On the Proof-theoretic Foundation of General Definition Theory
Abstract
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) that could provide a basis for a more systematic definitional approach to general proof theory.Other Versions
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Validity Concepts in Proof-theoretic Semantics.Peter Schroeder-Heister -2006 -Synthese 148 (3):525-571.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister &Thomas Piecha (eds.) -2015 - Cham, Switzerland: Springer Verlag.
Failure of Completeness in Proof-Theoretic Semantics.Thomas Piecha,Wagner de Campos Sanz &Peter Schroeder-Heister -2015 -Journal of Philosophical Logic 44 (3):321-335.
Characterizing generics are material inference tickets: a proof-theoretic analysis.Preston Stovall -2019 -Inquiry: An Interdisciplinary Journal of Philosophy (5):668-704.
References found in this work
Ideas and Results in Proof Theory.Dag Prawitz &J. E. Fenstad -1971 -Journal of Symbolic Logic 40 (2):232-234.
Intensional interpretations of functionals of finite type I.W. W. Tait -1967 -Journal of Symbolic Logic 32 (2):198-212.
Einführungin die operative Logik und Mathematik.Th Skolem -1957 -Zeitschrift für Philosophische Forschung 11 (4):631-633.
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