Semantic values for natural deduction derivations

Synthese 148 (3):623 - 638 (2006)
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.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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DOI 10.2307/20118712
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