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On the Proof-Theoretic Foundation of General Definition Theory

Lars Hallnäs
Synthese
Vol. 148, No. 3, Proof-Theoretic Semantics (Feb., 2006), pp. 589-602
Published by: Springer
Stable URL: http://www.jstor.org/stable/20118710
Page Count: 14
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On the Proof-Theoretic Foundation of General Definition Theory
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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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