Results for 'three-valued logic'

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  1.  96
    Three-Valued Logics in Modal Logic.Barteld Kooi & Allard Tamminga - 2013 - Studia Logica 101 (5):1061-1072.
    Every truth-functional three-valued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any three-valued logic into a modal formula. Second, we show that for every S5-model there is an equivalent three-valued valuation and vice versa. In general, our Translation Manual gives rise to translations that are exponentially longer than their (...)
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  2.  74
    Three-Valued Logic and Future Contingents.A. N. Prior - 1953 - Philosophical Quarterly 3 (13):317-326.
  3. Three-Valued Logic and Cut-Elimination: The Actual Meaning of Takeuti's Conjecture.J. Y. Girard - 1976 - Państwowe Wydawn. Naukowe.
  4. Correspondence Analysis for Strong Three-Valued Logic.Allard Tamminga - 2014 - Logical Investigations 20:255-268.
    I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each (...)
     
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  5.  72
    Kleene's Three Valued Logics and Their Children.Melvin Fitting - unknown
    Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear (...)
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  6.  69
    Three-Valued Logic.Hilary Putnam - 1957 - Philosophical Studies 8 (5):73 - 80.
  7.  83
    On a Three-Valued Logical Calculus and its Application to the Analysis of the Paradoxes of the Classical Extended Functional Calculus.D. A. Bochvar & Merrie Bergmann - 1981 - History and Philosophy of Logic 2 (1-2):87-112.
    A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.
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  8.  3
    Three-Valued Logic and Future Contingents.A. N. Prior - 1954 - Journal of Symbolic Logic 19 (4):294-294.
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  9.  36
    Foreword: Three-Valued Logics and Their Applications.Pablo Cobreros, Paul Égré, David Ripley & Robert van Rooij - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):1-11.
  10.  26
    Erotetic Search Scenarios and Three-Valued Logic.Dorota Leszczyńska-Jasion & Paweł Łupkowski - 2016 - Journal of Logic, Language and Information 25 (1):51-76.
    Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three- (...) logic, we will show how an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues. (shrink)
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  11. Three-Valued Logics for Incomplete Information and Epistemic Logic.Davide Ciucci & Didier Dubois - 2012 - In Luis Farinas del Cerro, Andreas Herzig & Jerome Mengin (eds.), Logics in Artificial Intelligence. Springer. pp. 147--159.
  12.  19
    Three Value Logics: An Introduction, A Comparison of Various Logical Lexica and Some Philosophical Remarks.Harold Hodes - 1989 - Annals of Pure and Applied Logic 43 (2):99-145.
  13.  12
    Generalized Correspondence Analysis for Three-Valued Logics.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (3-4):423-460.
    Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this (...)
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  14.  80
    Three-Valued Logic, Indeterminacy and Quantum Mechanics.Tomasz Bigaj - 2001 - Journal of Philosophical Logic 30 (2):97-119.
    The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must (...)
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  15.  23
    Intuitive Semantics for Some Three-Valued Logics Connected with Information, Contrariety and Subcontrariety.Dimiter Vakarelov - 1989 - Studia Logica 48 (4):565 - 575.
    Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.
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  16.  41
    Return of the Liar: Three-Valued Logic and the Concept of Truth.Brian Skyrms - 1970 - American Philosophical Quarterly 7 (2):153-161.
  17.  27
    Nondeterministic Three-Valued Logic: Isotonic and Guarded Truth-Functions.Peter Päppinghaus & Martin Wirsing - 1983 - Studia Logica 42 (1):1 - 22.
    Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T (true), F (false), U (undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four (...)
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  18. Was Łukasiewicz Wrong? : Three-Valued Logic and Determinism.Daisuke Kachi - 1996 - In Łukasiewicz in Dublin -- An International Conference on the Work of Jan Łukasiewicz.
    Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some (...)
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  19.  36
    Remarks on Lukasiewicz's Three-Valued Logic.Roman Suszko - 1975 - Bulletin of the Section of Logic 4 (3):87-90.
  20.  12
    The Three-Value Logic of Language—its Syntax, Semantics and Application in the Analysis of Language.Niels Öffenberger - 1979 - Philosophy and History 12 (1):14-16.
  21.  48
    A Note on Three-Valued Logic and Tarski Theorem on Truth Definitions.Andrea Cantini - 1980 - Studia Logica 39 (4):405 - 414.
    We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.
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  22.  12
    Three-Valued Logic.Hilary Putnam, Paul Feyerabend & Isaac Levi - 1960 - Journal of Symbolic Logic 25 (3):289-291.
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  23.  41
    Some Remarks on Three-Valued Logic of J. Łukasiewicz.J. Słupecki, G. Bryll & T. Prucnal - 1967 - Studia Logica 21 (1):45 - 70.
  24.  17
    Measurement, Empirical Meaningfulness, and Three-Valued Logic.Patrick Suppes, J. W. Addison, Leon Henkin & Alfred Tarski - 1970 - Journal of Symbolic Logic 35 (1):129-131.
  25. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic (...)
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  26.  7
    On a Three-Valued Logic with Blamey’s Interjunction for the Formal Description of Atomic Transactions.Mateusz M. Radzki - 2020 - Axiomathes 30 (2):177-191.
    The article demonstrates that to describe the property of atomicity of transactions in database systems, we need a three-valued logic with propositional connective characterized in the same way as Blamey’s interjunction. However, the article explains that since Blamey’s partial logic with interjunction is a logic without tautologies, it does not satisfy some salient conditions of being a logic of atomic transactions. The article introduces a logic of the considered kind, and provides an example (...)
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  27.  8
    Three-Valued Kripke-Style Semantics For Pseudo- And Weak-Boolean Logics.Eunsuk Yang - 2012 - Logic Journal of the IGPL 20 (1):187-206.
    This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each (...)
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  28.  93
    Three-Valued Temporal Logic Q T and Future Contingents.Seiki Akama, Yasunori Nagata & Chikatoshi Yamada - 2008 - Studia Logica 88 (2):215-231.
    Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to (...)
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  29.  43
    On Truth, Implication, and Three-Valued Logic.Håkan Törnebohm - 1956 - Theoria 22 (3):185-198.
  30. Handbook of Three-Valued Logics.Paul Egré & Lorenzo Rossi (eds.) - forthcoming - MIT Press.
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  31.  26
    On Axiom Systems of Słupecki for the Functionally Complete Three-Valued Logic.Mateusz Radzki - 2017 - Axiomathes 27 (4):403-415.
    The article concerns two axiom systems of Słupecki for the functionally complete three-valued propositional logic: W1–W6 and A1–A9. The article proves that both of them are inadequate—W1–W6 is semantically incomplete, on the other hand, A1–A9 governs a functionally incomplete calculus, and thus, it cannot be a semantically complete axiom system for the functionally complete three-valued logic.
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  32. A Three-Valued Temporal Logic for Future Contingents.Seiki Akama, Yasunori Nagata & Chikatoshi Yamada - 2007 - Logique Et Analyse 198:99-111.
     
