Déduction et Unification dans les Théories Permutatives

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HAL Id: tel-00011236

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Submitted on 19 Dec 2005

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Déduction et Unification dans les Théories Permutatives

Mnacho Echenim

To cite this version:

Mnacho Echenim. Déduction et Unification dans les Théories Permutatives. Autre [cs.OH]. Institut

National Polytechnique de Grenoble - INPG, 2005. Français. �tel-00011236�

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BO+MfO,$S0B¨I'o:<,.+QBON2f'<Su+M1BON¸*(R')PoB4,.6 '*,/ ')N2230/0,;BON¸Q «,.6 I'?§/5')(*+MB')N2

BO(BON.2N BONõ(*=2>@MB

BO+MfO,qSw' o:<,.+41O(M1/0NXSu,.+MB@fO(MBO/0+S0B(*=2>@RB35')(*,;BON§(f@:<¨30+M1O=2BON2*,/ ¨:<(*,o1

BO(¨:<(*,<')N§( e

/0+*(M:</0(u¨BO+MfO,L3:</0+(M:</0(MB@N2:f@:<N oBO+MR')(*,;:<N20MfO,;BON§(*,/.5?A/2B@u3:<6.,.(*,;?§/2B@§fO,.N21

¨h')(M:<P+R')30=0,;?§/2B@4BO(6.,.(*(M1O+R'),.+MB@L?§/0,$:<N§(1O(M19')/0(R')N§(QS0B-:</1@B@QSw: jPo>ON2B9Su/0+R')N§(f@B@7(*+M:<,;

')N0N21@B@

(9)

(10)

E C!"qÿHE C

úóã ú ùäø )ä !

" #

J $

¼ 7BO68')(*,;:<N2 %

¼ ¼

=21@:<+*,;B@71@?§/5')(*,;:<N0N2BO6.6;B@ &

¼ '% 7N0,/.5f')(*,;:<N¸1@?A/5')(*,;:<N0N2BO6.6;B (

¼ & B30+M:<-06;>O¨Bsjt ¾

$ )+*>C "-, C%ÿ/. K

0

%

+M:</03B@

% ¼

:<+*30=0,;M¨B@KBO('<fO(*,;:<N27S0BQP+M:</03B@ ¼

% '%

e

:</2 P+M:</03B@ 21

% & B@!P+M:</03B@7j¨1O(*+*,;?§/2B@ ¼

3 )+*>C FJ4, C E5* 46 ÿ " K7, CLÿ.K "98

& QB@!30+M:<-06;>O¨B@K3:<6§N2:<¨,8')/ ¼:(

& ¼ "'fO68'<MRBS0Bf@:<¨306;B j,.(M1S0Bw/ j %

& '% B30+M:<-06;>O¨B<;>=9Qtwp %?&

& '% 7N2BQ+MB@*(*+*,;fO(*,;:<N S0B@;A=9Qtwp %B1

& & :<N2fO6./2*,;:<N %B1

B C

ïED óä2åGF\ä0 ä0ó

C

ïED ó<ä5åGF\ä0HóåoøLóãJILK0 MON

P QSRT

E

3O

¿

+R')30=2B@K1O(*,;?§/2BO(M1@7BO(_£$s (MBO+*¨B@ U&F

¿ ¼ :<¨:<¨:<+*30=0,;M¨B@ U&G1

¿ '% 7N0,/.%')-0,.6.,.(M1S0B4s (MBO+*¨B@ ¿¿

¿ & !fO(*,;:<NS0BP+M:</03B*/0+7S0B@£$s (MBO+*¨B@ 1¼

¿ & _1.2N0,.(*,;:<N S0BQ6'<fO(*,;:<N¸S0BQP+M:</03B 1¼

¿ & ¼ q')+*(*,.(*,;:<N2_*(*+R')(*,/.51@B@ 1B%

(11)

