First-order characterization and modal analysis of indiscernibility and complementarity in information systems

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(1)First-order characterization and modal analysis of indiscernibility and complementarity in information systems Philippe Balbiani, Dimiter Vakarelov. To cite this version: Philippe Balbiani, Dimiter Vakarelov. First-order characterization and modal analysis of indiscernibility and complementarity in information systems. 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2001), Sep 2001, Toulouse, France. pp.772-781, �10.1007/3-540-44652-4_68�. �hal-03252571�. HAL Id: hal-03252571 https://hal.archives-ouvertes.fr/hal-03252571 Submitted on 7 Jun 2021. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(331) #$ !% & /0 % . pYd^_cft. +z.

(332)

(333) !%&

(334) * !"

(335) /0 ) . +z. oop. +z.

(336) !'

(337) ( /0 ) . a32

(338) 465d Rp+ow2t_cJm'lp'Y^kY2lnmefop+\F^_mYZ]RZ]\]co*¤ 1. ¶]DaLf¿769LM6:T2<8:¹aÃ.L]ºSISdB2¾<½LM¸ ?ANf<¸MLfNMS2D

(339) »d89¹¡6:D

(340) G

(341) 6:¸f½'<NfD

(342) 6:B

(343) 8:<!6_·J?R8:8LM5

(344) <6:NNf<¸M;.<½'Lf6:T2<I¸M<Lf¸SR· ;

(345) NMS2;=<NfLM6:<¸G

(346) <LM<NfK!69D7<G#Ba¹¡Lf5

(347) <?RLfLMNf6:B

(348) ¿

(349) LM<¸?RNM<6:D

(350) G

(351) 6:¸M½<NfD769B789<!º5

(352) <NM<-?R¸L]ºSIS2B2¾%<½Lf¸ ?ANf< ¸MLfNfSdD

(353) »28:¹!½S2K!;

(354) 8:<K<DaL?RNf¹6¦·P?R8:8sLf5

(355) <'69NwNf<¸M;.<'½Lf6:T2<¸f<'Lf¸SR·;

(356) NMS2;=<NfLM69<'¸G7<Lf<NMK6:D

(357) <G Ba¹Lf57<Û?ALfLMNf6:B

(358) ¿

(359) LM<¸?ANf<½S2K!;

(360) 8:<K<'D[L?RNM¹[ÀRÁ57<6:Da·FS2NfK?RLM69SdD*¸M¹a¸fLf<'K SA·&Lh?AB

(361) 8:<*Ôw6:¸¸f¿

(362) ½5 LM5.?RL Z Znzne"b ! ?AD

(363) GG *Z Z zf=gkZ h[i

(364) À ? S2NJ?A8:8 HLi 1 "!L# Ã7G

(365) <×.D

(366) <dÙ 7 [8 k > [ d.d..6dH:9S zni36¦ÂILf5

(367) <NM<69¸ )213¸f¿7½h5LM5.?RF L 8k)J9H:NS8k)J9i(:6< 7 [8 J@K[[C> .6dH;[zi36¦ÂLf5

(368) <NM<J6:F ¸ )21G¸M¿

(369) ½5Lf5=?RL 8CK)JLHJ:S'*),+.-C¢ 8k)J9i(::'À ¶]DaLf¿769LM6:T2<8:¹aÃL]ºSSdB2¾<½LM¸P?RNM<ºP<+?RQa8:¹6:D

(370) G769¸M½<NMD

(371) 6:B

(372) 8:<6_·=¸fS2K!<SR·sLf57<6:N&NM<¸f;=<½LM6:T2<¸f<LM¸SR· ;

(373) NMS2;=<NfLM6:<¸G

(374) <LM<NfK!6:D

(375) <G Ba¹Lf5

(376) <?RLMLfNM69B7¿

(377) Lf<¸?ANf<69D7G

(378) 6:¸f½<NMD

(379) 6:B

(380) 8:<Pº57<Nf<-?A¸L]ºSJS2B2¾%<½Lf¸?ANf< º<-?RQa8:¹½SdK;

