HAL Id: inria-00072048
https://hal.inria.fr/inria-00072048
Submitted on 23 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.
Introduction to Logical Information Systems
Sébastien Ferré, Olivier Ridoux
To cite this version:
Sébastien Ferré, Olivier Ridoux. Introduction to Logical Information Systems. [Research Report]
RR-4540, INRIA. 2002. �inria-00072048�
ISSN 0249-6399 ISRN INRIA/RR--4540--FR+ENG
a p p o r t
d e r e c h e r c h e
Introduction to Logical Information Systems
Sébastien Ferré, Olivier Ridoux
N˚4540
Septembre 2002
THÈME 2
,-/.10235476/8:9;6=<><?-@ACBD4FE476/<&GH47IJKL
MONQPRTSUVXWZY[]\^S _a`cb=\ad\^S?_
Sefd?gh_idjQ_lknmoRqp`c_a\ar/jQS
s;tu`hvwSefxgh[]yQS
z+gc{Q{|`=t}e+y~StuS?dNQS?tudN]S[qho/ VXoS{QenSRpQtuS Uc c /UVU=q{|ghbcS>k
H*?Qcc x`cbc\idgc_Q[~`=tnRgeu\^`=[om~k}enSRkZFx}Q;j|k}S_^`=bc\id+\a[HgjQ[]\`=tnROg5mqeu`&y~S>kndtn\apSenNQS?\^td`c[/enS?[=ek=en`&r/jQStum
\^e?eu`[]g5o\ab=ghenS euNQtn`=jQbcN\^e?eu`gc[]gh_amoS\^e?lgc[]yCeu`Rgh\a[/eugc\^[ \^e?¡ MONQS?mdgh[¢p|S&bc\acS?[¢gh[¢gcp]k}entgcd£ek}{S?d\¤dgeu\^`=[enN|ge
y~`oS>k [Q`he&y~S{S[]y¥`=[euNQSHdNQ`=\adST`h+gC{]ghtnen\idj]_agctZ_a`cb=\adcgc[]yd`c[|dtuSenS\a[]k}eugc[]dS>k dgh[pS¦`cpQeugh\a[QS>ypom\^[]k}eugc[/en\igen\a[Qb
euNQ\akk}{S?d\¤dgeu\^`=[C\euNCgT{|ghtnen\idjQ_ight_a`cb=\adc¡;[CFgcde?]gT_a`cb=\ad{Q_ig5m~kO\^[gx}enNQS tu`c_aS `h1gkndN]SRg&\^[ yQgheugh§Dp]g=k}S>k¡1¨¥S
{QtuS?knS[/eenN]S&{]tn\a[]d\a{Q_aS?k`c_a`cbc\idgc_\^[~`=tnRghen\a`c[knm~kweuSRk?(enNQSd`c[]k}entgh\a[/eukenNQS?m \aR&{`=knST`c[enNQSS©~{QtnS>knkn\a`c[ `c_a`cbc\idk?
gc[]yNQ\^[/ekª`ctOenN]S\at+S«S?den\acS\^RT{Q_aSRTS?[=egeu\^`=[l¡
¬/®¯n°± ²*c \a[~`ctuRgen\a`c[k}m~k}enSRk?\^[~`=tnRghen\a`c[¢knS?gctudN gc[]y tuSeutn\aSgh_D(r/jQStum`ctuRqjQ_igeu\^`=[ltnS?{QtnS>k}S?[/eugeu\^`=[_agc[~§
b=j]ghb=S?k?oyQS?y~j]den\a`c[gh[|y¦euNQS`=tnS?R³{Qtu`/\a[Qb|¡
´iµl¶}·¹¸>ºª¶»*¼i·¹½7¾¿
Unité de recherche INRIA Rennes
IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France) Téléphone : 02 99 84 71 00 - International : +33 2 99 84 71 00
Télécopie : 02 99 84 71 71 - International : +33 2 99 84 71 71
xS?kq~mok}enP?RTS?k y[~`ctuRgeu\^`=[¥x`cbc\ir/jQS?kTDowxZj~eu\^_a\ik}S?[=e_ig_^`=bc\ir/jQSy~STFg`c[¥jQ[Q\^`ctuR&ST{`cjQtyQY?dtu\atnS
_aSjQt+d`c[/enS?[ojlo{|`=jQtO_\^[/euStutn`=bcSt>c{`cj]tm[]g5o\^b=jQSt>={`cj]t_gh[]gc_^m~knStSe{|`=jQtO_^SRgh\a[/enS?[Q\^t>¡[H{Sj~e+_aSj]tOyQ`c[Q[QS?tOjQ[QS
kn{|Y>d\^¤|dghen\a`c[Hgcp]k}entgh\^enS+r/jQ\[QSy~Y?{|S?[]y{]g=kyQjHdNQ`c\^©yj][QSf_a`cb=\ar/jQS+{|ghtnen\idjQ_a\^P?tnS=cSeªy~S>k;\a[]kwegh[]dS?kªd`=[]dtuPeuS?k1{SjQ=S[/e
entuS `cp~euS[ojQS?k+{]ght\a[]k}eugh[|d\igen\a`c[Cy~SdSe}euSqkn{|Y>d\^¤|dghen\a`c[TjQ[QS _a`cbc\ir/jQS {]gct}eu\adjQ_^\aPtuSc¡[CFgh\^e?QjQ[]S _^`=bc\ir=j]SOvw`cjQSyQgc[]k
jQ[owx _aSftc_aS+yjQ[HkudNQYRgyQgc[]k;_aS?kp]gcknS?ky~SyQ`c[Q[QY?S?k?¡f`cj]k{QtuY?knS[/en`=[]k;_aS?k{Qtn\a[]d\^{S?ky~S?kªk}m~k}enP?R&S>ky\a[~`ctuRgen\a`c[
_a`cb=\ar/jQS>k~_aS?k+d`c[/entgh\a[/enS>kªr/j\a_ak\aRT{|`/k}S?[/efk}jQt_S©~{QtuS?kuk}\a`c[y~S?k_a`cb=\ar/jQS>kOSefy~S>kOY_aYRTS[/ek{|`=jQt+_aSjQt\aRT{Q_aYRTS[/eughen\a`c[
S«S>d£en\acS=¡
±
?
¯
"!
k}m~k}enPRTS>k+y\^[~`=tnRghen\a`c[lQtuS?dN]StdNQSZy\a[~`ctuRgeu\^`=[l~`ctuRqj]_aghen\a`c[Cy~StuS?r/j euS?k?~_agc[Qb=gcbcS>kªyQStnS?{QtuY?knS[~§
egen\a`c[]y~Y?yQj]d£eu\^`=[Se+y~YRT`c[|kweutughen\a`c[Cy~SZenNQY?`ctuPRTS?k?¡
+
oS?cS?tugc_(tnS>k}S>ghtdNQStkªN]g5cStuS?d`=bc[Q\aS>y¦euNQS ,'.-/1023'2 \a[C\^[~`=tnRghen\a`c[k}m~k}enS?RTkq7WZ\^«`=tuy($4c`=jQcS?_^`ce?|oN]S_iy~`c[l|gh[]y
M`o`=_^S=6571785:9*WZ`={]gh_Ogh[]y<; gh[opSt>6571717/£¡¥[ enN]S?knSknm~kweuSRk=?>@A@%qgctnSbc\acS?[B '%qgh[]y cStum¥`henS?[ g enNQ\a[Qb
