Results for 'Many-Valued Logic'

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  1.  56
    Many-Valued Logic.Nicholas Rescher - 1969 - New York: Mcgraw-Hill.
  2.  83
    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 With its selective bibliography and many useful historical references, this book provides (...)
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  3. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory (...)
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  4.  25
    Many-Valued Logics.J. Barkley Rosser - 1952 - Greenwood Press.
  5.  67
    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 (...)
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  6.  7
    Many-Valued Logic and Sequence Arguments in Value Theory.Simon Knutsson - forthcoming - Synthese.
    Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...)
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  7.  76
    Many-Valued Logics.Nicholas J. J. Smith - 2012 - In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge. pp. 636--51.
    A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a (...)-valued semantics in the loose but not the strict sense. A many-valued logic is one which arises from a many-valued semantics and does not also arise from any two-valued semantics [Malinowski, 1993, 30]. By a ‘logic’ here we mean either a set of tautologies, or a consequence relation. We can best explain these ideas by considering the case of classical propositional logic. The language contains the usual basic symbols (propositional constants p, q, r, . . .; connectives ¬, ∧, ∨, →, ↔; and parentheses) and well-formed formulas are defined in the standard way. With the language thus specified—as a set of well-formed formulas—its semantics is then given in three parts. (i) A model of a logical language consists in a free assignment of semantic values to basic items of the non-logical vocabulary. Here the basic items of the non-logical vocabulary are the propositional constants. The appropriate kind of semantic value for a proposition is a truth value, and so a model of the language consists in a free assignment of truth values to basic propositions. Two truth values are countenanced: 1 (representing truth) and 0 (representing falsity). (ii) Rules are presented which determine a truth value for every proposition of the language, given a model. The most common way of presenting these rules is via truth tables (Figure 1). Another way of stating such rules—which will be useful below—is first to introduce functions on the truth values themselves: a unary function ¬ and four binary functions ∧, ∨, → and ↔ (Figure 2).. (shrink)
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  8. Many-Valued Logic.Nicholas Rescher - 1970 - British Journal for the Philosophy of Science 21 (4):405-406.
     
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  9. 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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  10.  23
    Many-Valued Logic of Informal Provability: A Non-Deterministic Strategy.Pawel Pawlowski & Rafal Urbaniak - 2018 - Review of Symbolic Logic 11 (2):207-223.
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  11.  31
    Supersound Many-Valued Logics and Dedekind-MacNeille Completions.Matteo Bianchi & Franco Montagna - 2009 - Archive for Mathematical Logic 48 (8):719-736.
    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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  12.  26
    Many-Valued Logic.Siegfried Gottwald - 2008 - Stanford Encyclopedia of Philosophy.
  13.  4
    Many-Valued Logics.Leonard Goddard - 1954 - Philosophical Quarterly 4 (15):188-189.
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  14.  2
    Many-Valued Logic.Elliott Mendelson - 1970 - Journal of Philosophy 67 (13):457-458.
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  15.  42
    Many-Valued Logics of Extended Gentzen Style II.Moto-O. Takahashi - 1970 - Journal of Symbolic Logic 35 (4):493-528.
    In the monograph [1] of Chang and Keisler, a considerable extent of model theory of the first order continuous logic is ingeniously developed without using any notion of provability.In this paper we shall define the notion of provability in continuous logic as well as the notion of matrix, which is a natural extension of one in finite-valued logic in [2], and develop the syntax and semantics of it mostly along the line in the preceding paper [2]. (...)
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  16.  11
    Many-Valued Logics and Translations.Ítala M. Loffredo D'Ottaviano & Hércules de Araujo Feitosa - 1999 - Journal of Applied Non-Classical Logics 9 (1):121-140.
    ABSTRACT This work presents the concepts of translation and conservative translation between logics. By using algebraic semantics we introduce several conservative translations involving the classical propositional calculus and the many-valued calculi of Post and Lukasiewicz.
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  17.  71
    Systematization of Finite Many-Valued Logics Through the Method of Tableaux.Walter A. Carnielli - 1987 - Journal of Symbolic Logic 52 (2):473-493.
    his paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way. We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Lowenheim-Skolem theorem. The paper is completely self-contained and includes examples of (...)
