Deduction versus computation: The case of induction
Identifieur interne :
000778 ( PascalFrancis/Corpus );
précédent :
000777;
suivant :
000779
Deduction versus computation: The case of induction
Auteurs : Eric Deplagne ;
Claude KirchnerSource :
-
Lecture notes in computer science [ 0302-9743 ] ; 2002.
RBID : Pascal:03-0367824
Descripteurs français
English descriptors
Abstract
The fundamental difference and the essential complementarity between computation and deduction are central in computer algebra, automated deduction, proof assistants and in frameworks making them cooperating. In this work we show that the fundamental proof method of induction can be understood and implemented as either computation or deduction. Inductive proofs can be built either explicitly by making use of an induction principle or implicitly by using the so-called induction by rewriting and inductionless induction methods. When mechanizing proof construction, explicit induction is used in proof assistants and implicit induction is used in rewrite based automated theorem provers. The two approaches are clearly complementary but up to now there was no framework able to encompass and to understand uniformly the two methods. In this work, we propose such an approach based on the general notion of deduction modulo. We extend slightly the original version of the deduction modulo framework and we provide modularity properties for it. We show how this applies to a uniform understanding of the so called induction by rewriting method and how this relates directly to the general use of an induction principle.
Notice en format standard (ISO 2709)
Pour connaître la documentation sur le format Inist Standard.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
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| A05 | | | | @2 2385 |
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| A08 | 01 | 1 | ENG | @1 Deduction versus computation: The case of induction |
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| A09 | 01 | 1 | ENG | @1 AISC 2002 : artificial intelligence, automated reasoning, and symbolic computation : Marseille, 1-5 July 2002 |
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| A11 | 01 | 1 | | @1 DEPLAGNE (Eric) |
|---|
| A11 | 02 | 1 | | @1 KIRCHNER (Claude) |
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| A12 | 01 | 1 | | @1 CALMET (Jacques) @9 ed. |
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| A12 | 02 | 1 | | @1 BENHAMOU (Belaid) @9 ed. |
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| A12 | 03 | 1 | | @1 CAPROTTI (Olga) @9 ed. |
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| A12 | 04 | 1 | | @1 HENOCQUE (Laurent) @9 ed. |
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| A12 | 05 | 1 | | @1 SORGE (Volker) @9 ed. |
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| A14 | 01 | | | @1 LORIA & INRIA, 615 rue du Jardin Botanique, BP 101 @2 54602 Villers-lès-Nancy Nancy @3 FRA @Z 1 aut. @Z 2 aut. |
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| A44 | | | | @0 0000 @1 © 2003 INIST-CNRS. All rights reserved. |
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| A66 | 01 | | | @0 DEU |
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| C01 | 01 | | ENG | @0 The fundamental difference and the essential complementarity between computation and deduction are central in computer algebra, automated deduction, proof assistants and in frameworks making them cooperating. In this work we show that the fundamental proof method of induction can be understood and implemented as either computation or deduction. Inductive proofs can be built either explicitly by making use of an induction principle or implicitly by using the so-called induction by rewriting and inductionless induction methods. When mechanizing proof construction, explicit induction is used in proof assistants and implicit induction is used in rewrite based automated theorem provers. The two approaches are clearly complementary but up to now there was no framework able to encompass and to understand uniformly the two methods. In this work, we propose such an approach based on the general notion of deduction modulo. We extend slightly the original version of the deduction modulo framework and we provide modularity properties for it. We show how this applies to a uniform understanding of the so called induction by rewriting method and how this relates directly to the general use of an induction principle. |
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Format Inist (serveur)
| NO : | PASCAL 03-0367824 INIST |
|---|
| ET : | Deduction versus computation: The case of induction |
|---|
| AU : | DEPLAGNE (Eric); KIRCHNER (Claude); CALMET (Jacques); BENHAMOU (Belaid); CAPROTTI (Olga); HENOCQUE (Laurent); SORGE (Volker) |
|---|
| AF : | LORIA & INRIA, 615 rue du Jardin Botanique, BP 101/54602 Villers-lès-Nancy Nancy/France (1 aut., 2 aut.) |
|---|
| DT : | Publication en série; Congrès; Niveau analytique |
|---|
| SO : | Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 2002; Vol. 2385; Pp. 4-6; Bibl. 2 ref. |
|---|
| LA : | Anglais |
|---|
| EA : | The fundamental difference and the essential complementarity between computation and deduction are central in computer algebra, automated deduction, proof assistants and in frameworks making them cooperating. In this work we show that the fundamental proof method of induction can be understood and implemented as either computation or deduction. Inductive proofs can be built either explicitly by making use of an induction principle or implicitly by using the so-called induction by rewriting and inductionless induction methods. When mechanizing proof construction, explicit induction is used in proof assistants and implicit induction is used in rewrite based automated theorem provers. The two approaches are clearly complementary but up to now there was no framework able to encompass and to understand uniformly the two methods. In this work, we propose such an approach based on the general notion of deduction modulo. We extend slightly the original version of the deduction modulo framework and we provide modularity properties for it. We show how this applies to a uniform understanding of the so called induction by rewriting method and how this relates directly to the general use of an induction principle. |
|---|
| CC : | 001A02A01F; 001D02A04 |
|---|
| FD : | Démonstration théorème; Théorie preuve; Démonstration automatique; Induction; Réécriture; Calcul formel |
|---|
| ED : | Theorem proving; Proof theory; Automatic proving; Induction; Rewriting; Computer algebra |
|---|
| SD : | Demostración teorema; Teoría demonstración; Demostración automática; Inducción; Reescritura; Cálculo formal |
|---|
| LO : | INIST-16343.354000108487530010 |
|---|
| ID : | 03-0367824 |
|---|
Links to Exploration step
Pascal:03-0367824
Le document en format XML
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<ET>Deduction versus computation: The case of induction</ET>
<AU>DEPLAGNE (Eric); KIRCHNER (Claude); CALMET (Jacques); BENHAMOU (Belaid); CAPROTTI (Olga); HENOCQUE (Laurent); SORGE (Volker)</AU>
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<EA>The fundamental difference and the essential complementarity between computation and deduction are central in computer algebra, automated deduction, proof assistants and in frameworks making them cooperating. In this work we show that the fundamental proof method of induction can be understood and implemented as either computation or deduction. Inductive proofs can be built either explicitly by making use of an induction principle or implicitly by using the so-called induction by rewriting and inductionless induction methods. When mechanizing proof construction, explicit induction is used in proof assistants and implicit induction is used in rewrite based automated theorem provers. The two approaches are clearly complementary but up to now there was no framework able to encompass and to understand uniformly the two methods. In this work, we propose such an approach based on the general notion of deduction modulo. We extend slightly the original version of the deduction modulo framework and we provide modularity properties for it. We show how this applies to a uniform understanding of the so called induction by rewriting method and how this relates directly to the general use of an induction principle.</EA>
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