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  1. Einführung in die operative Logik und Mathematik.Paul Lorenzen - 1955 - Berlin,: Springer.
    in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...)
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  • The justification of deduction.Michael Dummett - 1978 - In Truth and other enigmas. Cambridge: Harvard University Press.
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  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Formal Reductions of the General Combinatorial Decision Problem.Emil L. Post - 1943 - Journal of Symbolic Logic 8 (1):50-52.
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  • On the Proof-theoretic Foundation of General Definition Theory.Lars Hallnäs - 2006 - Synthese 148 (3):589-602.
    A general definition theory should serve as a foundation for the mathematical study of definitional structures. The central notion of such a theory is a precise explication of the intuitively given notion of a definitional structure. The purpose of this paper is to discuss the proof theory of partial inductive definitions as a foundation for this kind of a more general definition theory. Among the examples discussed is a suggestion for a more abstract definition of lambda-terms (derivations in natural deduction) (...)
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  • Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
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  • Introduction to a general theory of elementary propositions.Emil L. Post - 1921 - American Journal of Mathematics 43 (3):163--185.
    In the general theory of logic built up by Whitehead and Russell to furnish a basis for all mathematics there is a certain subtheory which is unique in its simplicity and precision; and though all other portions of the work have their roots in this subtheory, it itself is completely independent of them. Whereas the complete theory requires for the enunciation of its propositions real and apparent variables, which represent both individuals and propositional functions of different kinds, and as a (...)
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  • A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
    The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.
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  • Towards a Foundation of General Proof Theory.Dag Prawitz - 1973 - In ¸ Itetsuppes1973. North Holland, Amsterdam.
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  • Konstruktive Begründung der Mathematik.Paul Lorenzen - 1953 - Journal of Symbolic Logic 18 (3):260-261.
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  • Implications-as-Rules vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW]Peter Schroeder-Heister - 2011 - Journal of Philosophical Logic 40 (1):95 - 101.
    The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form.
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  • Theory of Formal Systems.Raymond M. Smullyan - 1965 - Journal of Symbolic Logic 30 (1):88-90.
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