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  18.  18
    Kripke-Style Semantics for Many-Valued Logics.Franco Montagna & Lorenzo Sacchetti - 2003 - Mathematical Logic Quarterly 49 (6):629.
    This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important (...)
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  19.  13
    Convex MV-Algebras: Many-Valued Logics Meet Decision Theory.T. Flaminio, H. Hosni & S. Lapenta - 2018 - Studia Logica 106 (5):913-945.
    This paper introduces a logical analysis of convex combinations within the framework of Łukasiewicz real-valued logic. This provides a natural link between the fields of many-valued logics and decision theory under uncertainty, where the notion of convexity plays a central role. We set out to explore such a link by defining convex operators on MV-algebras, which are the equivalent algebraic semantics of Łukasiewicz logic. This gives us a formal language to reason about the expected value (...)
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  20.  7
    Finitely Many-Valued Logics and Natural Deduction.C. Englander, E. H. Haeusler & L. C. Pereira - 2014 - Logic Journal of the IGPL 22 (2):333-354.
  21. Truth Pluralism and Many-Valued Logics: A Reply to Beall.Christine Tappolet - 2000 - Philosophical Quarterly 50 (200):382-385.
    Mixed inferences are a problem for those who want to combine truth-assessability and antirealism with respect to allegedly nondescriptive sentences: the classical account of validity has apparently to be given up. J.C. Beall's response is that validity can be defined as the conservation of designated valued (Beall 2000). I argue that since it presupposes a truth predicate that can be applied to all sentences, this suggestion is not helpful. I also consider problems arising from mixed conjunctions and discuss the (...)
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  22.  5
    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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  23.  25
    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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  24.  23
    Sufficient Triangular Norms in Many-Valued Logics with Standard Negation.Dan Butnariu, Erich Peter Klement, Radko Mesiar & Mirko Navara - 2005 - Archive for Mathematical Logic 44 (7):829-849.
    In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem, together with convenient sufficient conditions. We list several families of strict t-norms having this property (...)
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  25.  46
    Many-Valued Logic and Cognition: Foreword.Shier Ju & Daniele Mundici - 2008 - Studia Logica 90 (1):1-2.
  26.  84
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the (...)
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  27.  66
    Dialogue Games for Many-Valued Logics — an Overview.C. G. Fermüller - 2008 - Studia Logica 90 (1):43-68.
    An overview of different versions and applications of Lorenzen’s dialogue game approach to the foundations of logic, here largely restricted to the realm of manyvalued logics, is presented. Among the reviewed concepts and results are Giles’s characterization of Łukasiewicz logic and some of its generalizations to other fuzzy logics, including interval based logics, a parallel version of Lorenzen’s game for intuitionistic logic that is adequate for finite- and infinite-valued Gödel logics, and a truth comparison game for (...)
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  28.  17
    Many-Valued Logics and the Lewis Paradoxes.Edward Schuh - 1973 - Notre Dame Journal of Formal Logic 14 (2):250-252.
  29.  17
    Many-Valued Logics and Systems of Strict Implication.Atwell R. Turquette - 1954 - Philosophical Review 63 (3):365-379.
  30.  73
    Many-Valued Modal Logics.Melvin C. Fitting - unknown
    Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.
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  31.  9
    An Interpretation of ManyValued Logic.Alasdair Urquhart - 1973 - Mathematical Logic Quarterly 19 (7):111-114.
  32.  24
    An Interpretation of Many-Valued Logic.Alasdair Urquhart - 1973 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 19 (7):111-114.
  33.  27
    An Introduction to Many-Valued Logics.Robert Ackermann - 1968 - Philosophical Quarterly 18 (71):174-174.
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  34.  89
    Dual Systems of Sequents and Tableaux for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - Bulletin of the EATCS 51:192-197.
    The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment (...)
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  35. Many-Valued Modal Logics II.Melvin Fitting - unknown
    Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal (...)
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  36.  61
    On Structural Completeness of Many-Valued Logics.Piotr Wojtylak - 1978 - Studia Logica 37 (2):139 - 147.
    In the paper some consequence operations generated by ukasiewicz's matrices are examined.
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  37.  45
    Paraconsistent Structure Inside of Many-Valued Logic.A. S. Karpenko - 1986 - Synthese 66 (1):63 - 69.
