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  1. Silver Type Theorems for Collapses.Moti Gitik - 2020 - Annals of Pure and Applied Logic 171 (9):102825.
    Let κ be a cardinal of cofinality \omega_1 witnessed by a club of cardinals (κ_\alpha | \alpha < \omega_1) . We study Silver's type effects of collapsing of κ^+_\alphas 's on κ^+ . A model in which κ^+_\alphas 's (and also κ^+) are collapsed on a stationary co-stationary set is constructed.
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  2. Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - 2020 - Studia Logica 108 (3):573-595.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...)
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  3. The Explosion Calculus.Michael Arndt - 2020 - Studia Logica 108 (3):509-547.
    A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules. Employed in the style of proof search, this calculus explodes a given sequent into its elementary structural sequents—the topmost sequents in a derivation thus constructed—which do not contain any logical constants. Some of the properties exhibited by the collection of elementary structural sequents in relation to the sequent they are derived from, uniqueness and unique representation (...)
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  4. Interpolation in Extensions of First-Order Logic.Guido Gherardi, Paolo Maffezioli & Eugenio Orlandelli - 2020 - Studia Logica 108 (3):619-648.
    We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, partial and linear orders, and various intuitionistic order theories such as apartness and positive partial and linear orders.
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  5. Formal Notes on the Substitutional Analysis of Logical Consequence.Volker Halbach - 2020 - Notre Dame Journal of Formal Logic 61 (2):317-339.
    Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...)
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  6. Factorials of Infinite Cardinals in Zf Part II: Consistency Results.Guozhen Shen & Jiachen Yuan - 2020 - Journal of Symbolic Logic 85 (1):244-270.
    For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that |p(x)|<|S(x)|<|seq^1-1(x)|<|seq(x)|, where p(x) is the powerset of x, seq(x) is the set of all finite sequences of elements of x, and seq^1-1(x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind infinite set (...)
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  7. Herbrand's Theorem as Higher Order Recursion.Bahareh Afshari, Stefan Hetzl & Graham E. Leigh - 2020 - Annals of Pure and Applied Logic 171 (6):102792.
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  8. Três Vezes Não: Um Estudo Sobre as Negações Clássica, Paraconsistente e Paracompleta.Kherian Gracher - 2020 - Dissertation, Federal University of Santa Catarina
    Could there be a single logical system that would allow us to work simultaneously with classical, paraconsistent, and paracomplete negations? These three negations were separately studied in logics whose negations bear their names. Initially we will restrict our analysis to propositional logics by analyzing classical negation, ¬c, as treated by Classical Propositional Logic (LPC); the paraconsistent negation, ¬p, as treated through the hierarchy of Paraconsistent Propositional Calculi Cn (0 ≤ n ≤ ω); and the paracomplete negation, ¬q, as treated by (...)
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  9. A Recovery Operator for Nontransitive Approaches.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Review of Symbolic Logic 13 (1):80-104.
    In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...)
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  10. Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability.Frederik Van De Putte & Dominik Klein - forthcoming - Studia Logica:1-47.
    We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein. The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.
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  11. Transfinite Meta-inferences.Chris Scambler - forthcoming - Journal of Philosophical Logic:1-11.
    In Barrio et al. Barrio Pailos and Szmuc prove that there are systems of logic that agree with classical logic up to any finite meta-inferential level, and disagree with it thereafter. This article presents a generalized sense of meta-inference that extends into the transfinite, and proves analogous results to all transfinite orders.
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  12. Computational Logic. Vol. 1: Classical Deductive Computing with Classical Logic. 2nd Ed.Luis M. Augusto - 2020 - London: College Publications.
    This is the 2nd edition of Computational logic. Vol. 1: Classical deductive computing with classical logic. This edition has a wholly new chapter on Datalog, a hard nut to crack from the viewpoint of semantics when negation is included.
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  13. Fregean Quantification Theory.Saul A. Kripke - 2014 - Journal of Philosophical Logic 43 (5):879-881.
