Filters








389 Hits in 1.7 sec

Automatic 'Descente Infinie' Induction Reasoning [chapter]

Sorin Stratulat
2005 Lecture Notes in Computer Science  
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]

Claus-Peter Wirth
2010 arXiv   pre-print
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

C.-P. Wirth
2012 Logic Journal of the IGPL  
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

Françoise Garcia
1988 RAIRO - Theoretical Informatics and Applications  
-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]

Claus-Peter Wirth
2005 Lecture Notes in Computer Science  
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

Yvon Gauthier
1997 Horizons philosophiques  
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

Mathieu Marion
1994 Philosophiques  
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  
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

Mathieu Marion
1995 Philosophiques  
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]

Sorin Stratulat
2010 Lecture Notes in Computer Science  
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  
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]

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
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

Arnaud Clément
2018 Méthodos  
), 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

M. L. Perkins
1958 Modern Language Quarterly: A Journal of Literary History  
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

Dov M. Gabbay, Jörg H. Siekmann
2017 IfColog journal of logics and their applications (FLAP)  
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
« Previous Showing results 1 — 15 out of 389 results