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  1. Robert John Ackermann (1967). An Introduction to Many-Valued Logics. New York, Dover Publications.
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  2. M. E. Adams & R. Cignoli (1990). A Note on the Axiomatization of Equational Classes of $N$-Valued Ł Ukasiewicz Algebras. Notre Dame Journal of Formal Logic 31 (2):304-307.
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  3. O. M. Anshakov, V. K. Finn & D. P. Skvortsov (1989). On Axiomatization of Many-Valued Logics Associated with Formalization of Plausible Reasonings. 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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  4. Hiroshi Aoyama (1994). The Strong Completeness of a System Based on Kleene's Strong Three-Valued Logic. Notre Dame Journal of Formal Logic 35 (3):355-368.
    The present work, which was inspired by Kripke and McCarthy, is about a non-classical predicate logic system containing a truth predicate symbol. In this system, each sentence A is referred to not by a Gödel number but by its quotation name 'A'.
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  5. A. Avron & B. Konikowska (2008). Rough Sets and 3-Valued Logics. Studia Logica 90 (1):69 - 92.
    In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the value t is (...)
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  6. Arnon Avron (1986). On an Implication Connective of RM. Notre Dame Journal of Formal Logic 27 (2):201-209.
  7. Matthias Baaz, Christian G. Fermüller, Gernot Salzer & Richard Zach (1998). Labeled Calculi and Finite-Valued Logics. Studia Logica 61 (1):7-33.
    A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite-valued logic if the labels are interpreted as sets of truth values (sets-as-signs). Furthermore, it is shown that any finite-valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the number (...)
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  8. Andrew Bacon (2013). Non-Classical Metatheory for Non-Classical Logics. Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)
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  9. Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.
    In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.
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  10. Andrew Bacon (2013). Curry's Paradox and Omega Inconsistency. Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  11. Tomás Barrero & Walter Carnielli (2005). Tableaux sin refutación. Matemáticas: Enseñanza Universitaria 13 (2):81-99.
    Motivated by H. Curry’s well-known objection and by a proposal of L. Henkin, this article introduces the positive tableaux, a form of tableau calculus without refutation based upon the idea of implicational triviality. The completeness of the method is proven, which establishes a new decision procedure for the (classical) positive propositional logic. We also introduce the concept of paratriviality in order to contribute to the question of paradoxes and limitations imposed by the behavior of classical implication.
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  12. Edward Baŀuka (1965). On Verification of the Expressions of Many-Valued Sentential Calculi. I. Studia Logica 17 (1):53 - 73.
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  13. Gordon Beavers (1993). Automated Theorem Proving for Łukasiewicz Logics. Studia Logica 52 (2):183 - 195.
    This paper is concerned with decision proceedures for the 0-valued ukasiewicz logics,. It is shown how linear algebra can be used to construct an automated theorem checker. Two decision proceedures are described which depend on a linear programming package. An algorithm is given for the verification of consequence relations in, and a connection is made between theorem checking in two-valued logic and theorem checking in which implies that determing of a -free formula whether it takes the value one is NP-complete (...)
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  14. Jean-Yves Beziau, Non Truth-Functional Many-Valuedness.
    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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  15. R. Brown, J. F. Glazebrook & I. C. Baianu (2007). A Conceptual Construction of Complexity Levels Theory in Spacetime Categorical Ontology: Non-Abelian Algebraic Topology, Many-Valued Logics and Dynamic Systems. [REVIEW] 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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  16. N. S. C. (1964). Modal and Many-Valued Logics. Review of Metaphysics 18 (1):188-188.
  17. Colin Caret & Ole Thomassen Hjortland (forthcoming). Logical Consequence: Its Nature, Structure, and Application. In Colin Caret & Ole Thomassen Hjortland (eds.), Foundations of Logical Consequence. Oxford University Press.
  18. Walter A. Carnielli (1987). Systematization of Finite Many-Valued Logics Through the Method of Tableaux. 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 application to (...)
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  19. ChristineTappolet (2000). Truth Pluralism and Many-Valued Logics: A Reply to Beall. Philosophical Quarterly 50 (200):382–385.
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  20. Michael Clark (1976). Review of Goddard & Routley, The Logic of Significance and Context. [REVIEW] Mind 85.
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  21. Robert E. Clay (1963). A Standard Form for Ł Ukasiewicz Many-Valued Logics. Notre Dame Journal of Formal Logic 4 (1):59-66.
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  22. Robert E. Clay (1962). A Simple Proof of Functional Completeness in Many-Valued Logics Based on Ł Ukasiewicz's $C$ and $N$. Notre Dame Journal of Formal Logic 3 (2):114-117.
