studia Logica 70 (2):157-182.score: 110.0
    ukasiewicz''s four-valued modal logic is surveyed and analyzed, together with ukasiewicz''s motivations to develop it. A faithful interpretation of it in classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed in the light of the presented results, ukasiewicz''s own texts, and related literature.
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  28. Gemma Robles (2013). A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Logica Universalis 7 (4):507-532.score: 110.0
    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 expected (...)
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  29. Melvin Fitting (1995). Tableaus for Many-Valued Modal Logic. Studia Logica 55 (1):63 - 87.score: 106.0
    We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cut-free tableau formulation is presented, and its completeness is proved.
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  30. Liu Renren & Lo Czukai (1996). The Maximal Closed Classes of Unary Functions in P‐Valued Logic. Mathematical Logic Quarterly 42 (1):234-240.score: 105.0
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  31. Matteo Bianchi & Franco Montagna (2009). Supersound Many-Valued Logics and Dedekind-MacNeille Completions. Archive for Mathematical Logic 48 (8):719-736.score: 102.7
    In Hájek et al. (J Symb Logic 65(2):669–682, 2000) the authors introduce the concept of supersound logic, proving that first-order Gödel logic enjoys this property, whilst first-order Łukasiewicz and product logics do not; in Hájek and Shepherdson (Ann Pure Appl Logic 109(1–2):65–69, 2001) this result is improved showing that, among the logics given by continuous t-norms, Gödel logic is the only one that is supersound. In this paper we will generalize the previous results. Two conditions (...)
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  32. Jaroslav Peregrin, Many-Valued Logic or Many-Valued Semantics?score: 102.0
    There have been, I am afraid, almost as many answers to the question what is logic? as there have been logicians. However, if logic is not to be an obscure "science of everything", we must assume that the majority of the various answers share a common core which does offer a reasonable delimitation of the subject matter of logic. To probe this core, let us start from the answer given by Gottlob Frege (1918/9), the person probably most (...)
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  33. J. Y. Girard (1976). Three-Valued Logic and Cut-Elimination: The Actual Meaning of Takeuti's Conjecture. Państwowe Wydawn. Naukowe.score: 102.0
     
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  34. Ryszard Stanislaw Michalski (1978). A Planar Geometrical Model for Representing Multidimensional Discrete Spaces and Multiple-Valued Logic Functions. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.score: 102.0
     
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  35. Robert Stepp (1979). Learning Without Negative Examples Via Variable-Valued Logic Characterizations: The Uniclass Inductive Program AQ7UNI. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.score: 102.0
     
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  36. Rostislav Horčík & Petr Cintula (2004). Product Ł Ukasiewicz Logic. Archive for Mathematical Logic 43 (4):477-503.score: 101.3
    Łu logic plays a fundamental role among many-valued logics. However, the expressive power of this logic is restricted to piecewise linear functions. In this paper we enrich the language of Łu logic by adding a new connective which expresses multiplication. The resulting logic, PŁ, is defined, developed, and put into the context of other well-known many-valued logics. We also deal with several extensions of this propositional logic. A predicate version of PŁ logic (...)
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  37. H. Rasiowa (1977). Many-Valued Algorithmic Logic as a Tool to Investigate Programs. In. In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel. 77--102.score: 101.0
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  38. Josep Maria Font & Ramon Jansana (2001). Leibniz Filters and the Strong Version of a Protoalgebraic Logic. Archive for Mathematical Logic 40 (6):437-465.score: 100.0
    A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of ?+ (...)
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  39. Alex Oliver & Timothy Smiley (2006). A Modest Logic of Plurals. Journal of Philosophical Logic 35 (3):317 - 348.score: 99.0
    We present a plural logic that is as expressively strong as it can be without sacrificing axiomatisability, axiomatise it, and use it to chart the expressive limits set by axiomatisability. To the standard apparatus of quantification using singular variables our object-language adds plural variables, a predicate expressing inclusion (is/are/is one of/are among), and a plural definite description operator. Axiomatisability demands that plural variables only occur free, but they have a surprisingly important role. Plural description is not eliminable in favour (...)
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  40. D. J. Shoesmith (1978). Multiple-Conclusion Logic. Cambridge University Press.score: 99.0
    Multiple-conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. (...)
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  41. John N. Martin (2002). Lukasiewicz's Many-Valued Logic and Neoplatonic Scalar Modality. History and Philosophy of Logic 23 (2):95-120.score: 99.0
    This paper explores the modal interpretation of ?ukasiewicz's n -truth-values, his conditional and the puzzles they generate by exploring his suggestion that by ?necessity? he intends the concept used in traditional philosophy. Scalar adjectives form families with nested extensions over the left and right fields of an ordering relation described by an associated comparative adjective. Associated is a privative negation that reverses the ?rank? of a predicate within the field. If the scalar semantics is interpreted over a totally ordered domain (...)
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  42. Stephen Pollard (2005). The Expressive Unary Truth Functions of N -Valued Logic. Notre Dame Journal of Formal Logic 46 (1):93-105.score: 97.7
    The expressive truth functions of two-valued logic have all been identified. This paper begins the task of identifying the expressive truth functions of n-valued logic by characterizing the unary ones. These functions have distinctive algebraic, semantic, and closure-theoretic properties.
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  43. Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.score: 97.0
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show (...)
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  44. Tommaso Flaminio (2007). NP-Containment for the Coherence Test of Assessments of Conditional Probability: A Fuzzy Logical Approach. [REVIEW] Archive for Mathematical Logic 46 (3-4):301-319.score: 96.0
    In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory T χ defined on the modal-fuzzy logic FP k (RŁΔ) built up over the many-valued logic RŁΔ. Such modal-fuzzy logic was previously introduced in Flaminio (Lecture Notes (...)
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  45. Aleksandr Zinoviev (1963). Philosophical Problems of Many-Valued Logic. Dordrecht, Holland, D. Reidel Pub. Co..score: 96.0
     
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  46. Matteo Bianchi & Franco Montagna (2011). N-Contractive BL-Logics. Archive for Mathematical Logic 50 (3-4):257-285.score: 94.0
    In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom ${\phi^n\rightarrow\phi^{n+1}}$ , for some ${n\in\mathbb{N}^+}$ ) axiomatic extensions of BL and their corresponding varieties: BL n , SBL n , BL n and SBL n . Concerning BL n we have that every BL n -chain (...)
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  47. Yoshihiro Maruyama (2010). Fuzzy Topology and Łukasiewicz Logics From the Viewpoint of Duality Theory. Studia Logica 94 (2):245 - 269.score: 93.0
    This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n -valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n -valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n -valued logic with truth constants, which generalizes Jónsson-Tarski duality for (...)
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  48. Bruce White (1974). A Note on Natural Deduction in Many-Valued Logic. Notre Dame Journal of Formal Logic 15 (1):167-168.score: 93.0
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  49. Peter W. Woodruff (1973). On Compactness in Many-Valued Logic. I. Notre Dame Journal of Formal Logic 14 (3):405-407.score: 93.0
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  50. José M. Mendez & Francisco Salto (1998). A Natural Negation Completion of Urquhart's Many-Valued Logic C. Journal of Philosophical Logic 27 (1):75-84.score: 93.0
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