Results for 'Many-valued logic'

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  1. Arithmetic and Truth in Lukasiewicz's Infinitely Valued Logic.in Lukasiewicz'S. Infinitely Valued Logic - 1992 - Logique Et Analyse 35 (140):303-312.
     
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  2.  9
    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]Many-Valued Logic - forthcoming - Filosofia.
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  3. Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic.J. C. Beall - 2003 - Oxford University Press.
    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.  5
    Franco Montagna’s Work on Provability Logic and Many-Valued Logic.Lev Beklemishev & Tommaso Flaminio - 2016 - Studia Logica 104 (1):1-46.
    Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic.
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  5.  45
    An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems.Merrie Bergmann - 2012 - Cambridge University Press.
    Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses 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 fuzzy (...). The major fuzzy logical systems - Lukasiewicz, Gödel, and product logics - are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems. (shrink)
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  6.  8
    N.A. Vasil’Ev’s Logical Ideas and the Categorical Semantics of Many-Valued Logic.D. Y. Maximov - 2016 - Logica Universalis 10 (1):21-43.
    Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and the idea of the notion of nonclassical negation, that is not based on incompatibility, is formalized in special cases of monoidal categories. For these cases, the variant of the law of “excluded n-th” suggested by Vasil’ev instead of the tertium non datur is obtained in some special cases of these categories. The paraconsistent law suggested by (...)
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  7.  13
    Many-Valued Logic.Nicholas Rescher - 1969 - New York: Mcgraw-Hill.
  8.  3
    Philosophical Problems of Many-Valued Logic.T. J. Smiley, A. A. Zinov'ev, Guido Kung & David Dinsmore Comey - 1963 - Philosophical Quarterly 16 (62):83.
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  9.  6
    A Complete Many-Valued Logic with Product-Conjunction.Petr Hájek, Lluis Godo & Francesc Esteva - 1996 - Archive for Mathematical Logic 35 (3):191-208.
    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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  10. Many-Valued Logic in the Jewish Short Stories.Vitaly I. Levin - 2015 - Studia Humana 3 (4):3-6.
    Jewish short stories are explained from the viewpoint of many-valued logic. On the basis of some examples, we show, how their contents may be logically interpreted.
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  11.  24
    Knot and Tonk: Nasty Connectives on Many-Valued Truth-Tables for Classical Sentential Logic.Tim Button - 2016 - Analysis 76 (1):7-19.
    Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution (...)
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  12.  14
    Łukasiewicz Negation and Many-Valued Extensions of Constructive Logics.Thomas Macaulay Ferguson - 2014 - In Proc. 44th International Symposium on Multiple-Valued Logic. IEEE Computer Society Press. pp. 121-127.
    This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any (...)
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  13. Algebraic Foundations of Many-Valued Reasoning.Roberto Cignoli - 1999 - Kluwer Academic Publishers.
    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.  51
    Many-Valued Logics.Grzegorz Malinowski - 1993 - Oxford University Press.
    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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  15.  8
    Two-Valued and Many-Valued Logic.A. A. Zinov'ev - 1963 - Russian Studies in Philosophy 2 (1):69-84.
    Various interrelationships between two-valued and many-valued logics are examined in . In the present article we propose to discuss questions bearing on these interrelations which have either not been clearly identified as philosophical in that book, were not given sufficiently detailed explanation, or were not touched upon at all.
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  16.  4
    Corrigendum to "Kripke-Style Semantics for Many-Valued Logics".F. Montagna & L. Sacchetti - 2004 - Mathematical Logic Quarterly 50 (1):104.
    This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.
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  17.  40
    On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics.Richard DeWitt - 2005 - Journal of Philosophical Logic 34 (5-6):545-560.
    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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  18.  9
    A Unification of Two Approaches to Vagueness: The Boolean Many-Valued Approach and the Modal-Precisificational Approach.Ken Akiba - forthcoming - Journal of Philosophical Logic:1-23.
    The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity and truth, but while the fuzzy-logic approach postulates linearly-ordered values between 0 and 1, the Boolean approach assigns to sentences values in a many-element complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a sentence (...)
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  19.  1
    The Maximal Closed Classes of Unary Functions in P‐Valued Logic.Liu Renren & Lo Czukai - 1996 - Mathematical Logic Quarterly 42 (1):234-240.
    In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved , and the (...)
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  20.  13
    Partially Undetermined Many-Valued Events and Their Conditional Probability.Franco Montagna - 2012 - Journal of Philosophical Logic 41 (3):563-593.
    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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  21.  34
    Weakening of Intuitionistic Negation for Many-Valued Paraconsistent da Costa System.Zoran Majkić - 2008 - Notre Dame Journal of Formal Logic 49 (4):401-424.
    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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  22.  28
    Many-Valued Logic or Many-Valued Semantics?Jaroslav Peregrin - manuscript -
    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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  23.  10
    Dual Equivalent Two-Valued Under-Determined and Over-Determined Interpretations for Łukasiewicz's 3-Valued Logic Ł3.Gemma Robles, Francisco Salto & José M. Méndez - 2013 - Journal of Philosophical Logic (2-3):1-30.
    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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  24.  36
    Commodious Axiomatization of Quantifiers in Multiple-Valued Logic.Reiner Hähnle - 1998 - Studia Logica 61 (1):101-121.
    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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  25.  36
    Tableaus for Many-Valued Modal Logic.Melvin Fitting - 1995 - Studia Logica 55 (1):63 - 87.
