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Abstract: Newman's Lemma states that a graph is confluent if it is locally confluent and has no infinite paths. Newman's Lemma requires essentially higher-order logic. We show that the induction step in Huet's inductive proof of Newman's Lemma is completely first-order and can be automated easily with the help of a resolution theorem prover. The resolution proof uses classical logic. For the automation of a constructive proof we consider Newman's Lemma in geometric logic and sketch an algorithm leading... (Update)
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...the model of computation. It is not known and probably not true that this theorem holds in the Turing model (see a popular discussion in [46]) The Kolmogorov Uspensky machines, which are usually used, are algorithms with semilocal transformation of information, see [18,...
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2: Algorithmic information theory - Chaitin - 1977
BibTeX entry: (Update)
Gurevich, Y. (1988) The logic in computer science column. Bull. European Assoc. Theor. Comp. Sci., 35, 71--82. http://citeseer.ist.psu.edu/bezem88newmans.html More
@article{ bezem03newmans,
author = "M. Bezem and T. Coquand",
title = "Newman's Lemma --- a Case Study in Proof Automation and Geometric Logic",
editor = "Gurevich, Y.",
journal = "Bull. European Assoc. Theor. Comp. Sci.",
month = feb,
year = "2003",
url = "citeseer.ist.psu.edu/bezem88newmans.html" }
Citations (may not include all citations):74 equivalence (context) - Newman, with et al. - 1942
30 Mathematical logic (context) - Kleene - 1967
26 Cambridge Studies in Advanced Mathematics (context) - Johnstone, Spaces - 1982
20 Con uent reductions: Abstract properties and applications to.. (context) - Huet - 1980
18 The Automation of Reasoning: an Experimenter's Notebook with.. (context) - Wos - 1996
16 A Fascinating Country in the World of Computing: Your Guide .. (context) - Wos, Pieper - 2000
11 Die Widerspruchsfreiheit der reinen Zahlentheorie (context) - Gentzen - 1936
4 Notes on Constructive Mathematics (context) - Martin-L - 1970
3 Selected Works in Logic (context) - Skolem - 1970
3 Contraction-free sequent calculi for geometric theories (context) - Negri
2 Toposes without points (context) - Barr - 1974
2 Topoi and computation (context) - Blass - 1998
1 Dynamical methods in algebra: e ective Nullstellensatze (context) - Coste, Lombardi et al. - 2001
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