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  1. 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 both with one (...)
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  • Natural Deduction for Four-Valued Both Regular and Monotonic Logics.Yaroslav Petrukhin - 2018 - Logic and Logical Philosophy 27 (1):53-66.
    The development of recursion theory motivated Kleene to create regular three-valued logics. Remove it taking his inspiration from the computer science, Fitting later continued to investigate regular three-valued logics and defined them as monotonic ones. Afterwards, Komendantskaya proved that there are four regular three-valued logics and in the three-valued case the set of regular logics coincides with the set of monotonic logics. Next, Tomova showed that in the four-valued case regularity and monotonicity do not coincide. She counted that there are (...)
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  • Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox.Yaroslav Petrukhin & Vasily Shangin - 2017 - Review of Symbolic Logic 10 (4):756-781.
    B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.
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  • Stone-Type Representations and Dualities for Varieties of Bisemilattices.Antonio Ledda - 2018 - Studia Logica 106 (2):417-448.
    In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces (...)
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  • The noneffectivity of Arslanov’s completeness criterion and related theorems.Sebastiaan A. Terwijn - 2020 - Archive for Mathematical Logic 59 (5):703-713.
    We discuss the effectivity of Arslanov’s completeness criterion. In particular, we show that a parameterized version, similar to the recursion theorem with parameters, fails. We also discuss the effectivity of another extension of the recursion theorem, namely Visser’s ADN theorem, as well as that of a joint generalization of the ADN theorem and Arslanov’s completeness criterion.
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  • Alan Turing and the Mathematical Objection.Gualtiero Piccinini - 2003 - Minds and Machines 13 (1):23-48.
    This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...)
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  • Construction Theory, Self-Replication, and the Halting Problem.Hiroki Sayama - 2008 - Complexity 13 (5):16-22.
    Complexity is pleased to announce the installment of Prof Hiroki Sayama as its new Chief Editor. In this Editorial, Prof Sayama describes his feelings about his recent appointment, discusses some of the journal’s journey and relevance to current issues, and shares his vision and aspirations for its future.
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  • Indefinite Extensibility in Natural Language.Laureano Luna - 2013 - The Monist 96 (2):295-308.
    The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...)
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  • Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...)
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  • 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.
  • The Geometry of Negation.Massimo Warglien & Achille C. Varzi - 2003 - Journal of Applied Non-Classical Logics 13 (1):9-19.
    There are two natural ways of thinking about negation: (i) as a form of complementation and (ii) as an operation of reversal, or inversion (to deny that p is to say that things are “the other way around”). A variety of techniques exist to model conception (i), from Euler and Venn diagrams to Boolean algebras. Conception (ii), by contrast, has not been given comparable attention. In this note we outline a twofold geometric proposal, where the inversion metaphor is understoood as (...)
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  • Exactly True and Non-Falsity Logics Meeting Infectious Ones.Alex Belikov & Yaroslav Petrukhin - 2020 - Journal of Applied Non-Classical Logics 30 (2):93-122.
    In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case (...)
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  • Reflexivity and Self-Augmentation.Kumiko Tanaka-Ishii - 2010 - Semiotica 2010 (180):1-17.
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  • Formes, Objets Et Négation Selon Granger.Fabien Schang - 2020 - Philosophiques 47 (1):3.
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  • Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.
    Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...)
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  • La historia y la gramática de la recursión: una precisión desde la obra de Wittgenstein.Sergio Mota - 2014 - Pensamiento y Cultura 17 (1):20-48.
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  • The Psychology of Uncertainty and Three-Valued Truth Tables.Jean Baratgin, Guy Politzer, David E. Over & Tatsuji Takahashi - 2018 - Frontiers in Psychology 9.
    Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...)
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  • Cut Elimination, Identity Elimination, and Interpolation in Super-Belnap Logics.Adam Přenosil - 2017 - Studia Logica 105 (6):1255-1289.
    We develop a Gentzen-style proof theory for super-Belnap logics, expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood proof-theoretically as logics which relax the structural rules of classical logic but keep its logical rules as well as the rules of Identity and Cut, super-Belnap logics may be seen as logics which relax Identity and Cut but keep the logical rules as well as the structural rules of classical logic. A generalization of the (...)
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  • On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
    The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of (...)
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  • Supervaluationism and Paraconsistency.Achille C. Varzi - 2000 - In Diderik Batens, Chris Mortensen, Graham Priest & Jean Paul Van Bendegem (eds.), Frontiers in Paraconsistent Logic. Research Studies Press. pp. 279–297.
    Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...)
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  • New Foundations for Imperative Logic I: Logical Connectives, Consistency, and Quantifiers.Peter B. M. Vranas - 2008 - Noûs 42 (4):529-572.
    Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...)
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  • Semantical Mutation, Algorithms and Programs.Porto André - 2015 - Dissertatio (S1):44-76.