    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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  26. Many-Valued Algorithmic Logic as a Tool to Investigate Programs.H. Rasiowa - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel. pp. 77--102.
  27.  35
    Many-Valued Logics and Suszko's Thesis Revisited.Marcelo Tsuji - 1998 - Studia Logica 60 (2):299-309.
    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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  28.  36
    Many-Valued Logic and Cognition: Foreword.Shier Ju & Daniele Mundici - 2008 - Studia Logica 90 (1):1-2.
  29.  10
    Lukasiewicz's Many-Valued Logic and Neoplatonic Scalar Modality.John N. Martin - 2002 - History and Philosophy of Logic 23 (2):95-120.
    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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  30.  3
    Philosophical Problems of Many-Valued Logic.Aleksandr Zinoviev - 1963 - Dordrecht: Holland, D. Reidel Pub. Co..
  31. Many-Valued Logic.Alasdair Urquhart - 1986 - In D. Gabbay & F. Guenther (eds.), Handbook of Philosophical Logic, Vol. Iii. D. Reidel Publishing Co..
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  32.  2
    An Interpretation of Many‐Valued Logic.Alasdair Urquhart - 1973 - Mathematical Logic Quarterly 19 (7):111-114.
  33.  12
    Relations Between Paraconsistent Logic and Many-Valued Logic.Newton Ca da Costa & Elias H. Alves - 1981 - Bulletin of the Section of Logic 10 (4):185-191.
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  34.  5
    On Compactness in Many-Valued Logic. I.Peter W. Woodruff - 1973 - Notre Dame Journal of Formal Logic 14 (3):405-407.
  35.  24
    A Natural Negation Completion of Urquhart's Many-Valued Logic C.José M. Mendez & Francisco Salto - 1998 - Journal of Philosophical Logic 27 (1):75-84.
  36.  8
    Peter Simons MacColl and Many-Valued Logic: An Exclusive Conjunction.an Exclusive Conjunction - 1998 - Nordic Journal of Philosophical Logic 3 (1):85-90.
  37.  11
    A Note on Natural Deduction in Many-Valued Logic.Bruce White - 1974 - Notre Dame Journal of Formal Logic 15 (1):167-168.
  38.  2
    Hájek Petr, Godo Lluis, and Esteva Francesc. A Complete Many-Valued Logic with Product-Conjunction. Archive for Mathematical Logic, Vol. 35 , Pp. 191–208. [REVIEW]Franco Montagna - 2000 - Bulletin of Symbolic Logic 6 (3):346-347.
  39.  1
    On a Simple Axiomatic System of the Infinitely Many‐Valued Logic Based on ∧, →.Akira Nakamura - 1963 - Mathematical Logic Quarterly 9 (16‐17):251-263.
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  40.  3
    92 Does Many-Valued Logic Have Any Use?R. Giles - 1976 - In J. P. Cleave & Stephan Körner (eds.), Philosophy of Logic: Papers and Discussions. University of California Press. pp. 92.
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  41.  3
    In § 2 I Shall Say Something About Logical Consequence, Starting From the Observation That Two Systems of Many-Valued Logic May Have Identical Truth-Values and Truth-Tables and Theorems and Still Differ Over the Inferences They Count as Valid.T. J. Smiley - 1976 - In J. P. Cleave & Stephan Körner (eds.), Philosophy of Logic: Papers and Discussions. University of California Press. pp. 74.
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  42.  3
    Review: Petr Hájek, Lluis Godo, Francesc Esteva, A Complete Many-Valued Logic with Product-Conjunction. [REVIEW]Franco Montagna - 2000 - Bulletin of Symbolic Logic 6 (3):346-347.
  43.  3
    Review: C.C. Chang, Algebraization of Infinitely Many-Valued Logic; C. C. Chang, Algebraic Analysis of Many Valued Logics; C. C. Chang, A New Proof of the Completeness of the Lukasiewicz Axioms. [REVIEW]Alfred Horn - 1971 - Journal of Symbolic Logic 36 (1):159-160.
  44.  4
    An Interpolation Theorem in Many-Valued Logic.Masazumi Hanazawa & Mitio Takano - 1986 - Journal of Symbolic Logic 51 (2):448-452.
  45. Review: A. A. Zinov'ev, Philosophical Problems of Many-Valued Logic[REVIEW]Atwell R. Turquette - 1964 - Journal of Symbolic Logic 29 (4):213-214.
  46.  2
    Duality in Finite Many-Valued Logic.Rangaswamy V. Setlur - 1971 - Notre Dame Journal of Formal Logic 12 (2):188-194.
  47.  1
    Review: Takeo Sugihara, Negation in Many-Valued Logic[REVIEW]Alan Rose - 1952 - Journal of Symbolic Logic 17 (4):278-279.
  48. Review: A. A. Zinov'ev, Philosophical Problems of Many-Valued Logic[REVIEW]David Dinsmore Comey - 1963 - Journal of Symbolic Logic 28 (3):255-256.
  49. Rescher Nicholas. Many-Valued Logic. McGraw-Hill Book Company, New York, Etc., 1969, Xv + 359 Pp. [REVIEW]George Epstein - 1977 - Journal of Symbolic Logic 42 (3):432-436.
  50. Review: Nicholas Rescher, Many-Valued Logic[REVIEW]George Epstein - 1977 - Journal of Symbolic Logic 42 (3):432-436.
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