(381) 8:<K!<DaLh?RNM¹*6¦·¸fSdK<wSR·Lf5

(382) <'69NwNf<¸M;.<'½Lf6:T2<¸f<'Lf¸SR·;

(383) NMS2;=<NfLM69<'¸G7<Lf<NMK6:D

(384) <G Ba¹Lf57<Û?ALfLMNf6:B

(385) ¿

(386) LM<¸?ANf<½S2K!;

(387) 8:<K<'D[L?RNM¹[ÀRÁ57<6:Da·FS2NfK?RLM69SdD*¸M¹a¸fLf<'K SA·&Lh?AB

(388) 8:<*Ôw6:¸¸f¿

(389) ½5 LM5.?RL *Z Z<9S z0j0)[Z gk_&+?RD

(390) IG *Z Z=;7z l=mnmn)=ÀaÁ5

(391) <¸MLfNf¿7½Lf¿

(392) NMn< =!$# LzL z 9S zd.;7zJ:6:¸ ½-?A8:89<'G§?RB7¸fLfN?R½Lw¸fLMNf¿

(393) ½LM¿

(394) Nf<G

(395) <NM6:T2<G·FNfS2K QP]À P¢<89<+?+T2<6:LPLMSLf5

(396) < NM<-?RG7<NJLMS;

(397) NfSRTd<LM5

(398) < ·Sd8:89SRº6:D

(399) »8:<K!K§?R¸+À N[@?BA$CEDF@G H%H HC9iI=1 "!LK# J H0 z HML H z HML N

(400) OHI z Q i P

(401) RS0Tni2 z MH L NUOVHJ z iVPUR(STni, z HML N

(402) OHIz0Q i GTW0i"X z IYPUR(STnH0z<IZL[NUOVHJ ziVGTW2i"zXI6P

(403) RS0TGH zIKL N

(404) OHIz0Q i GTW0i( =z I6P

(405) RS0TnH =z IZL NUOVHJ zV i GTW2i( 3z I6P

(406) RS0TnH0X z I(\ >N[ ]3A$CEDF@G H%H HC9i I=1 "!LK# J H 9S znMH L : H ;[zMH L N

(407) OH 9S z Q i P

(408) RS0Tni 9S z MH L NUOV( H;z6 i P

(409) RS0TXî ; z MH L N

(410) OH 9S z Q i GTW0i" z IYPUR(STnH 9S z IZL[NUOV(H ; z 6 i GTW0i" z I6P

(411) RS0TGH ; z IKL N

(412) OH 9S z Q i GTW0i( z I6P

(413) RS0TnH ; z IZL NUOV( H;z6 i GTW0i( z IYPUR(STGH 9S z I(\ <KK?Ô ?RD

(414) G8:<KK?JÌK!S2Lf6:T2?ALf<Lf57<·S28:8:SRº6:D

(415) »G

(416) <×.D769LM6:S2DÀ7ÖJDI?RB

(417) ¸MLfN?R½Lw¸fLfNM¿

(418) ½LM¿

(419) Nf< 6:¸?¸fLfNM¿

(420) ½LM¿

(421) Nf<G` _B92L 2 9S . ;7: º5

(422) <'Nf<2Ù ; _ 6:¸J? D

(423) SdD

(424) <K!;

(425) L]¹¸f<LwSR·;.Sd¸f¸f6:B

(426) 8:<ºS2Nf8:G

(427) ¸>< ?ANf<B

(428) 6:D.?ANf¹Nf<'8C?ALf6:S2D7¸S2DV_ ¸M¿

(429) B2¾<½'LJLfSLM5

(430) <½S2D7G

(431) 6:Lf6:S2D

(432) ¸SA·&8:<K!K§?Ô(< ; ?RD

(433) G3Ý 9 R ?

(434) D a G ; ?RNM< B

(435) 6:D.?ANf¹Nf<'8C?ALf6:S2D7¸S2D6_ ¸f¿7B2¾<½LLfSLf57< ½S2D7G

(436) 6:Lf6:S2D

(437) ¸SR·8:<K!K§?Ì

(438) À S ; >.