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  23. Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij (2010). Tolerant, Classical, Strict. Journal of Philosophical Logic 41 (2):347-385.
    In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...)
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  24. William S. Cooper (1968). The Propositional Logic of Ordinary Discourse. Inquiry 11 (1-4):295 – 320.
    The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...)
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  25. Fabrice Correia (2001). Priorean Strict Implication, Q and Related Systems. Studia Logica 69 (3):411-427.
    We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.
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  26. Fabrice Correia (1999). Adequacy Results for Some Priorean Modal Propositional Logics. Notre Dame Journal of Formal Logic 40 (2):236-249.
    Standard possible world semantics for propositional modal languages ignore truth-value gaps. However, simple considerations suggest that it should not be so. In Section 1, I identify what I take to be a correct truth-clause for necessity under the assumption that some possible worlds are incomplete (i.e., "at" which some propositions lack a truth-value). In Section 2, I build a world semantics, the semantics of TV-models, for standard modal propositional languages, which agrees with the truth-clause for necessity previously identified. Sections 3–5 (...)
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  27. Boris Čulina (2001). The Concept of Truth. Synthese 126 (1-2):339 - 360.
    On the basis of elementary thinkingabout language functioning,a solution of truth paradoxes isgiven and a correspondingsemantics of a truth predicateis founded. It is shown that it is precisely thetwo-valued description of the maximal intrinsic fixedpoint of the strong Kleene three-valuedsemantics.
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  28. M. V. Dougherty (2004). Aristotle's Four Truth Values. British Journal for the History of Philosophy 12 (4):585-609.
  29. Hércules Araújo Feitosa (2010). Translating Lukasiewicz's Logics Into Classical Logic: A Grade of Difficulty. Princípios 8 (10):109-120.
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  30. Thomas Macaulay Ferguson (forthcoming). Faulty Belnap Computers and Subsystems of FDE. Journal of Logic and Computation.
    In this article, we consider variations of Nuel Belnap's "artificial reasoner". In particular, we examine cases in which the artificial reasoner is faulty, e.g. situations in which the reasoner is unable to calculate the value of a formula due to an inability to retrieve the values of its atoms. In the first half of the article, we consider two ways of modelling such circumstances and prove the deductive systems arising from these two types of models to be equivalent to Graham (...)
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  31. Thomas Macaulay Ferguson (2015). Logics of Nonsense and Parry Systems. Journal of Philosophical Logic 44 (1):65-80.
    We examine the relationship between the logics of nonsense of Bochvar and Halldén and the containment logics in the neighborhood of William Parry’s A I. We detail two strategies for manufacturing containment logics from nonsense logics—taking either connexive and paraconsistent fragments of such systems—and show how systems determined by these techniques have appeared as Frederick Johnson’s R C and Carlos Oller’s A L. In particular, we prove that Johnson’s system is precisely the intersection of Bochvar’s B 3 and Graham Priest’s (...)
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  32. Thomas Macaulay Ferguson (2014). A Computational Interpretation of Conceptivism. Journal of Applied Non-Classical Logics 24 (4):333-367.
    The hallmark of the deductive systems known as ‘conceptivist’ or ‘containment’ logics is that for all theorems of the form , all atomic formulae appearing in also appear in . Significantly, as a consequence, the principle of Addition fails. While often billed as a formalisation of Kantian analytic judgements, once semantics were discovered for these systems, the approach was largely discounted as merely the imposition of a syntactic filter on unrelated systems. In this paper, we examine a number of prima (...)
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  33. Thomas Macaulay Ferguson (2014). On Non-Deterministic Quantification. Logica Universalis 8 (2):165-191.
    This paper offers a framework for extending Arnon Avron and Iddo Lev’s non-deterministic semantics to quantified predicate logic with the intent of resolving several problems and limitations of Avron and Anna Zamansky’s approach. By employing a broadly Fregean picture of logic, the framework described in this paper has the benefits of permitting quantifiers more general than Walter Carnielli’s distribution quantifiers and yielding a well-behaved model theory. This approach is purely objectual and yields the semantical equivalence of both α-equivalent formulae and (...)
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  34. Thomas Macaulay Ferguson (2014). Łukasiewicz Negation and Many-Valued Extensions of Constructive Logics. In Proc. 44th International Symposium on Multiple-Valued Logic. IEEE Computer Society Press. 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 n ≥ 2. These enriched (...)
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  35. Thomas Macaulay Ferguson (2012). Notes on the Model Theory of DeMorgan Logics. Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...)
