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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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  • Maximal Three-Valued Clones with the Gupta-Belnap Fixed-Point Property.José Martínez Fernández - 2007 - Notre Dame Journal of Formal Logic 48 (4):449-472.
    This paper gives a propositional reformulation of the fixed-point problem posed by Gupta and Belnap, using the stipulation logic of Visser. After presenting a solution for clones of three-valued operators that include the constant functions, I determine the maximal three-valued clones with constants that have the fixed-point property, giving different characterizations of them.
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  • Entailment: The Logic of Relevance and Necessity.Alan Ross Anderson - 1975 - Princeton University Press.
  • 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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  • Introduction to Metamathematics.Stephen Cole Kleene - 1952 - North Holland.
  • Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing.
  • The Logic of the Catuskoti.Graham Priest - 2010 - Comparative Philosophy 1 (2):24-54.
    In early Buddhist logic, it was standard to assume that for any state of a ff airs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time mak­ing sense of this, but it makes perfectly good sense in the se­mantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest (...)
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  • 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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  • The Connectives.Ian Humberstone - unknown
     
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  • Towards a Philosophical Understanding of the Logics of Formal Inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify (...)
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  • Faulty Belnap Computers and Subsystems of FDE.Thomas Macaulay Ferguson - forthcoming - 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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  • 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 bilattices the extensions do not produce any new equivalences.
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  • Nearly Every Normal Modal Logic is Paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.
    An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...)
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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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  • Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
  • Extensions of Priest-da Costa Logic.Thomas Macaulay Ferguson - 2014 - Studia Logica 102 (1):145-174.
    In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...)
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  • Classical Negation and Expansions of Belnap–Dunn Logic.Michael De & Hitoshi Omori - 2015 - Studia Logica 103 (4):825-851.
    We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and (...)
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  • Paraconsistent Analytic Implication.Harry Deutsch - 1984 - Journal of Philosophical Logic 13 (1):1 - 11.
  • The Fregean Axiom and Polish Mathematical Logic in the 1920s.Roman Suszko - 1977 - Studia Logica 36 (4):377-380.
    Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.
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  • A Note on Negation.CharlesB Daniels - 1990 - Erkenntnis 32 (3):423 - 429.
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  • Power Matrices and Dunn--Belnap Semantics: Reflections on a Remark of Graham Priest.Lloyd Humberstone - 2014 - Australasian Journal of Logic 11 (1).
    The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices whose underlying algebras are power algebras, where the power algebra of a given algebra has as elements textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis of (...)
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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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  • Multi-Valued Calculi for Logics Based on Non-Determinism.Arnon Avron & Beata Konikowska - 2005 - Logic Journal of the IGPL 13 (4):365-387.
    Non-deterministic matrices are multiple-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. We consider two different types of semantics which are based on Nmatrices: the dynamic one and the static one . We use the Rasiowa-Sikorski decomposition methodology to get sound and complete proof systems employing finite sets of mv-signed formulas for all propositional logics based on such structures with either of the above (...)
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  • A Semantical Analysis of the Calculi Cn.Newton C. A. da Costa - 1977 - Notre Dame Journal of Formal Logic 18:621.
  • 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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  • 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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  • 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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  • Logic of Antinomies.F. G. Asenjo & J. Tamburino - 1975 - Notre Dame Journal of Formal Logic 16 (1):17-44.
  • A Semantical Analysis of the Calculi C N.Newton C. A. Da Costa & E. H. Alves - 1977 - Notre Dame Journal Fo Formal Logic 18 (4):621-630.
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  • An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.
     
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  • The Connectives.Lloyd Humberstone - 2011 - MIT Press.
    It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.This landmark work offers both ...
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  • A Family of Conforming Relevant Logics.Harry Seton Deutsch - 1981 - Dissertation, University of California, Los Angeles
    Logic is easily misunderstood, especially relevant logic. Thus the philosopher Peter Geach deplores the current preoccupation with "inconsistent" logic that are non-trivial and yet inconsistent). But what use are these, anyway? And, as for entailment , the concept is well-developed and well-established. Why meddle with it? ;In this work, we do not meddle with logical consequence. Instead, we develop a group of well-behaved logics that are conforming; i.e. that conform to the Boolean Order of Things, according to which a contradiction (...)
     
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  • The Semantic Foundations of Logic.Richard L. Epstein - 1994 - Oxford University Press.
    This book presents modern logic as the formalization of reasoning that needs and deserves a semantic foundation. Chapters on propositional logic; parsing propositions; and meaning, truth and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The chapter on second-order logic shows how different conceptions of predicates (...)
     
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  • Paraconsistency, paracompleteness, and valuations.A. Loparic - 1984 - Logique Et Analyse 27 (6):119.
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  • The Logic of Nonsense.S. Hallden - 1949 - Upsala Universitets Arsskrift.
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  • Non-Deterministic Semantics for Logics with a Consistency Operator.Arnon Avron - unknown
    In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent. One of the oldest and best known approaches to the problem of designing useful paraconsistent logics is da Costa’s approach, which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. Da Costa’s approach has led to the family of logics (...)
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