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  1. The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
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  • (1 other version)Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
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  • A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
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  • Natural 3-valued logics—characterization and proof theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
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  • Logic of antinomies.F. G. Asenjo & J. Tamburino - 1975 - Notre Dame Journal of Formal Logic 16 (1):17-44.
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  • A Note on Freedom from Detachment in the Logic of Paradox.Jc Beall, Thomas Forster & Jeremy Seligman - 2013 - Notre Dame Journal of Formal Logic 54 (1):15-20.
    We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing.
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  • Axioms for finite collapse models of arithmetic.Andrew Tedder - 2015 - Review of Symbolic Logic 8 (3):529-539.
    The collapse models of arithmetic are inconsistent, nontrivial models obtained from â„• and set out in the Logic of Paradox (LP). They are given a general treatment by Priest (Priest, 2000). Finite collapse models are decidable, and thus axiomatizable, because finite. LP, however, is ill-suited to normal axiomatic reasoning, as it invalidates Modus Ponens, and almost all other usual conditional inferences. I set out a logic, A3, first given by Avron (Avron, 1991), and give a first order axiom system for (...)
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  • Inconsistent models of arithmetic part I: Finite models. [REVIEW]Graham Priest - 1997 - Journal of Philosophical Logic 26 (2):223-235.
    The paper concerns interpretations of the paraconsistent logic LP which model theories properly containing all the sentences of first order arithmetic. The paper demonstrates the existence of such models and provides a complete taxonomy of the finite ones.
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