On the Proof-theoretic Foundation of General Definition Theory

Synthese 148 (3):589-602 (2006)
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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.

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10.1007/s11229-004-6291-6

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Citations of this work

Proof-Theoretic Semantics.Peter Schroeder-Heister - forthcoming - Stanford Encyclopedia of Philosophy.
Advances in Proof-Theoretic Semantics.Peter Schroeder-Heister & Thomas Piecha (eds.) - 2015 - Cham, Switzerland: Springer Verlag.

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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.
On the idea of a general proof theory.Dag Prawitz - 1974 - Synthese 27 (1-2):63 - 77.
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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