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Abstract: The paper presents a constructive interpretation for proofs in classical logic of \Sigma 0 1 sentences and for a witness extraction procedure based on Prawitz's reduction rules. 1 Introduction Cut-elimination theorems play a fundamental role in Proof Theory. Many relevant properties of logics can be derived from them. In particular, for intuitionistic logic, cut-elimination allows you to "compute" with proofs. In fact, the constructive contents of an intuitionistic proof can be made explicit... (Update)
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BibTeX entry: (Update)
@article{ barbanera96constructive,
author = "Franco Barbanera and Stefano Berardi",
title = "A Constructive Valuation Semantics for Classical Logic",
journal = "Notre Dame Journal of Formal Logic",
volume = "37",
number = "3",
pages = "462-482",
year = "1996",
url = "citeseer.ist.psu.edu/149372.html" }
Citations (may not include all citations):181 Mathematical Logic (context) - Shoenfield - 1967
71 An intuitionistic theory of types: predicative part (context) - Martin-Lof - 1975
58 a proof theoretical study (context) - Prawitz, deduction - 1965
34 Classically and intuitionistically provably recursive functi.. (context) - Friedman - 1978
16 Zur Deutung der Intuitionistischen Logik (context) - Kolmogorov - 1932
10 Mathematical significance of consistency proofs (context) - Kreisel - 1958
7 Mathematische Grundlagenforschung (context) - Heyting - 1974
6 Witness Extraction in Classical Logic through Normalization (context) - Barbanera, Berardi - 1993
4 A constructive valuation interpretation for classical logic .. (context) - Barbanera, Berardi - 1992
1 Validity and normalizability of proofs in 1-st and 2-nd orde.. (context) - Prawitz - 1981
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