(439) ¶]D¸f<'½Lf6:S2DÏ

(440) Ã+Lf57<½S2D

(441) ½'<;

(442) LSR·¨?AB

(443) ¸fLMNh?R½'L¸fLMNf¿

(444) ½LM¿

(445) Nf<º6:8:82B=<SR·s¿

(446) ¸f<LMS¿

(447) ¸ ·S2NLf57<;

(448) ¿

(449) Nf;=S2¸M< SR·»26:Ta6:D

(450) »?«×.Nf¸ML]¼]S2NMG

(451) <N ½5.?ANh?R½'Lf<NM69Ú+?RLf6:SdD¢SR·P6:D

(452) G

(453) 6:¸M½<NfD769B7698:6:L]¹Nf<8n?ALf6:S2D

(454) ¸ ?AD

(455) Gª½'S2K;789<%¼ K<'D[L?RNM69L]¹Nf<'8C?ALf6:S2D7¸6:D6:Da·SdNfK§?ALf6:S2D¸M¹[¸MLf<K!¸-Àa¶]D!¸f<½LM6:S2D =Ã2LM5

(456) <J½'S2D

(457) ½<';

(458) LSR·&?AB

(459) ¸fLMNh?R½'L ¸fLMNf¿

(460) ½'Lf¿

(461) NM<#º6:8:8B.<¡SR·*¿7¸f<ILMS#¿

(462) ¸!·SdNLf57<I;

(463) ¿

(464) NM;.Sd¸f<¢SR· »d69Ta6:D

(465) »#? KSaG.?R8J?AD.?R8:¹a¸f6:¸SA· 6:D

(466) G

(467) 6:¸f½'<NfD

(468) 6:B

(469) 6:8:6:L]¹Nf<8n?ALf6:S2D

(470) ¸?RD7G§½'S2K;789<'K<DaLh?ANf6:L]¹ NM<8n?RLf6:SdD

(471) ¸6:D6:Da·SdNfK§?ALf6:S2D¸f¹a¸MLf<K!¸-À µf°d¯Ë±°

(472) ²V °#´&°]&´=¯ °

(473) µ ¯

(474) µf±®. . Á5

(475) <w½S2D

(476) ½'<;

(477) LSR·&?RB7¸fLfN?R½L¸fLfNM¿

(478) ½LM¿

(479) Nf< 6:¸SR·¿7¸f<JLMS¿

(480) ¸·FS2NLf5

(481) <w;

(482) ¿

(483) NM;.Sd¸f<JSA·¨»d6:T[6:D

(484) » ?w×=Nf¸fLj¼ S2NMG

(485) <N½5.?ANh?A½Lf<NM6:Ú-?RLM69SdD*SA·¨6:D

(486) G769¸M½<NMD

(487) 6:B

(488) 6:896:L]¹wNf<8n?RLM6:S2D

(489) ¸?RD7G ½S2K!;

(490) 8:<K<'D[L?RNM69L]¹NM<8n?RLM69SdD

(491) ¸ 6:Dª6:Da·FS2NfK?RLM69SdD¸f¹a¸fLM<K¸+ÀsÁ5

(492) <3·S28:8:SRº6:D

(493) »69K!;.SdNfL?RDaLLf5

(494) <'S2Nf<'KÇ<Øa;

(495) 8n?R6:D

(496) ¸wLf5

(497) <½SdD

(498) D

(499) <½¼ Lf6:SdD¢B.<L]º<<D?RB

(500) ¸MLfN?R½L ¸MLfNM¿

(501) ½Lf¿7Nf<¸?RD

(502) G¡6:Da·S2NMK§?ALf6:S2D¸f¹a¸MLf<K!¸-À ÖJ8:8Lf5

(503) <!¸f<½LM6:S2D§Ï!6:¸ G

(504) <TdS2LM<GILfS6:LM¸;

(505) NfSaSR·À.