N]g=kZ`c[Q_am g¦S? []gcRTS?kTtuS?r/jQS?[=eu_^m`=[Q_am`c[QS5£¡DC]`ctZ\^[]k}eugc[]dS=(\^[enN]S&RT`/kwetnj|y~\^RTS?[=eghtumC\^[~`=tnRghen\a`c[knm~kweuSRk?(_^\FEcS
NQ\aStghtdNQ\idgc_|¤|_^Sknm~kweuSRkQgeuNQ\^[]b&\ik+g¤]_aSgh[]y\^euk[]gcRTSZ\ikOeuNQS `c[Q_am¦{]ghenNenN|ge_^S>gcyQkªtu`cR enNQStu`o`heOen`TeuNQS¤]_aSc¡
MONQSf{Qtn`=pQ_aSR \^enNHN]g5o\^[Qb `=[Q_am&gZS? []ghRTS?k;\ak;enN]ghe;enNQS?mTRqj]k}epS+cS?tnm&dghtuSj]_^_amdNQ`/k}S?[&en` egcdEo_^S+`ctgc_^_]j~enjQtuS
j]kughb=S?k `cenNQS¦enNQ\a[Qb=k?¡ 1©~{Stu\^S?[]dSk}NQ`+k enN]gheqenN]\ak\akq\^RT{`=kuk}\apQ_aSen`y~``ct&g\iy~SHtgh[Qb=S`hOj~eujQtnSj]kughbcS>k¡GC]`ct
\a[]k}eugh[|dSc;enNQS?tnS\ak[Q`¥NQ\^S?tugctudN]\ad?gh_;`=tnb/gh[Q\a?ghen\a`c[`hfRgc[/m{Q\aS?dS?k`hfkn`hewOghtuSenN|ge&¤QeukTgh_a_enNQS[QSS>yQk`hkn`hewOghtuS1H
{Qtu`cb=tugcRTR&\a[Qb|~enS>kweu\^[Qb||y~`~djQRTS[/en\a[Qb]y~S?pQjQbcb=\^[]b]]Seudc¡.I [Q`c[Q§DwM S©QgcR&{]_^S \ikgd`o`1E/§Dp`o`1E¡.J`/`:E/§Dp`o`1E~k+ghtuS `heuS[
`=tnb/gh[Q\aS>y`c_a_^`\a[QbeuNQS&d`cjQtknS`hgHR&S>gh_D(gh[]y\^e\akfenNoj]kcS?tnmCy~\3KdjQ_^eeu`knS?gctudN`ctg¦tuS?d\^{Sg=dd`cty~\^[]ben``henN]St
dtn\^enS?tn\igQ_a\3E=S;euNQS jQ[|}g5gh\a_agcpQ\^_a\^ewmZ`c|g`cS[>`=t*gZy~\aSe1d`=[]kweutugc\^[/e>¡+`cenSenN]ghe*S?cS?[S_aS?dentu`c[Q\idd`o`1E/§Dp`o`1E~kl`cenS?[`c_a_a`
euNQ\akkweutnj|d£enj]tnS=¡ ;_^S>d£eutn`=[Q\adT`=t [Q`he>leuNQS¦d_igckuk}\idgc_;k}`=_^jQen\a`c[en`CenN]\ak {]tn`=pQ_^S?R \iken`knS?gctudN¥\^[¥euNQSNQ`c_aS\a[~`ctuRgen\a`c[
knm~kweuSRMLy~`~djQRTS[/een`C¤|[]yenN]SHy~S?kn\atnS>y¥enNQ\a[Qb]¡GNf`S?cSt>(euNQ\ak\ik`c[]_^m¥g{]ghtnen\igh_k}`=_^j~eu\^`=[p|S>dghj|k}SHr/jQS?tnm_agc[Qbcj|ghbcS
j]knS?y\a[k}S>ghtdNHS[]bc\a[QS?kgctnSZ`heuS[en`o`TtnS>kweutn\id£euS?y(¡
MONQS?tnS&N]g5=SqpSS[knScS?tugc_ghe}enS?RT{~eukZ`=tkn`c_ao\^[]b¦enN]S&[|ghRTS{]tn`=pQ_^S?RC¡¨STRTS[/eu\^`=[¢NQS?tnS&`c[Q_amCewª``c;enNQS?R enN|ge
ªSTN]g5cSTk}S?_^S>d£euS?y¥p|S>dgcj]k}S&euNQSm \a_a_^j]k}entgeuS&enNQS¦y~\3K¦djQ_^ewm `ceuNQSS[/enS?tn{]tn\ik}S=OC1 7WZ\^«`=tuy(P4c`=jQcS?_^`ce?oN]S_iy~`c[lgh[]y
M`o`=_^S=Q57175>gh[]yRNSISJ 7WZ`={]gh_;gc[]yR; gh[opSt>Q5717:7=¡&MONQS?m¢N]g5=S\a[ d`=R&RT`=[¢eu`Cd`cRpQ\^[]ST>O'>@U)A@
gc[]yV0F'RW2'#A@h¡
XY'>@Z/A[T\iktnS>r/jQS[/en_am&`cjQ[|y¦\a[d`=RT{Qj~enS?teu`o`c_ik2H*Sc¡b]¡a/¤]_^Sknmok}enS?Rk/p|`o`:E=§¹RghtE~k=`ctªR&S?[oj]k¡[HenNQ\ik
RT`~y~S_D~k}S>ghtdNQ\a[Qb \akªy~`=[QSfpom\]^[A[¦\^[Hgd_igckuk}\^¤|d?gen\a`c[k}entuj]d£eujQtuS+enN|ge\ik`henS?[HpQj]\^_^eªgc[]yRgh\a[/eugh\a[QS>yRgh[oj]gh_a_amc¡
g5/\ab=ghen\a[QbC\^RT{Q_a\aS?kg[Q`cen\a`c[`h6-3:'9S0'2A[A g{]_ag=dSc*gh[]yV[A@_(Tgh[Q`cenNQS?t {Q_igcdS=¡MI[Q`cen\a`c[`h`'2^>0>8
NQS?_^{|kfkn{|S>d\^m/\a[QbTeuNQSba}`henN]St{Q_igcdS?kdctuS_igeu\^=S_amen`TeuNQS{Q_igcdS `c[QS \ik+dj]tntuS[/en_amH\a[l¡U; gh[omgc{Q{Q_a\ad?geu\^`=[]ktuS?r/jQ\atnSZenN|geg
{Q_igcdS\ak+g&{Q_igcdSZen`tuS?gcy¦tn`=R g=kªS_a_g=kg{]_ag=dSZen`Ttu\euS `c[l¡
eb3'BW'2#A[¥\ik `cenS[`=jQ[]y\a[ \^[Q`ctuRTghen\a`c[ knStucStk knj]dN gckknS?gctudN¥S[Qb=\^[]S?k `=[euNQS¦¨¥Sp FSc¡b]¡a*WZ`o`cb=_^S5£¡
[euNQ\ikfRT`~y~S_Dk}S>ghtdNQ\^[]b\aky~`c[QSpomj]kn\a[Qb"W2''%£b=S[QS?tugc_^_amHS©~{QtnS>knknS?y\a[¢g Eo\a[]y`h;{]tn`={|`/k}\^en\a`c[]gc_l_a`cbc\idh¡.I S?_^_^§
tuS?d`cbc[]\^?S?yy~\3K¦djQ_^ewm`h;euNQ\ikRT`~y~S?_\ikenNQS&[QS?dS?kuk}\^ewmC`h;N]g5o\a[QbgHbc`o`~yGEo[Q`_aS?y~b=S`h1euNQSqeuStuRT\^[Q`=_^`=bcmj]knS?y \a[ euNQS
\a[~`ctuRgeu\^`=[ k}m~k}enSRCgh[]yC`c;N]g5o\^[]b¦g¦{QtuS?d\aknS \ayQS?g¦`c1N]geZ\akk}S>ghtdNQS?y`ct>¡.N+`ªS=St>Q\^e\ikfS>gckn\^S?ten`tnS>d`cb=[Q\aS gh[
`=p~vwS?deenN]gc[Heu`¦y~S?kudtu\^pS\e>]gh[|y¦euNQS [QS?dS?kuk}\^ewm¦`c*S©o{]tnS>knkn\^[]b&gTr/jQStumHd?gh[tnS?{|S?_ldgcknj]gc_(j]k}S?tuk?¡
MONQS?[llNQ\idNknS?gctudN¢R&`~y~S?_1k}NQ`=jQ_iy pS&{]tnSStutnS>yfHf[]g5o\ab=ghen\a`c[`ct r/jQS?tnmo\a[Qb[g [ Fgcde?l\^ey~S{S[|yQkZ`c[k}\^enj]ghen\a`c[]k?
