=Paper= {{Paper |id=Vol-42/paper-6 |storemode=property |title=Computing Proper Implications |pdfUrl=https://ceur-ws.org/Vol-42/paper4_taouil.pdf |volume=Vol-42 }} ==Computing Proper Implications== https://ceur-ws.org/Vol-42/paper4_taouil.pdf
                               !"#$
                                        '% &)(+* ,&)-/.+021435&)6+7 8:9/;=&/   ?:


    Ü/-/Øj02@BßwÖ @B- ×-/ÖIÙw.D@j;Ä02@Äî ÷_ñKæµ,ßw;F& åX&)Øp7D-
                                                                                a




                                                                           54
R. Taouil & Y. Bastide                                                                            ICCS’01 Int’l. Workshop on Concept Lattices−based KDD

                              &)6+7 ‘Ü/Øp& ãµ&/1®î ô)ñKۇã?ßw0½×pßß+& 9X;#&I֊&_éD02֊&/1£12;äÂ@Aàqß+&)6‡7ŵå¼×-X6X@jØj&X


                                >µ;F% ádå
                                    Ò -)@B@B1½-/áÝî2ï _ñqÛw&)6+7ÁèRÖIه;=×)æ
                                             4>                           ]


                        ï         ';FØB;XÛ+@jßw;Ç= á\;'@jßw;5ÖI&)éD02֊&)1\×-h¹ q y€ÓM†Q|¹‡†‡iM·YdQi¯h±SF³FoqWpŒRQioPF] Uh³X_` ¹ /] ’/WpY¯D“ WjUd,+”cX,^/Wj¹ UhrjsOoqŒRQifhrjŒif/QiWpoÕPF¶cXSŒASݕdSoRWÅQiWpkVSŒiTnP=UXo ­ Tn¯hop‚                                                                                           ¹ j~ƒ„j[\
                                                          Åj               j
       j                                                                             žö


            ’/¹?L'K釉Œ®jPSpq!s)KaSr sXQAc/dPÕ]q_SFt_Uh`XcÁ]q6L'* ¹M·qx]³F* ŽˆQASps´°Q[_Syz, k4Q¹Inˆ»O‘‡|TnUh^†]TnUh’³IQ|M|“ŒŒ ­ vWqx±IP=noqŒ'vKTnv”U_Œif•WjQiO‘WpqSoqOŠŒiq TnUhyE³Ç–‘QifhnCknWpn4op—¹ÇYhHK¯dmU S³=\Wpo?M[]_“p^a^ `ˆ_] ]~htI“]KЉS^/Q Y
                           M·‹ fh³FfhoqŒ?“ ,,+, ¹
           ^X¹'c/Wp¹dUhM‘rjTV¹hWjop¹WjQiš›UhlooqŒin%WjTVhXU+Y‡¹!“=‹)ÀÂs/^_U_ÃB² Œ =­ ”FWp”_oR ™T ˜pTnUX³5YŒ “ ­ T”QAa/c»¹ UXPFQi±#SFk+¶CPQi± QiWjk2SŒiTnP=Uho!¶½QiP=±õ¶½fhUhrBŒiTVPFUdSkcXWp¯DWjUX[
                ])¹‘t!]b}jAY/¯dSF³FWpo'“p^_”ud“u] * Yw‹/Wp¯/ŒiWp±5•DWjQµ“ ,+, ”)¹
             a/¹‘Sºt!¹rpP=t®UXSrpQiWp¯X¯XTnUhŒifhWjŒiSFP/k+Y rpºknfh¹FoqL!ŒiWjPFQi±#TnUX³SFUXSFPX¯XYF¯XSFQiUhP c5Sr ¹ ¹%”d¤ M·]{CcXSF¥S±¦KP/v ¹XKNOTH€]UXq§¶½WjvQRsGQiTnjPUhqS³K Q:c/s‘sWpO™¯DyzQ|Wpq§Uh^PcXQBWpY‡UX“urp]/TnWpÀÂo^ ÃB¶½QiY\PF“ ±ÓQiWp¹ kVSŒiTnP=UXop²
                                                      j




                 ”)¹'š›¹dXt!hXY¹Z^XTnoR² ’ r F­ ’aWj_Qu’gY ¨X¹ Y£‘“ c¹ ¨F’/P=¹ f‡YSFUhc 5­ ¹\ˆÁ¹ ¬ oRPFf‡¹I‹/fXrprpTnUhrjŒiUXWpoRo'TnUÅcXWp¯DWjUdcXWjUhrj,sÕ,+, oqs/oqŒiWp±op¹
                                                                   ÷                                                               }ö


                                                                           g                                        oö



              * ¹'·¹ SFU_ŒiWjQu¹ ¬ ´P‘•hSFoRTnrSkn³=PFQiTŒ ­ ±oTnU#rpP=UXrpWp¯XŒ®SFUhSFks/oRTVop¹ ¬ Wjr ­ UhTnruSFkdQiWj¯DPFQRŒuY ¬ Wjr ­ UhTnoRr ­ W
                                      j         4j                    j , ,*
                          !P_r ­ oRr ­ fXkVW ?SQi±oqŒASFc/ŒuYw“ ,* ^X¹
                            ÷



               , ¹'·¹ SU_ŒiWjQSFUhcÔL'
                            ‹)¯XQiTnUh³FWjQuYw“ ,,+, ¹ ¹ €ÝTVknknW=¹ ƒ]M|{Iv+s%d]q§^PQ ¥xK%b}q§vs “‡†O‘‡:©ˆfwvKЉ!Q|{žvKNOT^†v+sƒg]¦ qx vKNOT]q!‡i¹
                    g                                 Åö
                            K÷


