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Automatic 'Descente Infinie' Induction Reasoning
[chapter]
2005
Lecture Notes in Computer Science
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We present a framework and a methodology to build and analyse automatic provers using the 'Descente Infinie' induction principle. ...
Testing a set of conjectures consists in a successive application of 'Descente Infinie' inference rules. ...
In the paper, we will discuss the applications of a formulabased variant of the 'Descente Infinie' induction principle. ...
doi:10.1007/11554554_20
fatcat:sen7aduonbcerludou3fsda57m
A Self-Contained and Easily Accessible Discussion of the Method of Descente Infinie and Fermat's Only Explicitly Known Proof by Descente Infinie
[article]
2010
arXiv
pre-print
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We present the only proof of Pierre Fermat by descente infinie that is known to exist today. ...
We discuss descente infinie from the mathematical, logical, historical, linguistic, and refined logic-historical points of view. ...
aspects of Descente Infinie. ...
arXiv:0902.3623v4
fatcat:2nce5esnfzgbrdw5opkykh4f5e
Computer-assisted human-oriented inductive theorem proving by descente infinie--a manifesto
2012
Logic Journal of the IGPL
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Our main motivation is to explain--on an abstract but hopefully sufficiently descriptive level--why we believe that future progress in the field is to result from human-orientedness and descente infinie ...
Moreover, it is a pleasure to thank Tobias for the wonderful years we shared working on QUODLIBET and descente infinie. ...
Why Descente Infinie is Promising Now The theoretical research paper [111] provides us with the integration of descente infinie into deductive calculi. ...
doi:10.1093/jigpal/jzr048
fatcat:qps74fzzmngmzaluxlcaqogt4y
Étude et implémentation d'un système de déduction pour logique algorithmique
1988
RAIRO - Theoretical Informatics and Applications
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-Cet article présente la maquette d'un outil LAPD, automatisant la déduction dans une logique pour schémas de programme. ...
Ceci rend le système de déduction incomplet. La preuve de non-complétude est cependant présentée car elle précise les limites du système. ...
Une tactique est donc une opération de descente dans l'arbre de déduction. ...
doi:10.1051/ita/1988220100571
fatcat:vxlgk5ruvnb4ra2izimhayznau
History and Future of Implicit and Inductionless Induction: Beware the Old Jade and the Zombie!
[chapter]
2005
Lecture Notes in Computer Science
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In order to clear the fog a little, there is a short introduction to inductive theorem proving and a discussion of connotations of implicit induction like "descente infinie", "inductionless induction", ...
Researchers introduced to descente infinie by [57] (entitled "Lazy Generation of Induction Hypotheses") sometimes speak of "lazy induction" instead of descente infinie. ...
"descente infinie" and "implicit induction orderings". My main interest, however, was and still is to convince the community of the practical importance of "descente infinie", cf. [71] . ...
doi:10.1007/978-3-540-32254-2_12
fatcat:gyrzf5vcw5atnp2gzqbwjhwdam
Multiplicités
1997
Horizons philosophiques
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La descente infinie de Fermât permet de
rester dans ...
Le retour ultime à Fermât confirme le caractère naturel de la descente infinie. ...
doi:10.7202/801060ar
fatcat:dnekqrramnewvkngyzuvj6jcdy
« De la logique interne ». Yvon Gauthier, De la logique interne, Paris, Librairie philosophique J. Vrin, collection Mathesis, 1991, 140 p
1994
Philosophiques
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D'où vient le succès de la descente infinie dans ces cas ? ...
Mais cette induction, Gauthier veut la chasser pour la remplacer par la descente infinie. ...
+i de sorte que la descente devient élémentairement computable » (p. 85). Je me permets de mettre en doute cette affirmation. ...
doi:10.7202/027258ar
fatcat:qgulcpfuvrb2tavu6rway3h2he
Page 825 of Revue Des Deux Mondes Vol. 7, Issue
[page]
1912
Revue Des Deux Mondes
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Ainsi tout le réel se résume en un double mouvement de montée et de descente. ...
NOUVELLE, 825
Dans cette conception de l'être, la conscience est partout, comme la réalité originelle et fondamentale, toujours présente à mille et mille degrés de tension ou de sommeil et sous des rythmes infiniment ...
Yvon Gauthier, De la logique interne, Paris, Librairie philosophique J. Vrin, collection Mathesis, 1991, 140 pages
1995
Philosophiques
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D'où vient le succès de la descente infinie dans ces cas ? ...
Mais cette induction, Gauthier veut la chasser pour la remplacer par la descente infinie.
D. ...
doi:10.7202/027335ar
fatcat:vv642b7gmbfetasljbgm6tdtv4
Integrating Implicit Induction Proofs into Certified Proof Environments
[chapter]
2010
Lecture Notes in Computer Science
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The first part will prove the soundness of the 'Descente Infinie' induction principle instantiated for a particular wellfounded induction ordering. ...
The soundness of any implicit induction reasoning can be easily explained using 'proof-by-contradiction' arguments characterizing the 'Descente Infinie' induction-based approaches [21] . ...
doi:10.1007/978-3-642-16265-7_23
fatcat:dkssy7vlenekpbsmdlkkojrdmu
Page 447 of Mathematical Reviews Vol. , Issue 84b
[page]
1984
Mathematical Reviews
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The second concerns the discovery of the method of the “descente infinie”. ...
The first concerns the following theorem: There is no numerical right-angle triangle, the area of which is a square number, proved by Fermat with the method of the “descente infinie”; according to Genocchi ...
Automation of Mathematical Induction as part of the History of Logic
[article]
2014
arXiv
pre-print
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This completes the proof of the conjecture by descente infinie. ...
This completes the proof of our conjecture by descente infinie. ...
arXiv:1309.6226v5
fatcat:i7nzngq47zfd7its4kfynlfpti
De la phénoménologie à l'éthique : une généalogie de l'usage de Descartes chez Levinas
2018
Méthodos
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), Totalité et infini , p. 233 ...
Le cogito n’est que la première certitude acquise après la première formulation du doute, avant la renaissance du doute sur le cogito lui-même et la descente, d’affirmation en négation, jusqu’à l’ ...
doi:10.4000/methodos.4954
fatcat:p3xvsnzmjbczvftpzolnzrhmlm
Descartes and the Abbe De Saint-Pierre
1958
Modern Language Quarterly: A Journal of Literary History
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In the ascent, deduction from first principle permits a theoretic recorstitution of the elements of the descent until the shape of supranational government appears. ...
For him, analysis in- cludes both the inductive descent from observable fact in its com- plexity to simple principle (resolution) and the deductive ascent from principle to complex theoretic conclusion ...
doi:10.1215/00267929-19-4-294
fatcat:5ynj4dtwerb6pgfn4egvqcgxta
Algorithms in Philosophy, Informatics and Logic. A Position Manifesto 2017
2017
IfColog journal of logics and their applications (FLAP)
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This completes the proof of the conjecture by descente infinie. ...
Descente Infinie ("Lazy Induction"): Contrary to explicit induction, where induction is introduced into an otherwise merely deductive inference system only by the explicit application of induction axioms ...
The extension of the descente infinie inference systems of QuodLibet to the full [modal] higher-order logic of [Wirth, 2004; 2017] has not been implemented yet. ...
dblp:journals/flap/GabbayS17
fatcat:wvtsqquk3vhm3ohgsxn6lzc22u
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