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  1. Introduction to Metamathematics.H. Rasiowa - 1954 - Journal of Symbolic Logic 19 (3):215-216.
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  • Introduction to Metamathematics.Ann Singleterry Ferebee - 1968 - Journal of Symbolic Logic 33 (2):290-291.
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  • Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
  • The Logic of Nonsense.Sören Halldén - 1949 - Uppsala, Sweden: Upsala Universitets Arsskrift.
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  • Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
    Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...)
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  • Past, Present and Future.Arthur N. Prior - 1967 - Oxford, England: Clarendon Press.
    But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...
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  • Spandrels of Truth.J. C. Beall - 2009 - Oxford, England: Oxford University Press.
    In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth.
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  • Frege: Philosophy of Language.Michael Dummett - 1973 - London: Duckworth.
    This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...
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  • Time and Modality.Arthur N. Prior - 1955 - Greenwood Press.
    The relationship between formal logic and general philosophy is discussed under headings such as A Re-examination of Our Tense-Logical Postulates, Modal Logic in the Style of Frege, and Intentional Logic and Indeterminism.
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  • In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
    In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...)
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  • An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Cambridge University Press.
    This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and (...)
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  • Relevant Logic: A Philosophical Interpretation.Edwin D. Mares - 2004 - Cambridge University Press.
    This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles and natural language conditionals. The book ends by examining various applications of relevant logic and (...)
  • The Logic of Significance and Context.Leonard Goddard - 1973 - New York: Wiley.
  • Free Choice Disjunction and Epistemic Possibility.Thomas Ede Zimmermann - 2000 - Natural Language Semantics 8 (4):255-290.
    This paper offers an explanation of the fact that sentences of the form (1) ‘X may A or B’ may be construed as implying (2) ‘X may A and X may B’, especially if they are used to grant permission. It is suggested that the effect arises because disjunctions are conjunctive lists of epistemic possibilities. Consequently, if the modal may is itself epistemic, (1) comes out as equivalent to (2), due to general laws of epistemic logic. On the other hand, (...)
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  • Consistency and Realism.Bernard A. O. Williams - 1966 - Aristotelian Society Supplementary Volume 40 (1):1-22.
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  • Theories of truth based on four-valued infectious logics.Damian Szmuc, Bruno Da Re & Federico Pailos - 2020 - Logic Journal of the IGPL 28 (5):712-746.
    Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...)
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  • Defining LFIs and LFUs in extensions of infectious logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
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  • Significance logics.Ross T. Brady - 1976 - Notre Dame Journal of Formal Logic 17 (2):161-183.
  • Past, Present and Future.Arthur N. Prior - 1967 - Oxford University Press.
    Surveys and extens work that has been done in the past two years on 'tense logic' and is a sequel to the author's book, Time and Modality.
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  • Plurivalent Logics.Graham Priest - 2014 - Australasian Journal of Logic 11 (1).
    In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one (...)
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  • Contradiction, assertion and 'Frege's point'.Graham Priest & Alonso Church - 1989 - Analysis 49 (1):23-26.
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  • Contradiction, Assertion and 'Frege's Point'.Graham Priest & Richard Sylvan - 1989 - Analysis 49 (1):23 - 26.
  • Paraconsistency and Analyticity.Carlos A. OLLER - 1999 - Logic and Logical Philosophy 7 (1):91-99.
    William Parry conceived in the early thirties a theory of entail-
    ment, the theory of analytic implication, intended to give a formal expression to the idea that the content of the conclusion of a valid argument must be included in the content of its premises. This paper introduces a system of analytic, paraconsistent and quasi-classical propositional logic that does not validate the paradoxes of Parry’s analytic implication. The interpretation of the expressions of this logic will be given in terms of a (...)
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  • The true modal logic.Christopher Menzel - 1991 - Journal of Philosophical Logic 20 (4):331 - 374.
    This paper traces the course of Prior’s struggles with the concepts and phenomena of modality, and the reasoning that led him to his own rather peculiar modal logic Q. I find myself in almost complete agreement with Prior’s intuitions and the arguments that rest upon them. However, I argue that those intuitions do not of themselves lead to Q, but that one must also accept a certain picture of what it is for a proposition to be possible. That picture. though, (...)
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  • Relevant Logic: A Philosophical Interpretation.Reinhard Kahle - 2007 - Studia Logica 85 (3):419-424.
  • Towards a logic of significance.Leonard Goddard - 1968 - Notre Dame Journal of Formal Logic 9 (3):233-264.
  • On notation for ordinal numbers.S. C. Kleene - 1938 - Journal of Symbolic Logic 3 (4):150-155.
  • On Notation for Ordinal Numbers.S. C. Kleene - 1939 - Journal of Symbolic Logic 4 (2):93-94.
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  • Analytic implication.Kit Fine - 1986 - Notre Dame Journal of Formal Logic 27 (2):169-179.
  • A modification of Parry's analytic implication.J. Michael Dunn - 1972 - Notre Dame Journal of Formal Logic 13 (2):195-205.
  • The Logic of Significance and Context.K. Fine - 1978 - Philosophical Quarterly 28 (113):362-364.
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  • The Logic of Significance and Context.Nino B. Cocchiarella - 1984 - Journal of Symbolic Logic 49 (4):1413-1415.
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  • Investigations into Logical Deduction.Gerhard Gentzen, M. E. Szabo & Paul Bernays - 1970 - Journal of Symbolic Logic 35 (1):144-145.
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  • Logics of Nonsense and Parry Systems.Thomas Macaulay Ferguson - 2015 - 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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  • A computational interpretation of conceptivism.Thomas Macaulay Ferguson - 2014 - 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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  • Star and perp: Two treatments of negation.J. Michael Dunn - 1993 - Philosophical Perspectives 7:331-357.
  • Michael Dummett, Frege: Philosophy of Language. [REVIEW]Hidé Ishiguro - 1974 - Philosophy 49 (190):438-442.
  • A note on negation.CharlesB Daniels - 1990 - Erkenntnis 32 (3):423 - 429.
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  • Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - 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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  • 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 two properties that we call fixed-point negation property (...)
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  • A story semantics for implication.Charles Daniels - 1986 - Notre Dame Journal of Formal Logic 27 (2):221-246.
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  • Why is conjunctive simplification invalid?Bruce E. R. Thompson - 1991 - Notre Dame Journal of Formal Logic 32 (2):248-254.
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  • Don't care was made to care.Ross Brady & Richard Routley - 1973 - Australasian Journal of Philosophy 51 (3):211 – 225.
  • On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis.Stefano Bonzio, José Gil-Férez, Francesco Paoli & Luisa Peruzzi - 2017 - Studia Logica 105 (2):253-297.
    Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...)
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  • Off-Topic: A New Interpretation of Weak-Kleene Logic.Jc Beall - 2016 - Australasian Journal of Logic 13 (6).
    This paper offers a new and very simple alternative to Bochvar's well known nonsense -- or meaninglessness -- interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative -- and I think very elegant -- interpretation, not necessarily a replacement.
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  • Free of Detachment: Logic, Rationality, and Gluts.Jc Beall - 2015 - Noûs 49 (2):410-423.
  • Analetheism and dialetheism.J. Beall & D. Ripley - 2004 - Analysis 64 (1):30-35.
  • A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
     
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  • Bilattices are nice things.Melvin Fitting - 2006 - In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. CSLI Publications.
    One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artificial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while making (...)
     
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  • A counterexample to modus ponens.Vann McGee - 1985 - Journal of Philosophy 82 (9):462-471.