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Abstract: In this paper we give a strong normalization proof for a set of reduction rules for classical logic. These reductions, more general then the ones usually considered in literature, are inspired to the reductions of Felleisen's lambda calculus with continuations. 1 Introduction Recently, in the logic and theoretical computer science community, there has been an ever growing interest in the computational features of classical logic. The problem on which research is beginning to focus now is not... (Update)
Context of citations to this paper: More
...operators; we call such calculi classical calculi. In the overwhelming majority of cases see for example [8, 9, 15, 22, 34, 48, 49, 50, 51, 52, 56, 57, 64] the calculus considered is essentially the simply typed or polymorphic calculus; other calculi considered...
.... were followed by a series of papers on classical logic, control operators and the Curry Howard isomorphism, see for example [3,4,18,24,42,62 66,69 72,82]. Most of these works introduce one typed classical calculus, i.e. a typed calculus enriched with control operators, and...
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BibTeX entry: (Update)
F. Barbanera and S. Berardi. A strong normalization result for classical logic. Annals of Pure and Applied Logic, 76(2):99--116, December 1995. http://citeseer.ist.psu.edu/barbanera95strong.html More
@article{ barbanera95strong,
author = "Franco Barbanera and Stefano Berardi",
title = "A Strong Normalization Result for Classical Logic",
journal = "Annals of Pure and Applied Logic",
volume = "76",
number = "2",
pages = "99-116",
year = "1995",
url = "citeseer.ist.psu.edu/barbanera95strong.html" }
Citations (may not include all citations):254 The revised 3 report on the algorithmic language Scheme - Clinger, Rees - 1986
134 calculus: an algorithmic interpretation of classical natural.. (context) - Parigot - 1992
132 Interpr'etation fonctionelle et 'elimination des coupures da.. (context) - Girard - 1972
121 Intensional interpretation of functional of finite types (context) - Tait - 1967
110 A formulae-as-types notion of control - Griffin - 1990
61 Une extension de l'interpretation de Godel a l'analyse (context) - Girard - 1971
60 Extracting constructive content from classical proofs (context) - Murthy - 1990
58 a proof theoretical study (context) - Prawitz, deduction - 1965
46 CS conversion: a syntactic theory of control and state in im.. (context) - Felleisen, of - 1987
34 Reasoning with continuations (context) - Felleisen, Friedman et al. - 1986
34 Classically and intuitionistically provably recursive functi.. (context) - Friedman - 1978
22 the SECD machine and the -calculus (context) - Felleisen, Friedman et al. - 1986
14 Extracting constructive content from classical proofs via co.. - Barbanera, Berardi - 1993
10 Mathematical significance of consistency proofs (context) - Kreisel - 1958
6 Witness Extraction in Classical Logic through Normalization (context) - Barbanera, Berardi - 1993
2 Validity and normalizability of proofs in 1-st and 2nd order.. (context) - Prawitz - 1981
2 candidates de reductibilit'e (context) - Gallier, Girard's - 1990
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