    Frege’s system of first-order logic is presented in a contemporary framework. The system described is distinguished by economy of expression and an unusual syntax.
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  14. Fractional Semantics for Classical Logic.Mario Piazza & Gabriele Pulcini - forthcoming - Review of Symbolic Logic:1-19.
    This article presents a new semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of (...)
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  15. Formal Logic: Classical Problems and Proofs.Luis M. Augusto - 2019 - London, UK: College Publications.
    Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.
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  16. John L. Pollock. Introduction to Symbolic Logic. Holt, Rinehart and Winston, Inc., New York, Etc., 1969, Xii + 241 Pp. [REVIEW]B. G. Hurdle - 1975 - Journal of Symbolic Logic 40 (1):101.
  17. John L. Pollock. Introduction to Symbolic Logic. Holt, Rinehart and Winston, Inc., New York, Etc., 1969, Xii + 241 Pp. [REVIEW]B. G. Hurdle - 1975 - Journal of Symbolic Logic 40 (1):101.
  18. What is a Paraconsistent Logic?Damian Szmuc, Federico Pailos & Eduardo Barrio - 2018 - In Jacek Malinowski & Walter Carnielli (eds.), Contradictions, from Consistency to Inconsistency. Springer Verlag.
    Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is (...)
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  19. Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Synthese:1-17.
    When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...)
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  20. Rumfitt on Truth-Grounds, Negation, and Vagueness.Richard Zach - 2018 - Philosophical Studies 175 (8):2079-2089.
    In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.
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  21. V.—Some Controverted Points in Symbolic Logic.A. T. Shearman - 1904 - Proceedings of the Aristotelian Society 5 (1):74-105.
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  22. Translating Non-Classical Logics Into Classical Logic by Using Hidden Variables.Juan C. Agudelo-Agudelo - 2017 - Logica Universalis 11 (2):205-224.
    Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative procedure (...)
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  23. Second-Order Logic And Foundations Of Mathematics.Jouko V. "A. "An "Anen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
  24. Okres warunkowy a implikacja materialna / Conditional Sentence and Material Implication.Kazimierz Ajdukiewicz - 1956 - Studia Logica 4:117-153.
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  25. The Logic of Conditionals.Ernest Adams, Ernest W. Adams, Jaakko Hintikka & Patrick Suppes - 1974 - Journal of Symbolic Logic 39 (3):609-611.
  26. A Formalisation Of The M-valued Lukasiewicz Implicational Propositional Calculus With Variable Functors.Alan Rose - 1966 - Mathematical Logic Quarterly 12 (1):169-176.
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  27. Does Modern Symbolic Logic Contain Aristotelian Logic as a Part?Richard J. Connell - 1965 - Proceedings and Addresses of the American Philosophical Association 39:183.
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  28. Modus Tollens" revisited.Ernest W. Adams - 1988 - Analysis 48 (3):122.
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  29. Neat Embeddings, Omitting Types, and Interpolation: An Overview.Tarek Ahmed - 2003 - Notre Dame Journal of Formal Logic 44 (3):157-173.
    We survey various results on the relationship among neat embeddings, complete representations, omitting types, and amalgamation. A hitherto unpublished application of algebraic logic to omitting types of first-order logic is given.
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  30. Lewis's A Survey of Symbolic Logic.Norbert Wiener - 1920 - Journal of Philosophy, Psychology and Scientific Methods 17 (3):78.
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  31. Aquinas’ Third Way From the Standpoint of the Aristotelian Syllogistic.Charles J. Kelly - 1986 - The Monist 69 (2):189-206.
    This first part of Thomas Aquinas’ third way has provoked a variety of allegations on the theme of a quantifier shift fallacy. For even if it be granted that every thing at some time does not exist, that is.
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  32. Symbolic Logic.Irving Copi - 1954 - New York: Macmillan.
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  33. Symbolic Logic.Atwell R. Turquette & Frederic Brenton Fitch - 1953 - Philosophical Review 62 (4):617.