gc[]yH\^e+\ikk}`=R&Sen\aRTS?kO[QS?S?y~S>y¦eu`&j|k}Sp`henNC`cenN]SR \a[enNQS kughRTS k}S>ghtdNl¡hCQ`ct\a[]k}eugc[]dS=Qk}`=R&S?`c[QSd`=jQ_iyH\ik}Nen`TpSb=\^[
NQ\ikZk}S>ghtdNp/mCgHr/jQS?tnmCgh[|yCenNQS?[ tuS¤][QS\eZ\euN¢[]g5o\ab=ghen\a`c[l¡.Nfm/p]tn\iy knmok}enS?Rkd`cRqp]\^[Q\a[Qb¦N]\^S?tugctudNQ\idgc_d_igckukn\¤|d?geu\^`=[
gc[]yp|`o`c_aS?gc[r/jQS?tnmo\a[Qb&N]g5cSpSS[{Qtu`c{`=knS?y\^[euNQSy~`cRgc\^[`h¤]_^Sknm~kweuSRkH
V"8CCd!/'2,UijA3'b!#&%'2cWZ\^«`cty(:4=`cjQ=S_a`he>=oNQS?_ay~`=[lcgc[]y M`o`c_aScO57:7855lS©/euS[]y]kenNQSN]\^S?tugctudNQ\idgc_oR&`~y~S?_Q`h
j]knj]gc_¤]_^Sknmok}enS?Rk\^enNR]Ak A'2'%enN]ghed`ctutnS>k}{`c[|yTen`r/jQStu\aS?k?¡*MONQS>k}Sr/jQStu\aS?kOd`=[]dS?tn[H¤]_^SZ{Qtu`c{Stnen\aS?kenN|ge
gctnSZghj~eu`cRgeu\ad?gh_a_^m&S©oentgcdenS>yTp/m\%2 '%£ogh[]yHghtuSfS©~{QtuS?kuknS?yT\^enN¦gh_ajQS>yHgenentu\^p]j~enS>k¡;o`|cewª``ctub=gc[Q\a?geu\^`=[gh[]y
k}en`=tugcbcSRTSenN]`oy]kd`/S©~\ak}eHenNQSqk}eugc[]yQgctuyNQ\aStghtdNomenN]ghefbc\acS>k+g[]gcRTSen`¤]_aS?k?gh[]yo\^tnenj|gh_yQ\^tuS?den`ctu\aS?kªenN|geS?[]ghp]_^S
g=knkn`~d\igen\acSk}S>ghtdNQS?k`c[H\a[/entu\^[|k}\id¤]_aSZ{Qtn`={|S?t}eu\^S>k¡Qlf[~`ctnenjQ[|genS?_^m=/enNQS>k}Sew`RTSenN]`oy]kªd?gh[Q[]`heOp|Sd`=RqpQ\a[QS?ytnS?S_am\^[
b=S[QS?tugc_7¡[{]ghtnen\idjQ_ight>~o\^tnenj|gh_ly~\atnS>d£eu`ctu\^S>kªgctnSZ[Q`ce+{Q_ag=dS>kªen`Ttn\^enS \a[/en`|¡
VmNSISJ kXn'2>O#,ob/ Gpq$'2D|WZ`c{|gh_gc[]y\; gh[opSt>Z57:717=ªgc_akn`Tj]k}S>k+r/jQStu\aS?kªen`p]jQ\^_iyy~\atnS>d£eu`ctu\^S>kOp]gcknS?y`c[¤]_aS
d`c[/enS?[=ekp]j~e1enNQS>k}SOy~\atnS>d£eu`ctu\^S>kgctnSª\^[/euSbctgeuS?y \a[enNQSONQ\aStghtdNomc¡MONQ\ikS[|ghpQ_aS?ken`d`=RqpQ\a[QSªNQ\aStghtdN/m gc[]yqd`c[/enS?[=ek*\^[
knS?gctudNQS>k¡PN+`ªS=St>hj]knStkghtuS+gh_a_a`S>yqeu`qRT`cS+g ¤]_^S\^[¦gqy~\^tuS?den`=tnm&S=S[\^l\eyQ`/S>k[]`hekugeu\ak}mqeuNQSr/jQS?tnmTgckukn`od\aghenS>y
eu`TenNQSy~\atuS?d£eu`ctumcoNQ\idNCtnS>k}jQ_^eukO\a[Cd`c[|k}\ikweuS[]dm¦{Qtu`cpQ_aSRk?¡
MONQSy~tug5p|gcdEq`cenNQS>k}SN/mopQtu\iyk}m~k}enSRk\ak;enNQS?\^tª_ag=dEq`cd`c[|k}\ikweuS[]dmc¡*[]y~S?S?y(=enNQS?mTN]g5cSOewª`qknS?ghtdNTRT`oyQS_ik1enN|ge
gctnSZ[Q`heOeu\^b=N=eu_^m¦d`c[Q[]S?d£euS?y(~N]\adNRgEcS>k\^e+y~\3KdjQ_^een`Tk}\^eudNtn`=R `c[QSRT`~y~S_eu`euNQS`heuNQSt>~gh[]yHen`d`=RqpQ\a[QSZp|`cenN
\a[enNQSkughRTS k}S>ghtdNl¡
¨¥S{]tn`={|`/k}SªgfkudNQSRTSOdgh_a_aS?yx`cbc\idgc_=[Q`ctuRTghen\a`c[~mok}enS?Rk7xl}Q\a[qNQ\idNr/jQS?tn\aS?k*ghtuStuS?gc_^_am{Q_ag=dS>kleu`tuS?g=ytn`=R
gc[]yen`tu\euS \^[/en`|¡MONQSkudNQS?R&S \iksr]S©~\^pQ_aS \a[CenNQSknS[]knSenN|ge+euNQS [QS\abcNop`ctuNQ`o`~yHtuS_igeu\^`=[\ikcS?tnmy~S[|k}S¦F\7¡Sc¡a~enN]\^[Qb/k
N]g5=SRTgc[omH[]gcR&S>ku¡¹e+\a[]dj]tuk[]`\^[]d`c[]kn\ikweuS[]dm¦`ctfy]gh[Qb=_^\a[QbT_^\a[8E~k{Qtu`cp]_^S?R]p|S>dghj|k}SeuNQS [QS\abcNop`ctuNQ`o`~yHtuS_igeu\^`=[\ik
Rgh[|ghbcS>y¦ghjQen`cRghen\idgh_a_amc¡QC*\^[]gc_^_amco\^e+k}jQ{]{|`=t}ekp`heuNr/jQS?tnmo\a[Qbgc[]yH[|g5/\ab=ghen\a`c[l/gh[]yghtupQ\^entghtumTd`cRpQ\^[|gen\a`c[|k`cp|`cenN
pS?d?ghj]knSf[]gcRTS?kgc[]yr/jQStu\aS?k;pS_a`c[]b en`qenNQSZkngcR&Sf_agc[Qbcj]gcbcSDWZ`oyQ\^[lO;\ikukngc`cjQ\D=gc[]yTI+{]tn\a_757:71*9hxl\a[]y~\ab]5717/c¡MONQ\ik
kudNQSRTS \ik+p]g=k}S>y`c[ gTghtu\agc[/eO`cqCQ`ctuRgh_PJ`=[]dS?{~eSI+[|gh_amokn\ik¨ \a_^_aScP57:t=U89]Wgh[/enS?tfgh[]y¨ \a_^_aScu57:717=ªd?gh_a_^S>yxl`cb=\ad?gh_
J`=[]dS?{~eSI+[]gc_^m~kn\ak kCQS?tntuY gh[]yz\iy~`cj~©(]Uc c c /£¡
MONQSgct}eu\ad_^S \ik+`=tnb/gh[Q\aS>yHg=kO`c_a_^`+k?¡ª~S?d£eu\^`=[ U&{QtnS>k}S?[/eukOeuNQS {Qtu\^[]d\^{]_^S>k+`h1xl`=bc\idgc_uJ`c[]dS{~eSIf[]gh_am~k}\ik|gh[]yeuNQS[
oS>d£eu\^`=[M*knNQ`+k1NQ` \eOdgc[p|Sj]k}S>y&`ct[]g5o\^b/gen\a[Qb gh[|yr=j]Stum/\a[Qb|¡PNf` eu`qdtuS?ghenS+gc[]yjQ{yQgeuSenN]Sd`=[/enS[/e`clgxl}
\ikO{QtuS?knS[/enS>yH\a[C~S?d£eu\^`=[|¡;MONQS?knSk}S>d£en\a`c[|kOtnSStªen`g&_^`=bc\idf{|gckuk}S>yg=kªg&{]gctugcRTSenS?tN]\adN\akªeu`Tp|S j]knS?yH`ct[|ghRT\^[]b]
r/jQS?tnmo\a[Qbqgh[|yT[]g5o\^b/gen\a[Qb|¡*oS>d£en\a`c[{QtuS?knS[/euk1`cenNQS?t;jQ[|d£en\a`c[|k`cgxl}&_a\3E=SfghjQen`cRghenS?yTj]{yQghen\a[Qb]~yQgheugh§DRT\a[Q\^[]bgh[]y
_aS?gctn[Q\a[Qb|¡oS>d£eu\^`=[S©~{Q_igh\a[]k;NQ` gh_a_QeuNQ\ikdgc[p|Sy~`c[QSf{Qtug=d£eu\ad?gh_a_^m=¡uC*\^[|gh_a_^m=/d`c[]d_^j]kn\a`c[]k;gc[]yT{Stk}{S?den\acS?kghtuSbc\acS[
\a[ oS?den\a`c[o¡
ª ) q£%''
MONQS `=tn\abc\a[`h*enNQ\ikª`ctE\akOeuNQSknS?ghtdN`ctsr]S©o\apQ_aS `ctub=gc[Q\^>geu\^`=[]k;`=tRgh[]gcbc\a[Qb]~jQ{yQghen\a[Qb]]r/jQS?tnmo\a[Qb]~`=t[]g5o\^b/geu\^[Qb
\a[ yQgheug]¡ [ enN]\akTd`=[/enS©oe>;k}S?cStgh_ªtu`c_aS?kqgctnS{Q_ig5mcS?y p/m {`=kukn\^pQ_am y~\^«S?tnS?[=eT{S`c{]_^S:H¦Sc¡b]¡a1y~S?kn\^b=[QSt>;gcyQR&\a[Q\ikweutughen`=t?