    This article offers an explanation of perhaps Wittgenstein’s strangest and least intuitive thesis – the semantical mutation thesis – according to which one can never answer a mathematical conjecture because the new proof alters the very meanings of the terms involved in the original question. Instead of basing our justification on the distinction between mere calculation and proofs of isolated propositions, characteristic of Wittgenstein’s intermediary period, we generalize it to include conjectures involving effective procedures as well.
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  • Trivial Dialetheism and the Logic of Paradox.Jean-Yves Beziau - 2016 - Logic and Logical Philosophy 25 (1):51-56.
    In this paper we explain that the paraconsistent logic LP promoted by Graham Priest can only be supported by trivial dialetheists, i.e., those who believe that all sentences are dialetheias.
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  • Bochvar's Three-Valued Logic and Literal Paralogics: Their Lattice and Functional Equivalence.Alexander Karpenko & Natalya Tomova - 2017 - Logic and Logical Philosophy 26 (2):207-235.
    In the present paper, various features of the class of propositional literal paralogics are considered. Literal paralogics are logics in which the paraproperties such as paraconsistence, paracompleteness and paranormality, occur only at the level of literals; that is, formulas that are propositional letters or their iterated negations. We begin by analyzing Bochvar’s three-valued nonsense logic B3, which includes two isomorphs of the propositional classical logic CPC. The combination of these two ‘strong’ isomorphs leads to the construction of two famous paralogics (...)
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  • Jaśkowski's Criterion and Three-Valued Paraconsistent Logics.Alexander S. Karpenko - 1999 - Logic and Logical Philosophy 7:81.
    A survey is given of three-valued paraconsistent propositionallogics connected with Jaśkowski’s criterion for constructing paraconsistentlogics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.
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  • Truth and The Ambiguity of Negation.Teresa Marques - 2010 - In Erich Rast & Luiz Carlos Baptista (eds.), Meaning and Context. Peter Lang. pp. 2--235.
    This article has one aim, to reject the claim that negation is semantically ambiguous. The first section presents the putative incompatibility between truth-value gaps and the truth-schema; the second section presents the motivation for the ambiguity thesis; the third section summarizes arguments against the claim that natural language negation is semantically ambiguous; and the fourth section indicates the problems of an introduction of two distinct negation operators in natural language.
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  • Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
    An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.
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  • Normality Operators and Classical Collapse.Roberto Ciuni & Massimiliano Carrara - 2018 - In T. Arazim P. And Lavicka (ed.), The Logica Yearbook 2017. Londra, Regno Unito: pp. 2-20.
    In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.
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  • The Mathematical Work of S. C. Kleene.J. R. Shoenfield & S. C. Kleene - 1995 - Bulletin of Symbolic Logic 1 (1):8-43.
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  • Positive and Negative Properties. A Logical Interpretation.Janusz Kaczmarek - 2003 - Bulletin of the Section of Logic 32 (4):179-189.
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  • Non Truth-Functional Many-Valuedness.Jean-Yves Beziau - manuscript
    Many-valued logics are standardly defined by logical matrices. They are truth-functional. In this paper non truth-functional many-valued semantics are presented, in a philosophical and mathematical perspective.
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  • The Mathematical Import of Zermelo's Well-Ordering Theorem.Akihiro Kanamori - 1997 - Bulletin of Symbolic Logic 3 (3):281-311.
    Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...)
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  • The Proof Theory of Classical and Constructive Inductive Definitions. A 40 Year Saga, 1968-2008.Solomon Feferman - unknown
    1. Pohlers and The Problem. I first met Wolfram Pohlers at a workshop on proof theory organized by Walter Felscher that was held in Tübingen in early April, 1973. Among others at that workshop relevant to the work surveyed here were Kurt Schütte, Wolfram’s teacher in Munich, and Wolfram’s fellow student Wilfried Buchholz. This is not meant to slight in the least the many other fine logicians who participated there.2 In Tübingen I gave a couple of survey lectures on results (...)
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  • Reasoning Processes as Epistemic Dynamics.Fernando Velázquez-Quesada - 2015 - Axiomathes 25 (1):41-60.
    This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...)
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  • An Internal Determinacy Metatheorem for Lukasiewicz's Aussagenkalküls.Dale Jacquette - 2000 - Bulletin of the Section of Logic 29 (3):115-124.
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  • Automated Proof-Searching for Strong Kleene Logic and its Binary Extensions Via Correspondence Analysis.Yaroslav Petrukhin & Vasilyi Shangin - forthcoming - Logic and Logical Philosophy:1.
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  • Semantical Analysis of Weak Kleene Logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.
    This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.
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  • On Vidal's Trivalent Explanations for Defective Conditional in Mathematics.Yaroslav Petrukhin & Vasily Shangin - 2018 - Journal of Applied Non-Classical Logics 29 (1):64-77.
    ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is (...)
