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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)Proof theory.Gaisi Takeuti - 1975 - New York, N.Y., U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co..
    This comprehensive monograph is a cornerstone in the area of mathematical logic and related fields. Focusing on Gentzen-type proof theory, the book presents a detailed overview of creative works by the author and other 20th-century logicians that includes applications of proof theory to logic as well as other areas of mathematics. 1975 edition.
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  • Proof Theory.Gaisi Takeuti - 1990 - Studia Logica 49 (1):160-161.
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  • Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219-241.
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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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  • The semantic foundations of logic.Richard L. Epstein - 1994 - New York: 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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  • 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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  • Ideal Paraconsistent Logics.O. Arieli, A. Avron & A. Zamansky - 2011 - Studia Logica 99 (1-3):31-60.
    We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...)
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  • Gentzen-type systems, resolution and tableaux.Arnon Avron - 1993 - Journal of Automated Reasoning 10:265-281.
    In advanced books and courses on logic (e.g. Sm], BM]) Gentzen-type systems or their dual, tableaux, are described as techniques for showing validity of formulae which are more practical than the usual Hilbert-type formalisms. People who have learnt these methods often wonder why the Automated Reasoning community seems to ignore them and prefers instead the resolution method. Some of the classical books on AD (such as CL], Lo]) do not mention these methods at all. Others (such as Ro]) do, but (...)
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  • Sequents and bivaluations.Jean-Yves Béziau - 2001 - Logique Et Analyse 44 (176):373-394.
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  • An Introduction to Proof Theory.Samuel R. Buss - 2000 - Bulletin of Symbolic Logic 6 (4):464-465.
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