gc[]y¢S?[]yo§¹j]knSt>¡)N+\aStghtdNQ\idgc_`=tnb/gh[Q\a?ghen\a`c[]kghtuS[Q`cebr|S©~\^p]_^S=gh[]yjQ{yQgeu\^[]b]r/jQS?tnmo\a[Qbgc[]y[]g5o\^b/gen\a`c[ghtuSy~\3K¦djQ_^e
eu`d`c[]d\^_a\igenSFknSS`ctT\a[]k}eugh[|dSenNQSCo\^S?³jQ{yQgeuSC{Qtn`=pQ_aSR \a[ yQgheugh§Dp]g=k}S>kS_a_^S?t?s571t==}¡ MONQSC_^\^enS?tughenjQtuSknNQ`+k
euN]gebiu Qpq/'(-Qob#&%%i=pZo ]Wgh[/enS?tªgc[]y¦¨ \a_a_^S=f5717:7=;\akOgbc`o`~y¦dgc[]y~\iyQgeuSf`=tOknjQ{Q{`ctnen\a[Qb&r=j]Stum/\a[Qb&gh[]y
[]g5o\ab=ghen\a`c[l¡
MONQSp]g=k}\ik`cbCPJUI \ak&gM,S('1enN]gheTg=knkn`~d\igeuS?kqghe}eutn\apQj~euS?ken``cp~vwS>d£euk9`=p~vwS?deuk&ghtuS¦euNQS"?>@A@%\a[ euNQS
\a[/entu`oyQj]d£eu\^`=[lgh[|yenNQSCd`=_^_aS?den\a`c[ `hfgenentu\^p]j~enS>k&g=knkn`~d\igeuS?y¥en`¥`c[]S¦enN]\^[QbOL5`=p~vwS?de\ik\^euk / '¡VCPJUI N]g=kqtuS?dS\acS?y
ghe}enS?[/en\a`c[ `=t\^euk&gh{]{Q_^\idghen\a`c[ \a[ Rgc[/m y~`=Rgh\a[]kknj]dN g=kq\a[ kn`hewOghtuS¦S?[Qbc\a[QSS?tn\a[Qb Do[QS?_eu\^[Qb|s5717:t89*xl\a[]y~\ab]U5717/O9
tu`c[QSOgh[|yT~[QS_^en\a[Qb]5717c/¡MONQS\a[=euStuS?k}e1`hChJUI gck1gZ[]g5o\ab=geu\^`=[ en`o`=_Q\^[&bcS?[QStgh_oN]g=k1gh_ik}`pSS?[&tuS?d`cb=[Q\^?S?y7WZ`~y~\a[l
;\ikukngc`cjQ\D/gc[]yTIf{Qtn\a_D5717:*89cx\^[]yQ\^b|$5717=89 1`=bheªgc[]y¨ \a_^_aSc57:7ho£¡hN+`ªScS?t?=SfSS?_|\^eª\ik[Q`he6r]S©~\apQ_^SZS[]`cjQb=N¦gckFght
g=k;euNQS[|ghRT\^[]bq`h(euNQ\a[Qb=kª\ikd`c[]dStu[QS?y(ogh[|yTenNQSZ_a\euStgenj]tnS`c[MChJUI \a[]k}\ik}eukªRT`ctuS+`c[Hgc[]gh_amo\a[Qbqgqbc\acS[d`c[/euS©oeeuN]gh[
`=[RTgc[]ghb=\^[]b&S?c`=_^o\a[Qbd`c[/euS©oeuk?¡[CeuNQ\ikfknS?d£eu\^`=[l]ªS {QtuS?knS[/efgh[S©oenS[|k}\a`c[en` CPJUI euN]gegc_^_a`+kª`ctgtn\idNQS?t[]ghRTS
_igh[Qb=j]ghb=Sc¡
MONQSghtu\^Sewm¢`hfgc{Q{Q_a\ad?geu\^`=[ y~`cRgh\a[]kqpQtn\a[QbeuNQSH[]SS?y `ctqRT`=tnSHkn`c{]NQ\ak}en\idghenS>y¥`ctuRTgc_d`c[/enS©/ek euN]gh[ euNQSHRTS?tnS
{QtuS?knS[|dS&Lhghp]knS[|dS¦`cfge}eutn\apQj~euS?k?¡ CQ`=t\a[]k}eugh[|dSc1Rgc[/m gc{Q{Q_a\ad?gen\a`c[ y~`cRgh\a[]kj]knS[ojQRTStu\idgh_gh_ajQS?kCS=¡b|¡^*_aS[QbcenN]k?
{Qtu\idS?k?Qghb=S?k£Qgc[]yenNQS [QS?S?yHen`S©o{]tnS>knkª[QS?b=geu\^`=[gc[]yCy~\ikvwjQ[|d£en\a`c[C\ikO`heuS[S_^e?¡;[g&Rqj|dNRT`=tnSk}{S?d\agc_^\aS>yCknd`c{Sc
\^ef\ik+\aRTgcbc\a[]ghp]_^Seu`j]k}SenNQS ewmo{S`h1kn`hewOghtuSd`cRT{`c[QS?[=ek+gckfk}S>ghtdN E=Sm~k\qJ`=knR&`|f57:7=c¡ªoS?cS?tugc_(S[Qtu\adN]R&S?[/euk
eu`euNQSgenentu\^pQjQenSkweutnj|d£enj]tnSN]g5cSp|S?S[ {Qtu`c{`=knS?yfHSc¡b]¡a1RTgc[om 5gc_^j]S?y ge}eutn\apQj~euS?kC7Wgc[/enStgc[]y ¨ \a_a_^S==5717:7=;gh[]y
¤]tk}e}§¹`cty~SteuStuRkqJN|ghj]y~tu`c[ gc[]y_; gc\^_a_aSc5717:t=£¡.Nf`S?cS?t?Q[]`hegk}\a[Qbc_aSS©/euS[]yQS?y_ChJUI tugcRTSª`ctEd`=Stkgh_a_euNQS
d`c[]dtnSenS y~`cRgc\^[]k?Qgh[|yH[Q``=[QS dgc[{QtuSeuS[]yd`=Stu\^[]b&gc_^_euNQSd`=[]dtuSeuSyQ`cRgh\a[]ken`¦d`cRTSc¡
o`|Sª{Qtu`c{`=knS;eu`d`c[]k}entuj]de*gR&`=tnSªbcS?[QStgh_=tghRTSª`ctEf`=t1d`c[|dS{Qegc[]gh_am~k}\ikhx`cb=\ad?gh_@J`=[]dS?{~eqI+[]gc_^m~kn\akªFxhJUI
\a[¢NQ\idN euNQS&_^`=bc\id `hghe}eutn\apQj~euS?kp|S>d`cRTS>kgH{]ghtghRTSeuSt>¡ZMON]\ak\^_a_1gh_a_^` `=t\a[]k}eugh[/eu\aghen\a[Qb¦euNQSb=S[QS?tugc_ltghRTSª`ctE
pomHRTS?tnS?_^m¤|_^_a\^[]b&\a[gTy~S?y~\idghenS>y_a`cb=\adc¡
"!$#%
u1hpq/'(-hob^#&%%q7xPJUIZ1\ikg b=S[QS?tugc_^\a?ghen\a`c[&`hZCPJUIq=N]StuSfk}Seuk`hlgenentu\^pQjQenS?kghtuS+tuS{Q_igcdS?y&pomq`=tnRjQ_ag=k1`h
gc[¢Fgc_^RT`=k}eghtupQ\^entghtumq_a`cbc\idh¡Q;`=tnSy~Segh\a_akªghp`cj~eenNQStnS?_aghen\a`c[¦\^enNH{QtnS?o\^`=j]k;ª`ctE~k;\a[MCPJUI:dgh[Hp|S`cjQ[|y\^[¥C]StutnY
gc[]yCz\ayQ`cj~©(]Uh = c /£~gh[]yCgc_^_({Qtu`o`hFkd?gh[p|S`=jQ[]y\^[C]StutnY gc[]yCz\ayQ`cj~©(f57:717/£¡
¨¥S¤]tkwe+y~S¤][QS N]gheOªSdgc_^_lg 31 \a[HeuNQ\akfghtnen\id_aSc¡
&('*)*+ +F±,).-0/!±,12+(3 o _a`cbc\id,%D5476(k-/3'98:;=<>;@?A;@BA;DCE;@FHGD"Iu>8'2'
J : %n?>8'D3@:'d¢`ctuRqjQ_igckK
J < %`?>8'&knjQp]knjQRT{~en\a`c[<'F0L3-/'6 1'2)]&'2M:"NO
J ? / EB 'Y'%-8'2kA]'2#d`c[vwj][]d£eu\^`=[ / y~\ikvwjQ[|d£en\a`c[PL(02A#M-'8%QNO
J C RF 'D'%-8'2kA]'^#Heghj~eu`c_a`cbcm / d`=[=eutug=y~\id£en\a`c[SLd%($$)O3%QNUT
!> "31\@%P Fk'VLXW)]&'2#R ZYU'%3'2#O>[ \ \(]@NO9Iu>8%' :' % 1'2A]&' "A A>' @%$Ij#
?>8'=-'K6 1'2^<H6 %> ?>8_? / B 'Y'%k-'A]'# ?>8'\a[~¤]RjQR`L?1'('%637Ij'2D0O DN ,?>8'&knjQ{QtuSRjQR
L3'&%.-:-8'2T0O DNO. C / aF ' '%-8'2kA]'2#\A>'Ten`={ GA>'p`he}eu`cRbTdc/>8' /(Z: <0',@%2' G&%T
/ 'jYA>'YF1)3k'eT
¹*f<hgTgc[]yiga<Sf*jfgh[]ygTgctnSZdgc_^_aS?yH_^`=bc\idgh_a_amG'W2OA]&3'2D/N]\adN\akOy~S?[Q`heuS?yHg=kkfmlng9oªS\a_^_(d`c[]kn\ayQStenNQS?R
g=ky~\^«S?tnS?[/etnS?{QtuS?knS[/eughen\a`c[]k`ceuNQSfkughRTSS?r/jQ\agh_aS[]dSfd_igckuk?=gh[|y\a[Fg=d£eªS\^_a_d`c[|k}\iy~SteuN]geªS_aSRTS[/ek;`ho: gctnSOeuNQS
S>r=j]\^gh_aS[|dSqd_ag=knknS?k?¡O¨Svwj|kwegckuk}jQRTS=Q`ct{Qtgcd£eu\ad?gh_ltuS?g=k}`=[]k?~enN]ghef`c{Stgeu\^`=[]k><>;D?gc[]yB ghtuSd`=R&{]j~eugcpQ_^S=¡+o`cRTS
%2'2,%\ikj]knj]gh_a_amHj]knS?yeu`¦y~S¤][]SqgT_^`=bc\idhQp]j~efªSy~S_ig5m¦euNQSqy~\ikndj]kuk}\a`c[ghp`cjQe+\efj][=eu\^_oS?den\a`c[ZQ¡UTgck+Sy~`[]`he
[QS?S?y\^e+NQStuSc¡[C`cty~Stªeu`¦d_ightu\meuNQ\a[Qb=k?~NQStuS\akfgh[S©QghRT{Q_aS`h1g_a`cb=\adc¡
! -0/
± ± +
+F±,)
!!