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  • Logical Analyses of Vipassanā Meditation.C. P. Hertogh - 2018 - Contemporary Buddhism 19 (2):251-274.
    ABSTRACTIn this paper we propose logical analyses of Vipassanā Meditation as modus ponens or universal instantiation, as based upon identification, analysis, and interpretation of the meditation as a thought experiment.*The analyses consist in completing the unfinished enthymematic argument of the Sutta-nipāta by explication of hidden major. We speculate the thought experiment inference might be brought about by a faculty like mindfulness. The thought experiment analyses link the meditation to global cross-cultural theories and arguments in philosophy as Ibn Sīnā’s Flying Man (...)
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  • A 4-Valued Framework Encompassing Intuitionistic and Classical Logic.Tin Perkov - 2014 - Journal of Applied Non-Classical Logics 24 (1-2):138-143.
    A 4-valued framework is proposed to distinguish intuitionistically valid formulas within classical validities.
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  • Semantic Games with Chance Moves Revisited: From IF Logic to Partial Logic.Xuefeng Wen & Shier Ju - 2013 - Synthese 190 (9):1605-1620.
    We associate the semantic game with chance moves conceived by Blinov with Blamey’s partial logic. We give some equivalent alternatives to the semantic game, some of which are with a third player, borrowing the idea of introducing the pseudo-player called Nature in game theory. We observe that IF propositional logic proposed by Sandu and Pietarinen can be equivalently translated to partial logic, which implies that imperfect information may not be necessary for IF propositional logic. We also indicate that some independent (...)
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  • 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 originals. This fact raises the question whether there are (...)
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  • A Many-Valued Semantics for Category Mistakes.John Martin - 1975 - Synthese 31 (1):63 - 83.
    In this paper it is argued that herzberger's general theory of presupposition may be successfully applied to category mistakes. The study offers an alternative to thomason's supervaluation treatment of sortal presupposition and as an indirect measure of the relative merits of the two-Dimensional theory to supervaluations. Bivalent, Three-Valued matrix, And supervaluation accounts are compared to the two-Dimensional theory according to three criteria: (1) abstraction from linguistic behavior, (2) conformity of technical to preanalytic distinctions, And (3) ability to capture classical logic. (...)
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  • Russell and His Sources for Non-Classical Logics.Irving H. Anellis - 2009 - Logica Universalis 3 (2):153-218.
    My purpose here is purely historical. It is not an attempt to resolve the question as to whether Russell did or did not countenance nonclassical logics, and if so, which nonclassical logics, and still less to demonstrate whether he himself contributed, in any manner, to the development of nonclassical logic. Rather, I want merely to explore and insofar as possible document, whether, and to what extent, if any, Russell interacted with the various, either the various candidates or their, ideas that (...)
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  • Key Notions of Tarski's Methodology of Deductive Systems.Janusz Czelakowski & Grzegorz Malinowski - 1985 - Studia Logica 44 (4):321 - 351.
    The aim of the article is to outline the historical background and the present state of the methodology of deductive systems invented by Alfred Tarski in the thirties. Key notions of Tarski's methodology are presented and discussed through, the recent development of the original concepts and ideas.
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  • An N -Player Semantic Game for an N + 1-Valued Logic.Shier Ju & Xuefeng Wen - 2008 - Studia Logica 90 (1):17-23.
    First we show that the classical two-player semantic game actually corresponds to a three-valued logic. Then we generalize this result and give an n-player semantic game for an n + 1-valued logic with n binary connectives, each associated with a player. We prove that player i has a winning strategy in game G if and only if the truth value of φ is $t_i $ in the model M, for 1 ≤ i ≤ n; and none of the players has (...)
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  • Facts and the Semantics of Gerunds.John Martin - 1975 - Journal of Philosophical Logic 4 (4):439 - 454.
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  • Normality Operators and Classical Recapture in Extensions of Kleene Logics.Ciuni Roberto & Massimiliano Carrara - forthcoming - Logic Journal of the IGPL.
    In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we establish a classical recapture (...)
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  • The Method of Socratic Proofs Meets Correspondence Analysis.Dorota Leszczyńska-Jasion, Yaroslav Petrukhin & Vasilyi Shangin - 2019 - Bulletin of the Section of Logic 48 (2):99-116.
    The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. (...)
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  • Many-Valued Logic, Partiality, and Abstraction in Formal Specification Languages.Reiner Hähnle - 2005 - Logic Journal of the IGPL 13 (4):415-433.
    The purpose of this article is to clarify the role that many-valued logic can or should play in formal specification of software systems for modeling partiality. We analyse a representative set of specification languages. Our findings suggest that many-valued logic is less useful for modeling those aspects of partiality, for which it is traditionally intended: modeling non-termination and error values. On the other hand, many-valued logic is emerging as a mainstream tool in abstraction of formal analyses of various kinds, and (...)
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