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  34. Aristotle's Syllogistic From the Standpoint of Modern Formal Logic.Joseph T. Clark & Jan Lukasiewicz - 1952 - Philosophical Review 61 (4):575.
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  35. Fundamentals of Symbolic Logic.Max Black - 1950 - Philosophical Review 59 (3):391.
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  36. Elements of Symbolic Logic.Nelson Goodman - 1948 - Philosophical Review 57 (1):100.
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  37. Symbolic Logic.Daniel J. Bronstein - 1934 - Philosophical Review 43 (3):305.
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  38. On Polynomial Semantics for Propositional Logics.Juan C. Agudelo-Agudelo, Carlos A. Agudelo-González & Oscar E. García-Quintero - 2016 - Journal of Applied Non-Classical Logics 26 (2):103-125.
    Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.
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  39. Mathematical Logic and Formal Arithmetic: Key Definitions and Principles.John-Michael Kuczynski - 2016 - Amazon Digital Services LLC.
    This books states, as clearly and concisely as possible, the most fundamental principles of set-theory and mathematical logic. Included is an original proof of the incompleteness of formal logic. Also included are clear and rigorous definitions of the primary arithmetical operations, as well as clear expositions of the arithmetic of transfinite cardinals.
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  40. Solving Natural Syllogisms.Guy Politzer - 2010 - In D. Over K. Manktelow (ed.), The science of reason. Psychology Press. pp. 19-35.
    Natural syllogisms are expressed in terms of classes and properties of the real world. They exploit a categorisation present in semantic memory that provides a class inclusion structure. they are enthymematic and typically occur within a dialogue. Their form is identical to a formal syllogism once the minor premise is made explicit. It is claimed that reasoners routinely execute natural_syllogisms in an effortless manner based on ecthesis, which is primed by the class inclusion structure kept in long term memory.
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  41. An Introduction to Symbolic Logic.E. N. - 1938 - Journal of Philosophy 35 (22):613.
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  42. Symbolic Logic.Henry Bradford Smith - 1933 - Journal of Philosophy 30 (11):302.
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  43. Henkin L.. Boolean Representation Through Propositional Calculus. Fundamenta Mathematicae, Vol. 41 No. 1 , Pp. 89–96.Łoś J.. Remarks on Henkin's Paper: Boolean Representation Through Propositional Calculus. Fundamenta Mathematicae, Vol. 44 No. 1 , Pp. 82–83. [REVIEW]Ann S. Ferebee - 1973 - Journal of Symbolic Logic 38 (3):521-522.
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  44. A Formalisation of the ℵ 0 -Valued Lukasiewicz Implicational Propositional Calculus with Variable Functors.B. Scarpellini & Alan Rose - 1970 - Journal of Symbolic Logic 35 (1):143.
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  45. Elements of Symbolic Logic.J. van Heijenoort - 1966 - Journal of Symbolic Logic 31 (4):675.
  46. Shepherdson J. C.. On the Interpretation of Aristotelian Syllogistic. [REVIEW]J. A. Faris - 1957 - Journal of Symbolic Logic 22 (4):381-381.
  47. Basson A. H. And O'Connor D. J.. Introduction to Symbolic Logic. University Tutorial Press Ltd., London 1953, Viii + 169 Pp. [REVIEW]Alonzo Church - 1955 - Journal of Symbolic Logic 20 (1):84-86.
  48. Lewis Clarence Irving and Langford Cooper Harold. Symbolic Logic. Dover Publications, Inc., New York 1951, 7 Pp. + Pp. 3–506. [REVIEW]Alonzo Church - 1951 - Journal of Symbolic Logic 16 (3):225-225.
  49. Henkin Leon. The Completeness of the First-Order Functional Calculus.W. Ackermann - 1950 - Journal of Symbolic Logic 15 (1):68-68.
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  50. Quine Willard V.. Theory of Deduction. Parts I–IV. Mimeographiert. Harvard Cooperative Society, Cambridge, Mass., 1948, 156 S. [REVIEW]W. Ackermann - 1949 - Journal of Symbolic Logic 14 (3):190-191.
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