¿ ¿ 1@*/0¨1 1

QSR T E K E E

1

:<(*,<')(*,;:<N2 1

1 ¼ e

,.PN5')(*/0+MB@_*(*+R')(*,/.51@B@ (

1 '%

e

(*+R')(*,/.5f')(*,;:<NõSw/0N £$s (MBO+*¨B (<¿

1 & +M:<30+*,;1O(M1@_*(*+*/2fO(*/0+MBO6.6;B@S0B@K+M1@*,;Su/2

R

T

(v)

⁽

1 ¿ 1@1@fO+*,.(*/0+MB*(*+R')(*,/.51@B4BO(7'<fO(*,;:<N S0BQP+M:</03LB ¼

1 '1 £$s (MBO+*¨B@_*(*+R')(*,/.51@KBO(K=2:<¨:<¨:<+*30=0,;M¨B@ 1

1 ( :<¨¨BON§(R'),.+MB@ ¼

BB åoúå§ãJK0óBK0 ùä0 C ï D óä2åGF\ä0 óåoøLóoãI K0 N

8 C /,<ÿ >H E E

8

( N2B+MBO68')(*,;:<NSw1@?§/0,<')6;BON2f@B :(

( ¼ ')6;fO/06qS0B@

≈

fO68'<MMB@ ¾B%

( '% :<¨306;B u,.(M1Su/I30+M:<-06;>O¨BS0B4S01@fO,;*,;:<N ¾B1

( & 1@*/0¨1 ¾

# C J J J" "ÿHE C 0

e

,.PN5')(*/0+MB@_*(*+R')(*,/.51@B@7 ')(*/0+M1@B@ ¼

¼ £$s (MBO+*¨B@_*(*+R')(*,/.51@KR')(*/0+M1@ &

'% :<¨306;B u,.(M1S0B30+M:<-06;>O¨B@S0BS01@Su/2fO(*,;:<N 21

& <8= f@:<¨306;1O(*/2S0B

¿ 1@*/0¨1 ¼B%

ø ?)ä0¸ùä óoâ K2ú"åAãä0!ä5åGFóøLóoã"ä !

E JEG

" 8

qBO+*¨/0(R')(*,;:<N2Q,.N2Su/0,.(MB@ ¼:(

¼ e

,.PN5')(*/0+MB@_*(*+R')(*,/.51@B@7M(R')-06;B@ 2%

'% B430+M:<-06;>O¨BSu/ ¨:<(KPo1ON21O+R')6.,;M1 2%?&

& NI30+M:<-06;>O¨B4Sw/0N0,/.5f')(*,;:<NõS0BQ( j3LB4,.N.2N0,.(R'),.+MB 2%

¿ 1@*/0¨1 &A¼

"!$# &%T E JEG 3 $

¾

=21@:<+*,;B@/0N0,/ M(R')-06;B@ &G%

¾ ¼ 9 u(MBON2*,;:<N¸/0N0,/ *(R')-06;B &'

¾ '% Q1@Su/2fO(*,;:<N¸BO(7/0N0,/*(R')-0,.6.,.(M1 ¿B%

¾ & <8= f@:<¨306;1O(*/2S0BS0B@7')/0(*+MB@730+M:<-06;>O¨B@ 21

¾ ¿ 1@*/0¨1 21?&

(12)

0 # T E J EG KEÿ H E C P

7N0,/.5f')(*,;:<N¸*/0+7S0B@£$s (MBO+*¨B@ &21B1

¼

E

/0N0,/.5f')(*,;:<N¸M/0+KS0B@_£$s (MBO+*¨B@ &5( 1 '%

BO+*¨,.N5'),;M:<N BO(7f@:<¨306;B u,.(M1 &

¼

& 71@*/0¨1 &

" J E . 2. HE

K

C E E C

$

ì£$s (MBO+*¨B@ &B%

¼ e

(R')-0,.6.,.(M1 &

(13)