(506) d[ [ MA SP S _B9 9 2 9S ,;[:SXGT GP"F,GPP'F0PZF.S\3R(SF.S! GT"%T# $ %&'P'S'$ Q S . "!$# &%('V),+.-B/J)T1 465798:(R P

(507) RGP "!$# S _ GTW. ODF GP )DT ODF$G H%H. H9i21 =!$K# J HnzIi) * HI iZL H 9S zni) *H 9S iZL HJ z ) i * H iZL H; z i% * H(;7i(\ ÖJ¸?½SdD

(508) ¸f<6a¿

(509) <'D

(510) ½<2Ã

(511) ?AB

(512) ¸fLMNh?R½'L¸fLMNf¿

(513) ½LM¿

(514) Nf<'¸@?AD

(515) G*6:Da·FS2NfK?RLM69SdDJ¸M¹[¸MLf<K!¸5.?+T2<<&[¿=?R8

(516) K?RLf5V¼. <K?RLf6:½-?A8R½S2DaLM<DaL&?R¸=·]?RN?R¸ 6:D

(517) G

(518) 6:¸f½<'NfD

(519) 6:B

(520) 6:8:6:L]¹Nf<8n?RLM6:S2D

(521) ¸?AD

(522) G½S2K!;

(523) 8:<K<DaL?RNf6:L]¹NM<8n?RLM69SdD

(524) ¸ ?RNM< ½SdD

(525) ½<NMD

(526) <G,À +wS28:G

(527) 6:D

(528) »LM5

(529) < ;

(530) NMS[SA·SR·Lf5

(531) <'S2Nf<'K Ï6:DÅ?AB.<'¹[?RD7½< ·FS2NJ?º5

(532) 6:8:<2Ã

(533) º<;

(534) NfSA¼ ½<<'G#LfS6:DaLfNMS[G7¿

(535) ½<Lf5

(536) <½SdD

(537) ½<;7Lf¸SR·P6:D

(538) G

(539) 6:¸M½<NfD769B7698:6:L]¹¸f<L+Ãs;=S2¸f6:LM69Td<*¸M<L-Ã D

(540) <»a?RLM69Td< ¸f<'L ?RD7G¢»2SaSaGª¸M<L-À ÁºPS¸M¿

(541) B

(542) ¸f<'Lf2¸ ?RD

(543) G eÜSR@· _ ?RNM<½-?R8:8:<G¡½S2K!;.?RN?RB

(544) 8:< 6¦· M eÜS2N eM *ÀaÖ ¸f<LSA·;.?R6:Nfº6:¸M<J½SdK;.?ANh?RB789<¸M¿

(545) B

(546) ¸M<Lf¸wSR· _ 6:¸½-?R8:8:<G§?Û½h5=?R6:DÀaÖ ¸f¿

(547) B

(548) ¸M<L SR· _ ¸M¿

(549) ½5ILf5=?RL·SdNJ?R8:8 H9i21Q_ÝÙ G HI1G Lf5

(550) <'BD i21G < ; ¶F· Hni?RD

(551) 3 F ¶ · n H i R ?

(552) D G H%1G- Lf5

(553) <'BD i.1G- < 3 ; º6:8:8B=< G

(554) <×.D7<GªLMSB.<?RD6:D

(555) G

(556) 6:¸M½<NfD769B7698:6:L]¹¸M<L-À=ÖwDI6:D

(557) G

(558) 6:¸f½<'NfD

(559) 6:B

(560) 6:8:6:L]¹¸f<L Ý¸M¿

(561) ½5ILf5=?RL ·SdNJ?R8:C8 HC9i=1Q_ÝÙ G HG1G Lf5

(562) <3D i/1X- 2< ; ¶F· H i!?RD

(563) G º6:8:8B.<G7<×.D

(564) <G¢LMSIB=<?;=S2¸M6:Lf6:T2<¸M<L-À ÖJD¢6:D

(565) G

(566) 6:¸M½<NfD769B7698:6:L]¹¸f<2L ¸f¿

(567) ½5ÆLf5.?ALJ·FS2N*?A898 HLi21V_ÝÙ G H"1G- Lf5

(568) <3D iW1X2< ; ¶F· H i!?RD

(569) G º6:8:8&B=<G

(570) <×.D

(571) <'G¢LfSB.<?!D

(572) <»a?RLf6:Td< ¸f<L+ÀsÖJD¡6:D

(573) G

(574) 6:¸f½'<NfD

(575) 6:B

(576) 6:8:6:L]¹¸f<"L ¸M¿

(577) ½5ªLM5.?RL 6:¸Û? ;=S2¸f6:LM69Td< ¸f<'L?RD73G Ý6:¸J?D7<»[?ALf6:T2<¸f<'Lº6:8:8sB=<*G

