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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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  1. Department of Computing Science, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Lars Hallnäs

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  1. Lars Hallnäs
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Correspondence to Lars Hallnäs.

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Hallnäs, L. On the Proof-theoretic Foundation of General Definition Theory. Synthese 148, 589–602 (2006). https://doi.org/10.1007/s11229-004-6291-6

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  • DOI: https://doi.org/10.1007/s11229-004-6291-6

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