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Normality Operators and Classical Collapse

In T. Arazim P. And Lavicka (ed.), The Logica Yearbook 2017. Londra, Regno Unito: pp. 2-20 (2018)

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  1. Vagueness in Context.Stewart Shapiro - 2006 - Oxford University Press UK.
    Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professional basketball players. The main feature (...)
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  • In Contradiction: A Study of the Transconsistent.Graham Priest - 2006 - 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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  • The Revision Theory of Truth.A. Gupta & N. Belnap - 1993 - MIT Press.
    In this rigorous investigation into the logic of truth Anil Gupta and Nuel Belnap explain how the concept of truth works in both ordinary and pathological..
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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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  • Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
  • Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
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  • Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • Formal Inconsistency and Evolutionary Databases.Walter A. Carnielli, João Marcos & Sandra De Amo - 2000 - Logic and Logical Philosophy 8 (2):115-152.
    This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...)
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  • Sorting Out the Sorites.David Ripley - 2013 - In Francesco Berto, Edwin Mares & Koji Tanaka (eds.), Paraconsistency: Logic and Applications. pp. 329-348.
    Supervaluational theories of vagueness have achieved considerable popularity in the past decades, as seen in eg [5], [12]. This popularity is only natural; supervaluations let us retain much of the power and simplicity of classical logic, while avoiding the commitment to strict bivalence that strikes many as implausible. Like many nonclassical logics, the supervaluationist system SP has a natural dual, the subvaluationist system SB, explored in eg [6], [28].1 As is usual for such dual systems, the classical features of SP (...)
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  • The Revision Theory of Truth.Vann McGee - 1996 - Philosophy and Phenomenological Research 56 (3):727-730.
  • Vagueness in Context. [REVIEW]Stewart Shapiro - 2008 - Philosophy and Phenomenological Research 76 (2):471-483.
  • Lp+, K3+, Fde+, and Their 'Classical Collapse'.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):742-754.
    This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+.
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  • Multiple-Conclusion Lp and Default Classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.
    Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of . With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.
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  • Tautological Entailments.Alan Ross Anderson & Nuel D. Belnap - 1962 - Philosophical Studies 13 (1-2):9 - 24.
  • A Paraconsistent Theory of Belief Revision.Edwin D. Mares - 2002 - Erkenntnis 56 (2):229 - 246.
    This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.
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  • The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
  • Minimally Inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.
    The paper explains how a paraconsistent logician can appropriate all classical reasoning. This is to take consistency as a default assumption, and hence to work within those models of the theory at hand which are minimally inconsistent. The paper spells out the formal application of this strategy to one paraconsistent logic, first-order LP. (See, Ch. 5 of: G. Priest, In Contradiction, Nijhoff, 1987.) The result is a strong non-monotonic paraconsistent logic agreeing with classical logic in consistent situations. It is shown (...)
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  • 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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  • Tautological Entailments.Alan Ross Anderson & Nuel D. Belnap - 1968 - Journal of Symbolic Logic 33 (4):608-608.
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  • Analytic Inference and the Informational Meaning of the Logical Operators.Marcello D'Agostino - forthcoming - Logique Et Analyse.
     
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  • On the Theory of Inconsistent Formal Systems.Newton C. A. Da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.
  • Vague Inclosures.Graham Priest - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 367--377.
  • Paraconsistent Belief Revision.Graham Priest - 2001 - Theoria 67 (3):214-228.
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