±21,+
3
ob '[.-/3'M31MA>b<0'T@%' A"=pZox%¦{]tn`={|`/k}\^en\a`c[]gc__a`cb=\ad(Tbs
?>8'Y%#(12kn% :'D6A>'`%2'sd6-/-&%A8% $A8%Y(.--8%A%iL( :'2A" %'2>Ne)OF&%_/ U
n%.23&%2' `O :'.02A#D/'2A]&'% / / `O#`'2kA]'MT'=%#`A>PU--8%A_%U%0%O,'
02#\A>','G% ] )-/-&%AnL eN Tbc/>8'2jM8!;"*;#k;$k;% ;# GY%2%!&U'%HW)''&q$Ak [7=0'@%2'
AU%nA>'9Ij'2A6' 7IQ 03'V['02 T
c/>@%)'@S-3'Y%>8UIh%`?>8j?>81>GA>'YA$'2?1'dn?>8'Y31)%nA)A(' ( ?>8'Yk-/3' 8:;=<>;@?A;@BA;DCE;@FHGDqR:
31D #,>8]'D,')'2kA]'%)(`'eT T* A_?>@%)'[.-/3'eT
¨¥SO[Q` y~S¤][QSªenN]SRTgc\^[&[Q`cen\a`c[]kgh[|yqtuS?knjQ_^euk`hxPJUIDH(':D'(-P3'=gc[]y\(':,+' %0%OS-|¡
"!$#%.-/R%o0214365718-*09;:<-*/$#>=d%o003r%1j# 0
I 316$':f{Q_ig5m~kfeuNQSTtn`=_^S&`heugcpQ_^S>k\^[gCyQgeghp]g=k}S=lgckZ\^eb/geuNQStkenNQS,Eo[Q`_aS?y~b=S`=[QSN|gck ghp`cjQe`=p~vwS?deukZ`h
\a[/enStuS?k}eS=¡b|¡^~¤|_^S>k~pQ\apQ_a\^`=bctgh{QN]\adZtuSStuS[|dS?k?otnS>d\a{|S>ku¡
&('*)*+ +F±,)<?S/!±,12+c ! ±,) @ O3 o _^`=bc\idgh_ld`c[/enS©oeaLd(':n%>8N %D -3'ACB 8ED; :;#F(G Iu>8'2'G(
J D %D&qA('`%2'2s Y10IH2'k%@
J : %D F1 L(%nA5W'I&jAV[DNe
J
F%DT,-1-A@ JD (>: A>fyQS?kudtu\^pS?k':>10IH2'.02#M.O3 T
MONQS?[loSy~S¤][QSew`RTgc{Q{Q\a[Qb=kªpSewªSS?[knSeuk`h`cp~vwS>d£eukEKMLgc[]y`=tnRjQ_ag=k:ª\a[g&d`c[/euS©oeNA =euN]geOªS{Qtu`cS
eu`pSgWgh_a`c\ikqd`c[Q[]S?d£eu\^`=[:g5=Sm gh[]y s;tn\aS?k}en_aSms57:7c /£¡ I³¤]tk}eRgh{Q{]\^[QbPO%Q d`c[Q[QS>d£ekqS>gcdN `=tnRjQ_ag f en`¥\ek
A%(/'%£\D¡Sc¡al`cp~vwS>d£ek NQ`=knSy~S?kudtu\a{~en\a`c[¥\ak knjQp]knjQRTS?y¥pom fP9RO%Q 8fGZ\ikeuNQS':('$f`cMf*¡TI knS?d`c[]yRgh{Q{Q\a[QbTSUQ
d`c[Q[QS>d£ekS?g=dN k}Seq`h`=p~vwS?deukWVYXZD en`euNQSHRT`/kweq{]tnS>d\ik}S`=tnRjQ_igk}jQp|k}jQRT\a[Qb¢gc_^_ªy~S?kudtu\^{Qen\a`c[]kq`h`cp~vwS>d£ek\a[8V9
SUQi8'V>GO\ikªenNQS A$'2ª`h*V&¡
&('*)*+ +F±,)\[n/ 4R +) 1 O Q ) ² S Q 3 '2ACB 8ED;: ;>F G)0'M$':]V^X<Di6/ f _ :
J S Q L!SGn%>N`MK@Lba :;cS Q 8EV>G7`dBfehg"ikjF,8IlUG
J
O%Q LmOTn%>8Nc`U:naoK@LM;O%Qi8fGN`pBrqslt_ DvuwF,8IlUGM<Sfx
y - />z !±2+T ±,) )* h +7±2) 3 '2A 0'M(':TEc/>8'.-A 8'S Q ;{O Q GY%DWgc_^`=\akd`c[Q[QS>d£eu\^`=[<0'@%2'
| V}X<Di;@fT_m:<`kSUQi8'V>G<SfZ~ V}XnO%Q 8fG)
[enN]S`c_a_^`\a[Qb]oªS\^_a_y~tu`c{enNQSknjQp]kudtu\a{~eA N]S[C{|`/knkn\apQ_^S=¡
!T?S/G 3 ob '@S-3' $':IQAAPAA^@%'?>8''%Sd,O, 1'2]&'23-/,'2 spo9T.pq('1AU#,_%
:'0'2('2#R% A=/ %AS-F'_&%MAn%\A ' nAA@%kkA@RA>''2k6/8%@D/ "D % >7IQA@ "'%
-1-^k d)=po9T c/>8' 31 @%' _A<?>@% $':S%T?>8'n--8%A/s3W L%2''"[.-/3'm[@NbIQA?><G%2'nd
)`--8%A%JBvqG,;#7;>sx T' :'I&j' $':AU#0#m8EDU#,j;;>F@>7G@MIu>8'2'D#,BqGr;>,;#x s
Iu>''cF@U#Brqa,;{aoO;#a*V8'cG"x(T
I x`cb=\ad?gh_[~`=tnRgeu\^`=[om~kweuSRFxl}]\aklS?kuk}S?[=eu\agc_^_amgO_a`cb=\ad?gh_hd`c[/enS©/eS?r/jQ\a{Q{|S>y\euN []g5o\^b/geu\^`=[Zgc[]yZRTgc[]ghb=SRTS[/e
eu`/`=_ak?¡sCQ`ctuRqj]_ag=kk}S?tn=Sg=k+r/jQStu\aS?k?]gh[]yCS©oenS[|k}\a`c[]kg=k+gh[|k}ªStkOo\agTRgh{]{Q\^[]bO Q ¡ªMON]\ak\ik+`=[Q_amgTtu`cjQb=NCyQS?kudtu\^{~eu\^`=[l¡
¨¥S\^_a_+knSSC\^[ oS>d£en\a`c[ *enN]ghe¦g¥x} gc[]knS?tTd?gh[ gh_ik}`¥p|S g`=tnRjQ_ag]¡ C]`ctT\^_a_aj]kweutughen\a`c[ {QjQtu{|`/k}S=ªSd`c[|k}\iy~Stg
pQ\apQ_a\^`=bctgh{QN]\ad?gh_\^[Q`ctuRTghen\a`c[Ck}m~k}enS?R¡
![n/ 3 u'2B 8ED; ;>F G,0', 3h$':AIu>'' 10IH2'2k%' 02021-8>@q'k''2'%@AIu>8%2'
:'%22- ',.-&%2' Gd,Mk#-'5Ld'=T(T=k23'=A 6F-'' A[%QNO= %SdO?>8%. kA3's \ #1' =-/0t6
oT c/>',3 =@%2' ,'-'%%A@_ 1'%2-/k8%@.%D%AA3,( A>'S--8%Akj31 L%''t_@.-/3'a[DN
'@'(-DA>D()%\'\'(-F1' V0#R]&' Vk02O('%MAB?>8'Y ghe}eut&gc_^jQS(¥ge}eutG%M?>8'\/ '_d\ k0O('
Ld'eT Tc k¡4¢@£¥¤k¦,§¨ M¦ NO) gh_ajQS '-'%%'%_V3h--8'2#<10OA>'G]'Rd\?>8'"k02O('=T iuGA%'D
$O,'2 k02O'% 0' 1'%20' A A$'2]SF1Ld'=T(Tc§¨ M¦ª©G«¬s@®¯¯{°®@®® §¨ k¦±©«¬G² NO
%A[ k02O'% 0' 1'%20' 02#< %A[PLd'=T(T¢.©s¢¥³M¨ª©M´rµ¶4¤M·.©@¸¹ 4³»ºG«¼4¤k¦¹½. M¢.©w¤k«<¾k§´w¢¨s½¿´¥µKNRV%0K6
%A[ZLd'eT T¿¢.©s¢¥³@¨f¸k¤¹«4¢ U©G«´Àµs¾M§´s¢¨s½µKNUTh,'`UI %>7I %n"'@.-/3'n?>8'Y31h 1'%2- dYO`k23'
=pZo Li'2 Eb 1 Á ] ] ]DN T
"!#$
%#'&)(*+-, .