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  33.  16
    A. N. Prior. Three-Valued Logic and Future Contingents. The Philosophical Quarterly , Vol. 3 , Pp. 317–326. [REVIEW]Takeo Sugihara - 1954 - Journal of Symbolic Logic 19 (4):294-294.
  34.  57
    Some Modal Logics Based on a Three-Valued Logic.Krister Segerberg - 1967 - Theoria 33 (1):53-71.
  35.  32
    The Consistency of the Axioms of Abstraction and Extensionality in a Three-Valued Logic.Ross T. Brady - 1971 - Notre Dame Journal of Formal Logic 12 (4):447-453.
  36.  11
    Sugihara Takeo. A Three-Valued Logic with Meaning-Operator. The Memoirs of Fukui University, Librasi Arts Department, I. Humanities and Social Sciences, No. 8 , Pp. 59–60. [REVIEW]Gene F. Rose - 1960 - Journal of Symbolic Logic 25 (3):293-293.
  37.  28
    A Modal Interpretation of Three-Valued Logic.Peter W. Woodruff - 1974 - Journal of Philosophical Logic 3 (4):433 - 439.
  38.  8
    A. N. Prior. Three-Valued Logic and Future Contingents. The Philosophical Quarterly , Vol. 3 , Pp. 317–326.Takeo Sugihara - 1954 - Journal of Symbolic Logic 19 (4):294-294.
  39.  8
    Axiom Systems for Three-Valued Logic.Alan Rose - 1951 - Journal of Symbolic Logic 16 (4):277-277.
  40.  15
    The Cylindric Algebras of Three-Valued Logic.Norman Feldman - 1998 - Journal of Symbolic Logic 63 (4):1201-1217.
  41.  9
    Review: Takeo Sugihara, A Three-Valued Logic with Meaning-Operator. [REVIEW]Gene F. Rose - 1960 - Journal of Symbolic Logic 25 (3):293-293.
  42.  5
    An Axiom System for Three-Valued Logic.Alan Rose - 1953 - Journal of Symbolic Logic 18 (4):344-344.
  43. Bourne on Future Contingents and Three-Valued Logic.Daisuke Kachi - 2009 - Logic and Logical Philosophy 18 (1):33-43.
    Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the (...)
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  44.  12
    Review: Hilary Putnam, Three-Valued Logic; Paul Feyerabend, Reichenbach's Interpretation of Quantum-Mechanics; Isaac Levi, Putnam's Three Truth Values. [REVIEW]Leon Henkin - 1960 - Journal of Symbolic Logic 25 (3):289-291.
  45.  5
    On Foundations of the Three-Valued Logic.Tsurukichi Takamatsu - 1968 - Kagaku Tetsugaku 1:31-44.
  46.  25
    Algebraization of the Three-Valued BCK-Logic.Francisco M. García Olmedo & Antonio J. Rodríguez Salas - 2002 - Mathematical Logic Quarterly 48 (2):163-178.
  47.  4
    Modal Interpretations of Three-Valued Logics. II.Michael J. Duffy - 1979 - Notre Dame Journal of Formal Logic 20 (3):658-673.
  48.  10
    Putnam Hilary. Three-Valued Logic. Philosophical Studies , Vol. 8 , Pp. 73–80.Feyerabend Paul. Reichenbach's Interprétation of Quantum-Mechanics. Philosophical Studies , Vol. 9 , Pp. 49–59.Levi Isaac. Putnam's Three Truth Values. Philosophical Studies , Vol. 10 , Pp. 65–69. [REVIEW]Leon Henkin - 1960 - Journal of Symbolic Logic 25 (3):289-291.
  49.  20
    Note on a Six-Valued Extension of Three-Valued Logic.Josep M. Font & Massoud Moussavi - 1993 - Journal of Applied Non-Classical Logics 3 (2):173-187.
    ABSTRACT In this paper we introduce a set of six logical values, arising in the application of three-valued logics to time intervals, find its algebraic structure, and use it to define a six-valued logic. We then prove, by using algebraic properties of the class of De Morgan algebras, that this semantically defined logic can be axiomatized as Belnap's ?useful? four-valued logic. Other directions of research suggested by the construction of this set of six (...)
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  50.  4
    Representing Voting Rules in Łukasiewicz’s Three-Valued Logic.Adrian Miroiu & Mircea Dumitru - 2022 - Journal of Applied Non-Classical Logics 32 (1):72-88.
    We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove tha...
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