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Semantic Values for Natural Deduction Derivations

Göran Sundholm
Synthese
Vol. 148, No. 3, Proof-Theoretic Semantics (Feb., 2006), pp. 623-638
Published by: Springer
Stable URL: http://www.jstor.org/stable/20118712
Page Count: 16
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Semantic Values for Natural Deduction Derivations
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Abstract

Drawing upon Martin-Löf's semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between (logical) consequence among propositions and inference among judgements. Derivations in Gentzen's (1934-5) format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects (of propositions), whereas derivations in Gentzen's (1936) sequential format are (blue-prints for) proof-acts.

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