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  36. C. G. Fermüller (2008). Dialogue Games for Many-Valued Logics — an Overview. 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 (...)
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  37. Hartry H. Field (2008). Saving Truth From Paradox. Oxford University Press.
    A selective background -- Broadly classical approaches -- Paracompleteness -- More on paracomplete solutions -- Paraconsistent dialetheism.
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  38. Josep Maria Font & Petr Hájek (2002). On Łukasiewicz's Four-Valued Modal Logic. Studia Logica 70 (2):157-182.
    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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  39. Joseph S. Fulda (1985). Alpha Beta Pruning. SIGART Newsletter 94:26.
    Alpha-beta pruning is a technique for pruning trees in artificial intelligence game-playing. This note draws an analogy between the technique, which is, in essence, an application of many-valued logic to the cut-off of the evaluation of conditionals in computer programs (for efficiency).
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  40. Christopher Gauker, Kripke's Theory of Truth.
    This is not a research paper. It is just a handout that I prepared for a course some years ago. It is a presentation of Kripke's theory of truth that I intend to be understandable even to people who have had only a first course in logic. Although elementary, it is completely precise. All the terms are defined and all the proofs (except one trivial induction) are given in detail. I am putting this on the web because I think there (...)
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  41. Christopher Gauker (forthcoming). Presuppositions as Anaphoric Duality Enablers. Topoi:1-12.
    The key to an adequate account of presupposition projection is to accommodate the fact that the presuppositions of a sentence cannot always be read off the sentence but can often be identified only on the basis of prior utterances in the conversation in which the sentence is uttered. In addition, an account of presupposition requires a three-valued semantics of assertibility and deniability in a context. Presuppositions can be explicated as sentences that belong to the conversation and the assertibility of which (...)
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  42. Christopher Gauker (2006). Against Stepping Back: A Critique of Contextualist Approaches to the Semantic Paradoxes. Journal of Philosophical Logic 35 (4):393 - 422.
    A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can 'step back' and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this 'stepping back' idea is a mistake that results from failing to relativize truth (...)
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  43. Stamatios Gerogiorgakis (2012). Privations, Negations and the Square: Basic Elements of a Logic of Privations. In Jean-Yves Beziau & Dale Jacquette (eds.), Around and beyond the Square of Opposition. Birkhäuser-Springer. 229--239.
    I try to explain the difference between three kinds of negation: external negation, negation of the predicate and privation. Further I use polygons of opposition as heuristic devices to show that a logic which contains all three mentioned kinds of negation must be a fragment of a Łukasiewicz-four-valued predicate logic. I show, further, that, this analysis can be elaborated so as to comprise additional kinds of privation. This would increase the truth-values in question and bring fragments of (more generally speaking) (...)
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  44. J. Gispert (2002). Universal Classes of MV-Chains with Applications to Many-Valued Logics. Mathematical Logic Quarterly 48 (4):582-601.
    In this paper we characterize, classify and axiomatize all universal classes of MV-chains. Moreover, we accomplish analogous characterization, classification and axiomatization for congruence distributive quasivarieties of MV-algebras. Finally, we apply those results to study some finitary extensions of the Łukasiewicz infinite valued propositional calculus.
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  45. Patrick Greenough (2010). Deflationism and Truth-Value Gaps. In Nikolaj Pedersen & Cory D. Wright (eds.), New Waves inTruth. Palgrave Macmillan.
    Central to any form of Deflationism concerning truth (hereafter ‘DT’) is the claim that truth has no substantial theoretical role to play. For this reason, DT faces the following immediate challenge: if truth can play no substantial theoretical role then how can we model various prevalent kinds of indeterminacy—such as the indeterminacy exhibited by vague predicates, future contingents, liar sentences, truth-teller sentences, incomplete stipulations, cases of presupposition failure, and such-like? It is too hasty to assume that these phenomena are all (...)
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  46. L. H. Hackstaff & Józef M. Bocheński (1962). A Study in Many-Valued Logic. Studies in East European Thought 2 (1):37-48.
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  47. William H. Jobe (1962). Functional Completeness and Canonical Forms in Many-Valued Logics. Journal of Symbolic Logic 27 (4):409-422.
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  48. Fred Johnson (1984). Trees for a 3-Valued Logic. Analysis 44 (1):43-6.
    Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.
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  49. Fred Johnson (1976). A Three-Valued Interpretation for a Relevance Logic. The Relevance Logic Newsletter 1 (3):123-128.
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  50. Daisuke Kachi (2009). Bourne on Future Contingents and Three-Valued Logic. 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 significance of the intermediate truth-value so (...)
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