* 0/21
*-3
*4
567%8
*79:/
*
;<===
TA>'s%2'W'2$ sA>O%.k23'u?>8'b(':¥ ''2%=DA[pspu!D-02%sO$kAO?>8'S#1'[ \ \ \U Iu>O> 8%%k%
A Á(]U\\10IH2'k%KT
?> @ 0%.3BA1 /-R11j# %.3 -*09 /-DC3]/{/#{0!
IB,u'(-DQdS?[=eutugc_[Q`heu\^`=[`c*xPJUIq~\akªeuNQS gckuk}`~d\aghen\a`c[¦`c*gTk}Seª`c`=p~vwS?deukgh[|y¦`hg`ctuRqjQ_igQoNQ\idN\ikk}eughp]_^S
`=tOenNQSqWgc_^`=\akd`c[Q[QS>d£eu\^`=[ 8'So;{O G£¡
&('*)*+ +F±,)FE /HG¹± ! ±,) 73 (':A B 8ED;:;#F(GDV `ctuRTgc_&d`c[]dS{~e Ld/'(-Y %>8N %
-AB 8'VR;@fG>Iu>8'2'cV^X<Di6/ EfT_5:Q%>GA>S Q 8'V>G$l.f / O Q 8fGBÀViT
c/>8'Y%2'UdY10IH2'k%V % ?>8')'(-OS©oenS?[/eaLQIQAk('JIGLK8IKGNe"Iu>''%qO3 f<% Ak%\a[=euS[/eLQIQAk('2NMOK8IKG NUT
¨¥STtn\^enSBQP`ct d`c[]dS{~e S?r/j]gc_^\^ewmc¡&MONQSTk}Se`cªgc_^_1d`=[]dS?{~eukZeuN]ged?gh[¢pSTpQjQ\a_e\a[gd`c[/enS©/etA \ak yQS[Q`cenS?y¢pom
R Q&(gh[]yC\ikf{|ghtnen\igh_a_^m`cty~StuS?ypom7STPyQS¤][QS>ypS_a` ¡fMONQSj][]yQghRTS?[=egh_enNQS?`ctuSR `h;xPJUI \akfenN|geVUR QXWSTPZY`ctuRkg
3k']NQ\adNC\ikª¤][Q\^enS=]NQS?[]dS d`=RT{Q_^SenS=¡
&('*)*+ +F±,)\[S/*Q> + ! ± ² STP 3 '2]M/ t^ 0'DA R Q
]_STP^~`IGaK8']KGNX5IGaK8'^=G L.~ ?MOK8']Gk<nNMOK8I^eGQN T
bdc o± - / ±,) * !FQ + 3 '2A 0'`)$':QTEc>'j-8kA# 1'2' D%2'eUR QVWSTP0YS%b&jA('SFk' Iu>8%2'
%-'O AG&qO ')%qA3UIh%6)'2]'#,%2'2s `A '%gf(
JFh
P
i
ij 8'V
i
;@f
i
GBQP 8OQi8IS¥Q 8Nk
i
ijV
i
GGD;DB
i
ij
f i G
JFl
P
i
ij 8'V
i
;@f
i
GBQP 8?m
i
ijV
i
;>S Q 8O Q 8Q?
i
ij
f i GGG
4 5
1 2 3
0 6
x a z c y b
a \/ c b \/ c
a \/ b a \/ b \/ c
0
concept
object formula
extent intent {x,y,z}
{x,z} {y,z}
{z}
{x} {y}
{}
c /\ (a \/ b) b
a
a \/ (c /\ b) b \/ (c /\ a) a \/ b
0 0
1 2 3
4 5
6
concept
(a) (b)
C\abcj]tnS,51H1MONQSd`c[]dS{~e_igenen\idS `hd`=[=euS©oeA > 7g=Ogh[|y\^eukO_ighpS_a_a\^[Qb Fp|£¡
!nE /G 3 ij^1O'M[ TLdDNb'(-'%2'$%6A>'QXD&%%2's q?>8'=/'(-fFk'=ds$':@A#,iLA$k '
A _@.-/3'ÁN T\pq'-/%,','-/'%2'2(' 02#GM$O,0'2 \G0K_$AA@ A>'A ':('$. A>'3'kS/ A>'A
A$'2n A>'M^&>@TPc/>8'T>O^>'\'(-k%M'Y-F1' A A>'\ 21 A>')1'('MA>'#' `-= :'oSTPeT
= 0',10%2']' M?>8sA>''-/s3k'%Y/s%2 -8>O,(T?>8'.-7Ij'2D6%'2=3k' ):0H2'2%XUEKMLpW%XTY=TS/ 1'' O
%2'2qGr;{xT%Y/j?>8''1('26D$#M'(-60'@%2'O 8IS_8qr;>xOG G2B<O 8'cGBrqr;>o;>¥x T
M`RgEcSeuNQSqd`c[]dS{~ef_igenen\idS RT`ctuS tuS?gcy]ghpQ_aScQ\^ef\ik{`=kuk}\apQ_aS en`_ighpS_\ef\^enNC`=tnRjQ_igck+gc[]y`cp~vwS>d£euk?¡s; gh{Q{]\^[Qb)q
_ighpS_ik \^enN g`ctuRqjQ_igZfenN]S¦d`c[|dS{QeNQ`=knSTS©oenS?[=e \ikenN]SS©oenS?[=e`cf*¡T; gc{Q{Q\a[Qbsr _agcp|S?_ak\euNgc[`=p~vwS?del¦euNQS
d`c[]dS{~e+NQ`/k}S\a[/enS[/e\ikOenNQS \a[/enS?[=e+`cRlo~euN]ge+\ikO\^euk+y~S>kndtn\a{~eu\^`=[l¡
&('*)*+
+F±,)n/
!F~
!!
+) 1 3
u'RACB 8ED; : ;>F G)0'M$':¿lh_TD U Ef_m:
J q Q LqGn%>8N` :na R Q ; IGaK8q Q 8fGGB O Q 8fG
J
rQ Lr `%>8N`@D}a R QR;NMOK8r4QR8IlUGGkl<F,8IlUG)
MONQST\a[/enStuS?k}en\a[QbenN]\^[QbC\^enN¥enN]\ak _ighpS_a_a\^[QbC\ikZenN]ghe \eS?[]ghpQ_aS?kZeu`CtnSentu\^S?cSTgh_a_;yQgeg`ceuNQS¦d`=[=euS©oeH gc[`=p~vwS?del
kugeu\ak}¤]S?kZ<fgq`ctuRqjQ_igEf\a[kn`cRTSZd`c[/euS©oeNA \*gh[]yH`c[Q_amT\enNQSd`=[]dS?{~e_ighpS_a_^S>y¦\^enNl \ikpS_a` STP;enNQSd`=[]dS?{~e
_ighpS_a_^S>y\euNZf \^[euNQSd`=[]dS?{~e_aghe}en\idS `cA ¡
y ?/ !7~ !!+)*1 3 :'`?>8' Ak8%) W)''&q$Ak 4e
F28'lUG<nfZ~ r4Q 8IlUG S P
q¿QR8fG
! [S/G 3 ij^1O'i[ TLd0NT'(-'%2'$%Y?>8'D%2 ','(-s3',% iq^1O' [ TLdDNL%'',%_@.-/3'7NOs02O
Ak%`/'-/% 'n 1'(' RIQA?> ?>8' q 310'2AA[TA8%': IQA?> ?>8'Y':'2k%S A$'2k%KT6iuO3&%`dbA>'Q
h
Iu>''
X L
h
l<UN,'U-F1' MA>'`^>Os A>'D/'(-jA>j?>8'2#,310'2T=i`A8%'q'-/ %`310'2A3'
02#b)O3hSLTA'eT q"8' G7BQPN TSGij^1O' [ TLd0NaIj'Y>8]&''%k2(' M3:0'2%D( 0'U)O3%dDA>'s
h
=0OUA
%D$#T(D>8]&',&qA('DO 0'2Yd`3:0'%Y?>8U'Y/=AuA_A>'j,P$':QT
@ 0213¿5N1-/#63]9 =pCc= A1j# 0
[R&`/kwed`=[/enS©oek/\e\ik{`=kukn\^pQ_aSen`q`=tuyQStOk}`=R&S{Qtu`c{Stnen\aS?k?/gc_euNQ`cjQb=NenN]Sm¦ghtuSf[]`hed`cRT{]gctugcpQ_aS+pom5< ¡QC]`ctª\^[]k}eugc[]dS=
\^\a[:kn`cRTSd`c[/enS©oeS?cStum pQ\atuy r|\^S>kenNQS?[ ªS¥d?gh[ kug5m enN]ghe{]tn`={|S?t}ewm a}pQ\^ty[c¢\ikV(':A#<%0%O ' p/m euNQS
{Qtu`c{StnewmMadr]m:clgc_euNQ`cjQb=N¢ªSTN]g5cS[Q`he [QS>dS?kukughtu\^_amT$sF < f\a[ :f¡&¨ST\a[=eutn`~y~j|dSgR(':,+' %0%OS-
g=k+g&bcS[]Stgh_a\^>gen\a`c[`h\^RT{Q_a\idgeu\^`=[]kpSewªSS?[Cghe}eutn\apQj~euS?k?~enN]ghefghtuSj]k}S>y\^[ k}eugc[]yQghtyGJUI `ct=Eo[Q`_aS?y~b=Sg=dr/jQ\ik}\^en\a`c[
{Qtu`~dS>knknS?k7Wgc[/enSt+gc[]y¨ \^_a_aScZ5717179Qo[QS_^en\a[Qb|f5717:t=¡
&('*)*+
+F±,)S/
±,)
@
* !