(578) <%×.D

(579) <G¡LfSB=< ?»dSaS[G¸M<L-À=Á5

(580) <;

(581) NfSaSA· SR·LM5

(582) <w·S28:8:SRº6:D

(583) »89<'KK§?A¸6:¸P8:<·FLJ?R¸J?RD<Øa<NM½6:¸f<·FS2NLf57<NM<-?RG7<N-À N710EA ;32 GTW:_ GF,S(%TW!S0FT45

(584) H!%P6&

(585) SP4\ ; C DF@G^H%HHI1V_87@kHJ:9!@GT%%TW:;S0FT<'

(586) H!%P&S0P"\ : !$GT))TW!S0FT<'

(587) H>)P&?SP"\ ; C DF@G^H%HHLi=1 _87CkHJ : =TUKi(( >.

(588) ! <5 > 6&9 < 97F _ ¢ :(! GT %T(W!SFT<'

(589) H>%P6&

(590) S0P'\ $( > n /gW1,:6D.O)%TW!S0FT45

(591) H!%P6&.SP4 7G. /Ng01,:)!aGT ; ! <' > 6&? G. /gd1 (:(!$GT))TW!S0FT<'

(592) H>)P&?SP"\ >N[ 3A ;32 !$G

(593) KD ;)P0S

(594) S0P'\ C D $ F ^ G % H H I H 1 _8C7 UKH:?! G

(595) KD %PS? SP"\ ; C D $ F ^ G % H H H L i21V_87 OVH ViVP

(596) RS0TnUKH: B = ki,:(!$G

(597) D %P6S S0P"\ ; ; C DF$G^H%H

(598) D %P6S? SP4F ?F7 `_ ¢ *:(!@GXTSGP60S9 S0P'\ . / gd1 (: D.O

(599) KD %PS

(600) S0P< 7 I. / g1,:9!$G

(601) KD ;)P0S? S0P"\ ; C DF$G^H%H RG)T >N[ 3A ; _ !$GXTSGP60S9 S0P'\ C D $ F ^ G % H H I H 1 _87 U - KH:?! G<TSGPS( S0P'\ ; C D $ F ^ G % H H H L 2 i V 1 8 _ 7 OVH ViVP

(602) RS0T"U - KH: - ki,:(!$GXTSGP6S? SP"\ ; C D $ F ^ G % H E H T S G 6 P ? S S 4 P 9 7 F _ ¢ 9 : ! $. G K

(603) D ;)P0S

(604) S0P'\ ; C D $ F ^ G % H H R G )T . . / d g. 1 ( : . D $ O T S G P ? S S 4 P 7 / g1,:(!$GXTSGP6S? SP"\ ; >N[BA9E S0Pd S:G

(605) D %P60S( S0PGT(WXHT1 _ S R P

(606) RGPd = kHJ: : TDPG

(607) D %P60S

(608) SP"\3 RS0T6P

(609) RS0F,S9:4i 1Q_ RVP

(610) RGP@i21G GTW0H i(\ >N[ 3A9E S0Pd S:G T(SGP60S( SPGTWnH 1 _ S( RQP

(611) RGPd - kHJ:(! TDPG TSGP60S9 S0P'\ 3 RS0T6P

(612) RS0F,S(!iW1V_ ; R6P

(613) RGP@i/1X- GTW2H i(\ ;. C DF$G^H%H %TW SFT +H %P S0P C DFaG H)HEOG

(614) H )S %T(W SFT

(615) H %P S0PGTW. Ö K!S2Nf<w6:K;=S2NfL?RDaL·¿7NfLf57<N½S2D7¸f<6a¿

(616) <D7½<6:¸PLM5

(617) <·Sd898:SRº6:D

(618) »8:<KK?

(619) À >N[ 3A9ES0P S G

(620) D %P60S9S0P<7Ce S M e:\3RS0T = K H:?! G!