    “p`/¹ ºbe¹dgµf«PFŒRh Œij knP=ko•+be¹+dˆtšXP=¬±h ¯Xj kofXŒifmTnUhlo³µn%rpP¬hg jWjQikoo£b}¶CPF­>Q šAWp±ºh!“•D{>Wuch¥c/]‡†WuO‘c'¦ {'¶½fhUX] rjqžŒiTn\P=UdMPO‘Sq§kD^:cXO ¥xWj¯DsQ|Wp‡4Ud]~c/tWpneUhrpvTnKWpv+op®P¹hv HK‡uLU Qˆ\hSM[“ ]_‡P^aK `Q|{œª KЇi‰ Y
           Y÷                     ÷


                          ¯hSF³FWpo!] _a ¹wM·t°ˆÁYDˆISQir “ ”)¹
     “F“=¹ oR¨/fX¹ [€kN£ŒASF¹ U_µŒ·fh* cGTn¤³=fhfX,UWpoŒASFS•XUdkVcŠWpSFbºfй c/W?f cX_­PFfhUhWjUh,+UhŽj* UhWpo:WF¹:•hZdTnUdSFS±TnQiTnWjknknopWº¹4±fATnvUXKŠTV‰S±#`cSh§knWº^:O¯c`G¤°CTV±¦{ž¯XknTV`VrpY SŒi^XTnP=À UÕ]=ÃBTnUX² ]u¶½dPF“Qi±#YS“ ŒiTng Wja/o!¹ QiŽj[
                                      [÷                                                  *ö         *l


      “ )¹ H€¨/U²¹ µ\›SFM~U+]_+Y^a`4¨/¹ bedgWpTÂf³YFSFUhhecj k±ºfm¹ ±µloTnn´U‡¹XjPˆ»qSKaTnUhr sCTnUhd³!] ¶½q_Qit_W `}_]fhqWjU)fwŒ¯dvSqxŒRv_ŒiyzWBQiQ|Uh{oQ|´:q!KœTŒ ­ ]~tPFfXneŒ£v ruKSvFUdY~, cX¯dTVcXSFS³FŒiWpW®o»*³F“PWpdUh“ Wj,_QA* Y°SŒiˆITnP=SpU‡s ¹
                                                                                                                                                                                                                                j
    _j                      g                                                                                                                 _l


                             `=`F`/¹                                                                                                                                                                                                                                              cj


       “p’/¹‘TnˆÁU#¯¹ S'µ?chknSWpŒA±S?WB±ŒRŒiTVTVUXUXTnWpUhU‡³?Y WpºU)¹+g)TˆIQiP=SUhUh±UhTnWjkVU)S/ŒuY‡¹hSHKUdUŒcÕ\M‘M[]_¹w^aH€`cSU ]~R tˆWjQiKЉST\Qb ¶+Wj†QM[RF%SF·›±¦ P/M[¹]P¥!M·Q†v oRoRqŒP_\orpTVCSŒinCTnP=nUUÁQidfh] knq_Wpt_o`VY=oRWpU)knfhWp±5rBŒi•DTVPFWBU Q
                        j
                                                                           *g


                              “u”F`^TVU»N‡JµM!HBY/¯hSF³=Wjoµ’=” __’ ”F”)Y+‹)Wp¯XŒiWp±º•DWjQ“ ¹
        “j^X¹ º¹/N\SFf/QiWpU_Œu!Y ¨X¹dN+Wpr ­ ŒiWjU/§• ¸Qi³=WjQuY/J‘¹X‹/¯_s)QASŒiP=opYX,+S,+Ud, c º¹hb~P=oRoRWpU+¹~tP=±¯XknWp±WpU_Œio ¶½PFQ!chSŒAS
                                                                                                4j


                      ´®^ S`_Qi_W ^­ P=fXYoRWp“ op¹?HKU ¹ \M[]_^a`]­}Q ¥xM[Q|‡:Q|qSKvKNOT] qw{žQPQ|KN‡ˆnevKv+®Pv ‡uQ|‡aÂe–‘­ˆnC×uY/¯dS³=Wpo“ , h“u’ , YwM·fh³=fXoqŒ
                                                                                                                                                        l




      )¹'ZcX`=S¹/`FŒAb~S)`/P=¹»¹ ³H€Œ·8U SFUd\›c#M~]_L'^a`%¹€ÝknÅTVknknW=r Æu¹ ÇX¬ Y‡‰?g P=‹Xknt®fhM!±JW M-Ä ^ŠPSº>¶ ³F¢cQA£”S¯ dX­ hhTVrpYSF¯hkwSFŒi³FP_WpP=o kw¶CPFFQ!_a  SFUd’FSF’/ks¹ ˜p‹)TnUh¯X³"QiTnUhSF³FUdWjc#QuY£Wjv/‰µ¯hrjknŒiPPFQi•DTVUXWj³ Q
                                                                                                                                                                                                                                 _j
             j
jj


              “   ,+, ])¹
                                                                                                                         *,                                                          ijj             j


’/¹±º´®S¹¯QiÈ W ­ fhP=fX³=WFoRTVY UXº³º¹ WjU/g)STQiQirpP=TVUXS±[Kˆ»WpP=U_knŒuTn¹wUdHKS)ŒU Y¨X\¹ M[]_^aS`¯±be±dgWjfÉQuYdh Sj Udkoc•fm¨Xlo¹x€ÝnÊT2jPc/qSP=Ka±Ir s¹·dbµ]q_Tnt_Wj`´Ó]qŒ±#SFfwTnU_vŒiqxWpv_UdyzSQ|Uh{rpW'Q|q!TnKoU ]~S t
                                  ­
j                                          g        [÷                                                          g


             nvKvFYX¯dS³=Wpo!’/“paa )’ =”_Y“ ,, ])¹          4j




                                                                                                                                       61