+c
² *
+7±2)
3
u'6ACB 8ED;: ;>F Gn0'n,$':Q/ ^f,; g_5:^T U/'S%#&%b?>8rf
%d`=[/enS©oeuj]gh_a_^mknjQp]knjQRTS?yV02#g_A$':¿Ad Iu>@>\% (' >fZ< Q g2hn #,2O Q 8fGNXnO Q 8tgjG@QTA'eTq '2]'#
:0H2'2U?>8q%2%&6'%fB%2,%2k%&6'%gT
U]'2# dH< Q %)A3' M$':k,+' ,A.-/oT
J`=[=euS©oenj|gh_a\^?S?yk}jQp|k}jQRT{~eu\^`=[N|gckgd_a`=knSd`c[][QS?den\a`c[\euNeuNQSd`=[]dS?{~e+_ige}eu\adSc¡
bdc o± ?/ ±,) @ * !+c ² * +7±2) ±2) * !7~ + 3 u'A 0'V $':QT c/>8' -A#BD6
:'' G%'2 =O3&%JU:TWK< Q YD 1'2A]&' A ?>8'M@%_Ij#Y ?>8'n-'K6 1'2i< Q S% %2 ->@ (G?>8'M'-/
3k'pUR Q WSTPZY=TEc/>8'.,-8>@% O3&%s(n'(-k%6%Dq Q LXW)''&q$Ak 4NP `?>8'.,-8>@% '(-k%
(.)O3%Y%?MOK LXW'I&jAUNUT
I d`=[/enS©oe{Q_ig5m~kqeuNQStu`c_aS`cZgenNQS?`ctum S©oeuS[]y~\a[Qb¥enN]SCknjQp]knjQRT{~eu\^`=[ tuS_igeu\^`=[ gc[]y S?[]ghp]_^\a[Qb¥[QS S[/eugc\^_aRTS[/euk?¡
J`=[=euS©oenj|gh_a\^?S?y¥k}jQp|k}jQRT{~eu\^`=[¥d?gh[¥gh_ik}`p|SknSS?[¥g=kZgRTS?gc[]k`ct S©/eutug=d£eu\^[Qb Eo[Q`_aS?y~b=Stu`cR d`c[/enS©/ek¡&MONoj]klew`
Eo\a[]yQk`cUEo[Q`_aS?yQbcSdgc[¥pSS©oeutug=d£enS>yfHYEo[Q`_aS?y~b=Sghp`cj~eqd`c[/enS©/epom¥y~S?y~j|d£en\a`c[*gc[]yRE/[]`_^S>y~bcST`c[¥euNQSHy~`=RTgc\^[
tu`cR NQ\adNenN]Sd`c[/euS©oe\akS©oentgcd£euS?yHp/m\^[|y~j]d£eu\^`=[ Sc¡b]¡a~bcS?[QStgh_a\a\a[Qb`a}S=StumpQ\atuyMr]\aS?kdctu`cR! #"%$'&5<
Q(*)
£¡
!+n/G 3 o`%U?>8'S(':,+' %0%OS- %s%2 ->@bnA>'. :'SM'(-k%^LKc/>8''^ÁNOAu%
-&%%0F'=( @%'U?>8'UF10'AF' D'(-Z3k'HL%2''qij^1O' [ TL(0 N@Nb(S% #n$':k,+' S%0%OS-,AT$':AU#,jT
iuYA%'Ds&%D'(-K\%n% A3'2Y?>8V/'(--,G'3k H<Q/.103254* ,% &%@$Iu>O>%D^'1 # k'DA T
6' ['/'A#O,A 0'G%''2 ?>8A.] %0%OS-% A '_'2A' VA (':,+' "%0%OS-,T
_@)A/R A>'n3:0'2A3' M'-/j3k'`%>8UIh% ?>8j?>8'Y(':6: 1 &%n/'I ]& M'2(A^,'2k%n0'2Ij''2YO3&%%(
'eT T^<Q7.103254ce60'@%2'98 STP;:T
[¥enN]ST`c_a_^`\a[Qbk}S>d£eu\^`=[]kl`ctuRTgc_;d`=[=euS©oeuk\^_a_;pSj]k}S>yen``ctuRgh_a\^?SeuNQSHd`c[/enS?[=e `cOgc[\a[~`ctuRgeu\^`=[¥knm~kweuSRC
gc[]yenNQSqd`c[]dS{~e+_igenen\idS¦F`ct+S>r=j]\^gh_aS[/eu_^m=~enNQSd`c[/euS©oenj]gc_^\aS>yknjQp]knjQRT{~eu\^`=[|O\a_^_lpSj]knS?yeu`¦`ctub=gc[Q\^?SfeuNQ\a[Qb=k?¡¹e+\ik
euNQSd`=[=euS©oenj|gh_a\^?S?yS?r/jQ\a5gc_^S?[]dStuS_igeu\^`=[HeuN]gebc\acS>kk}`TRgh[om¦[|ghRTS?kªeu`euNQ\a[Qb=k?¡
3¿-R1 3 @V021436571
x`cbc\idgc_=_igh[]bcj]gcbcS?k*d`=[/eugh\a[]k*j]knj]gh_a_am \^[~¤|[Q\euS_amRgh[om`ctuRqj]_ag=k5NQ`/k}SOd`=R&{]_^S©o\^ewm \ikjQ[op|`=jQ[]y~S>y(hNQ\idNq\ik1gf{]tn`=pQ_^S?R
`=tgc_^b=`ctu\euNQRk(euN]ge{|S?t}`=tnR gk}S>ghtdNghRT`c[Qbf`ctuRqjQ_igckS=¡b|¡^5_aS?ghtu[Q\a[Qb]Wgh[/euStgc[]y j][QSeukn`5Uh = 85>¡CQ`=tS2K¦d\aS[]dm
gc[]ytnS>gcyQgcpQ\^_a\^ewm¦`h*tnS>k}jQ_^euk?QªStnS>kweutn\id£eeuNQSk}S>ghtdNkn{]gcdS`h*`ctuRqjQ_igckªeu`¦gq¤|[Q\euSk}j]p]k}Se Xh: NQ`/k}SS?_^S?R&S?[/euk+gctnS
d?gh_a_^S>yM'O'%¡YC]S?ghenjQtuS?kZy~\^«S?ttu`cR ghe}entu\apQj~enS>kZ`hk}eugc[]yQghtyC`=tnRgh_d`=[/enS©oekf\a[ euNQtnS?SOg5m~k2H 5>+S?ghenjQtuS?kZpS_a`c[Qb
eu` g¤Q©~S?y¥_^`=bc\idgc_1_agc[Qbcj]gcbcSTgh[]ykn`]N]g5cSTgk}S?Rgh[/en\idk?DUcS?ghenjQtuS?k gctnSgcj~en`=RTghen\idgc_^_am `cty~S?tnS>yg=dd`=tuyQ\^[Qben`CeuNQS
knjQp]knjQRT{~en\a`c[ < Qgc[]y*=ªgT[QS?_^mH\^[/entu`~y~j]dS?yHS?geujQtuSdgh[N]g5=SZg&[Q`=[~§DS?RT{~ewm¦S©oeuS[/e?¡
¹eO\ak{`=kuk}\apQ_aSfeu`qS©oeutug=d£eªg`ctuRgh_d`c[/euS©oe?o\^enN g=k;euNQSk}Seª`cge}eutn\apQj~euS?k?/tn`=RenNQSZ_^`=bc\idgc_|d`=[/enS©oeHªSZd?gh_a_|\^e
euNQS.'O'D$':7¡1MONQ\ikd`=[/enS©oe\ik[Q`he\a[/enS[|y~S?yen`TpSgcdenj]gc_^_ampQjQ\a_aytu`cR euNQS _a`cbc\idgc_(d`c[/euS©oe?~pQjQe+\e+\iky~S¤|[QS?y
eu`¦gh_a_^` tuS?g=k}`=[Q\a[Qb&gcp|`=j~eOenNQS _a`cb=\ad?gh_(d`=[/enS©oe+\^enNgTd`/ghtk}S?tb=tugc\^[HenN]gc[euNQSjQ_a_l_a`cbc\idh¡