(621) D %P60S

(622) SP TSGP60S9S0P GTW" M # e U - KH:"\. $. ? 0HI1 S?;RVPUR(GP "

(623) = kHJ: M e!" #Ke# U - KH:

(624) !@G. G<TS GP 0S S0P GTW _ GTW XDF. %a<'< >@?A8:B

(625) 6n?RD

(626) 6s?RD

(627) GOP?AQ2?RNM<8:SRTÈ:ÔMÊs·S2NG

(628) <'Lh?R6:8:¸-À. F.DD.O\. ÖwD§6:K!;.SdNfLh?ADaLNf<8n?ALf<GNf<'¸f¿

(629) 8:LJ6:¸LM5

(630) <w·S28:8:SRº6:D

(631) »;

(632) NfSd;.Sd¸f6:Lf6:S2D À. & J 6K>. (' 9

(633) 6

(634) 0e e 1 9! ) df C M f $ a% <'< >@?A8:B

(635) 6n?RD

(636) 6s?RD


(638) <'Lh?R6:8:¸-À :\ 3RS0T6PUR(SF.S. ? 3A SP S G D $G D0DW S0P. %P 0S SP GTW R6P

(639) RGP. 6 9. S$GXT(S GP 0S S0P GT(W :\. F.DD.O\. fM e. RYPUR(GPM. Ö ¸M<LV)SA·&»2SaSaG¸f<LM¸J¸M¿

(640) ½5ILf5.?AL·S2N?R8:8CHLi=1 _ÝÙ - < ; ¶FF· H%9S - iLf5

(641) <DLf5

(642) <NM< 6:¸ 13)¸f¿7½h5LM5.?RVL HI13 6¦ÂBi)1G F ¶ · F H 7 ; i M L

(643) 5 < D f L 7 5 < f N. < : 6 ¸ 3 1 ) M ¸

(644) ¿ ½ 5 f L . 5 A ? L V G H G 1 _ 6 B Â W i X 1 2< ; º6:8:8.B=< G

(645) <%×.D

(646) <GILMS*B=<*?3D

(647) 6:½< ¸M<L-À7Á5

(648) <w·S28:8:SRº6:D

(649) » 8:<KK?6:¸<-?A¸f¹LMS½5

(650) <½QsÀ N[@?B?=A 3R(S9S0P >. $. *. D,O G H%H DD0W. SP49! G<T<S9S0P'\. %a<'< >@?A8:B

(651) 6n?RD

(652) 6s?RD


(654) <'Lh?R6:8:¸-À. F.DD.O\. Ö 8:<¸M¸S2BaTa69Sd¿

(655) ¸Nf<¸M¿

(656) 8:LJ6:¸Lf5

(657) <w·Sd8:89SRº6:D

(658) »8:<K!K§?

(659) À.

(660) N7 ?K]MA C DF$G^H%HHLi21V_ J ; H0i% * ODF G^H%HET<S?SP4V)QGTW@ODF@G^H%H 13)7dHI1X * i01G$L i * ODF$G^H%HET<S?S0P44)YGTW@ODF@G H%HJ1B) 7CHI13 * i.1X - L ; HJ ) H i % *

(661) P R 0 S , F 9 S ! $ < G T < 9 S 0 S @ P ) V R U P ( R G = P O D @ F ^ G % H H 3 1 ) d 7 I H X 1 * i01G$L 9 S ; H ( 7 ; i % *

(662) P R 0 S , F ? S ! $ X G T < ? S S d P ) . V R

(663) P R G B P O D @ F. G % H H 3 1 ) @ 7 I H G 1 * i/1X- \ ; >. $. %a<<3>@?A89B76C?AD

(664) 6?RD7GOP?AQ2?RNf<'89SRT!È9Ô%Ês·S2NG7<Lh?A698:¸+À. F.DD.O\. <%·<NfNM6:D

(665) » LfS8:<K!K§? Ô+Ì

(666) Ã+º<<-?R¸M698:¹ SdB

(667) Lh?A6:D ?;7NfSaSR·sSR·sLf5

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