  38.  3
    Many-Valued Logic in the Jewish Short Stories.Vitaly I. Levin - 2014 - 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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  39. Many-Valued Modal Logics: A Simple Approach: Many-Valued Modal Logics: A Simple Approach.Graham Priest - 2008 - Review of Symbolic Logic 1 (2):190-203.
    1.1 In standard modal logics, the worlds are 2-valued in the following sense: there are 2 values that a sentence may take at a world. Technically, however, there is no reason why this has to be the case. The worlds could be many-valued. This paper presents one simple approach to a major family of many-valued modal logics, together with an illustration of why this family is philosophically interesting.
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  40.  19
    On Compactness in Many-Valued Logic. I.Peter W. Woodruff - 1973 - Notre Dame Journal of Formal Logic 14 (3):405-407.
  41.  50
    On Axiomatization of Many-Valued Logics Associated with Formalization of Plausible Reasonings.O. M. Anshakov, V. K. Finn & D. P. Skvortsov - 1989 - Studia Logica 48 (4):423 - 447.
    This paper studies a class of infinite-valued predicate logics. A sufficient condition for axiomatizability of logics from that class is given.
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  42.  32
    Two Theorems on Many-Valued Logics.Z. Stachniak - 1988 - Journal of Philosophical Logic 17 (2):171 - 179.
  43. Systematic Construction of Natural Deduction Systems for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. Los Alamitos, CA: IEEE Press. pp. 208-213.
    A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
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  44.  20
    Philosophical Problems of Many-Valued Logic.T. J. Smiley - 1966 - Philosophical Quarterly 16 (62):83.
  45.  14
    Philosophical Problems of Many-Valued Logic.P. S. - 1965 - Review of Metaphysics 18 (3):596-596.
    Here is an informal treatment of many-valued logic, especially propositional logic, using Polish notation. The relations of n-valued logics with 2-valued logics are considered, and numerous systems are drawn on for illustrations. The book is written with an eye to scientific applications of many-valued logics, and considers empirical application of formal calculi. A short section on the relation of formal and "dialectical" logics appears. The work is introductory in nature.—P. S.
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  46.  15
    Interpolation and Beth’s Property in Propositional Many-Valued Logics: A Semantic Investigation.Franco Montagna - 2006 - Annals of Pure and Applied Logic 141 (1):148-179.
    In this paper we give a rather detailed algebraic investigation of interpolation and Beth’s property in propositional many-valued logics extending Hájek’s Basic Logic [P. Hájek, Metamathematics of Fuzzy Logic, Kluwer, 1998], and we connect such properties with amalgamation and strong amalgamation in the corresponding varieties of algebras. It turns out that, while the most interesting extensions of in the language of have deductive interpolation, very few of them have Beth’s property or Craig interpolation. Thus in the (...)
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  47.  21
    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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  48.  17
    Philosophical Problems of Many-Valued Logic.Aleksandr Zinoviev - 1963 - Dordrecht: Holland, D. Reidel Pub. Co..
  49.  13
    Normality Operators and Classical Recapture in Many-Valued Logic.Roberto Ciuni & Massimiliano Carrara - 2020 - Logic Journal of the IGPL 28 (5):657-683.
    In this paper, we use a ‘normality operator’ in order to generate logics of formal inconsistency and logics of formal undeterminedness from any subclassical many-valued logic that enjoys a truth-functional semantics. Normality operators express, in any many-valued logic, that a given formula has a classical truth value. In the first part of the paper we provide some setup and focus on many-valued logics that satisfy some of the three properties, namely subclassicality and (...)
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  50. A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems. [REVIEW]R. Brown, J. F. Glazebrook & I. C. Baianu - 2007 - Axiomathes 17 (3-4):409-493.
    A novel conceptual framework is introduced for the Complexity Levels Theory in a Categorical Ontology of Space and Time. This conceptual and formal construction is intended for ontological studies of Emergent Biosystems, Super-complex Dynamics, Evolution and Human Consciousness. A claim is defended concerning the universal representation of an item’s essence in categorical terms. As an essential example, relational structures of living organisms are well represented by applying the important categorical concept of natural transformations to biomolecular reactions and relational structures that (...)
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