&('*)*+ +F±,)n/HG¹ Q ±,) @ O3 u'7A B 8ED;UX:_WK<TY;>F G 0'\_F1=(': / RQ;X : 0' W&q$A'T%2'nd
'O'%@b?>8` # :'-'/ AT c/>8'S?ghenjQtuSHd`c[/enS©/e\dtA %TA>'S,s$':2AB 8Di;Q ;)Q G@ Iu>''
)QTBrq 8Il ;{oG7_TDQ uwF28'lUGM< ¿x T,'Y%2 1''&q'&y~S>kndtn\a{~eu\^`=[¦S?ghenjQtuS?kjD$#M10IH2'lG0#Q_8'lUGBPF28'lUG@
Iu>''UD# f _5: f BrqG_uUf< ]x T
MONQS d`c[/enS?[/eT`cRQ \ak[]`he¦kweutn\id£eu_^m y~SeuStuRT\^[QS>y pQj~ey~S?{|S?[]yQk`=[ enNQS d`c[/enS©/eA ¡ ¹eHk}N]`cjQ_iy d`c[/egh\a[ kn\^RT{Q_aS
`=tnRjQ_ag=kHknjQp]knjQRT\^[]b _a`cbc\idgc_y~S>kndtn\a{~eu\^`=[]k¢F\^[fA£+tnS>r=j]S[/en_am j|k}S>y `ctuRqjQ_igck\a[:r/jQS?tn\aS?k£+gc[]y RT`ctuS¢b=S[QS?tugc_^_amc
gc_^_ª`ctuRqj]_ag=keuN]geTj]knStkqS©o{S?deTen`k}S?SH\a[ gc[]k}ªStk?¡[ Fgcde?RQ gcdeuk&gckqenNQSC=`od?ghpQj]_agctnmenN]gheTg¥xl} j]knS?k&\^[ \ek
gc[]k}ªStk?¡MCQtu`cR enNQS¦yQS?kudtu\^{~eu\^`=[bc\acS[\a[ 1©QghRT{Q_aSM*Q`c[QSdgh[S©/eutug=d£e euNQS`c_a_a`\^[QbS>genj]tnS>k¦FgcR&`=[Qb=k}e`heuNQStkH
k¡4¢@£¤M¦r¸k¤k«4¢4 U©G«.´»µ©4¤k¡! 6µ=M§4¨ M¦}©G« ¬s²®¯¯{°®®@®|¡
C]S?geujQtuS&d`c[]dS{~ekZd?gh[¥p|Sy~S?tn\acS>ytu`cR gHS?ghenjQtuS&d`c[/enS©oe g=k`ct`cty~\a[]ghtumC_^`=bc\idgh_d`=[/enS©oek¡&xlSRTRg *HtuS_igeuS?k
euNQSqWgh_a`c\ikd`=[Q[QS?den\a`c[]kO`c_a`cb=\ad?gh_(gh[]yS>genj]tnS d`=[/enS©oek¡
y
[S/
!
±21,+
= !
G¹
Q
Pz
!
±,+
T
±,)*)
h
+F±,)
73
'2RV^X D #"X$R
J S Q
$8'V>GB
S Q 8'V>G
J O Q _8%"VGB O Q 8?&"VGeT
MONQS?`ctuSR *¦k}N]`+kªenNQSS©~\ak}enS?[]dS `c;gRgh{Q{Q\a[QbeuN]geZgh{Q{Qtu`5©~\^RghenS?kg¦_^`=bc\idgh_ld`c[]dS{~e\^[ gTS>geujQtnSd`c[|dS{Qefgh[]y
euNQS[y~S¤][QS S?r/jQ\agh_aS[]dS d_igckuk}S>kªgcRT`c[QbT_a`cbc\idgc_(d`c[|dS{Qeuk?¡
bdc o± [S/ 4* ± + Q +F±,) ±LG ±,) *O3 u' 8EVR;fGc_ R Q 0' 31q/'(-TVc/>'='O' '(-j['/'D6
' ) V LA('$(WS Q "8'V>GN"/ G?>8' 'O'M/'-/=['2'2(' Y f Ld'1('2(tO Q _8' fG N_'MA 12`A>'
%2 '6'kO'D/'(-k8O Q "8' fG;( fG@q?>8'n%,A3'%s'(-jA R Q hIu>8&%2','1('2Q%n3:'2`A>"D'W2f(tViT
) * pC,+O%o021436571
¹e\ik1`cenS[Tj]knSj]_Qen` tuS?g=k}`=[q`=[Tg)%0K6 (':*pomqtuS?k}entu\aden\a[QbZenNQS+knSe;`c`=p~vwS?deuk;gc[]yenNQS+knSe;`c|S>genj]tnS>k¡hCQ`=t1\^[]k}eugc[]dS=
euNQS [QSS>y`ctn]'Ih% N]g=kOp|S?S[CtnS>d`=bc[Q\aS>y¦\a[Cy]geugcp]gcknS?kkl+_a_^Rgh[Z57:t1t=FknSSgc_akn` fS¤][Q\^en\a`c[ 5o£¡
&('*)*+ +F±,)-n/ ¯ ±,) @ 73/. A]' y~`cRgc\^[0 XDi '%2kA@ ?>8'_%2' dR10IH2'2k%M o\aS21 X3R
'%k2A[ ?>8'B%'2d\'O'%@ Ij' :'I&j' A>' knjQp~§d`c[/euS©oe dBV'O'B$':A 02# A>'G M(':
AM84Z;1EGB 84Z;1$;5%Q6V8%781 G GeT
xSRTRgTtuS_igeuS?kªenN]SqWgh_a`c\ikªd`c[Q[]S?d£eu\^`=[]kO`h*S?ghenjQtuS d`=[=euS©oeukgc[]yk}jQpQ§¹d`c[/enS©/ek¡
y En/ G¹ ~ ¯ ±,) @ z !±,+T ±2)*) c +F±,) 3 u'V^X9m6 :";X;1
J S Q=<?>A@B&C 8'V>G2B SUQ_8'V>G&61
J O Q=<?>A@B&C 8'"VGB<O Q $8'"VG=6T
I y~`cRgc\^[¢d?gh[p|STk}{S?d\¤|S?y pomCeuNQSS©oenS[|k}\a`c[TOQi8IUGf`hg¦`ctuRqjQ_igQ\D¡S=¡^enN]S&gc[]k}ªStkOQi8IUG+en`CgHr/jQStumo¡MONQS
kn{|S>d\^¤|dghen\a`c[`hgo\^S? dgc[pSk}{S?d\¤|S?yqg=kenNQSknSe1`hQS>geujQtnS>kk}jQp|k}jQRTS>yqpomgZr=j]Stum |h\D¡Sc¡aD hBrqG_usb< ¥x/¡
+¡b]¡a\^[euNQS_a`cb=\ad {]tnS>k}S?[=euS?y\a[ 1©QghRT{Q_aSD*Q|enN]S `ctuRqjQ_igFE$ k¡4¢M£¥¤M¦f¸k¤¹«4¢ U©G«´»µµb ¢.©s¢¥³M¨r¸¹¤k«4¢ U©«.´Àµk¸k¤¹«.¸k¨HG4¢6µ
§¨ k¦±©«v¬s@®®¯¯{°@®®®JI ª`cjQ_iyknS_aS?deOgc_^_S>geujQtnS>kª`h*ghe}eutn\apQj~euS?k k¡¢@£¥¤M¦M¢.©s¢¥³M¨&gc[]y§¨ M¦=tuS?k}entu\adenS>yen`Tm=S?ghtk\^[
euNQS _ag=kwefdS[/enj]tnm=Qgh[]yHen\^en_aS?kOeuN]gefd`c[/eugc\^[enN]S `=tuya}d`c[]dS{~e c¡
³)O% "¥qªS )
> »- #!-1j#>0 ! =,3 #{0 !
[~`=tnRghen\a`c[knm~kweuSRkO`h«StORTS?gc[]kª`ctO`=tnb/gh[Q\a\a[Qby]geug]~gh[]yH`ctO[]g5o\ab=geu\^[]b&gc[]yHr/jQS?tnmo\a[Qb]¡1MONQ`=jQbcN[]g5o\^b/gen\a`c[gh[]y
r/jQS?tnmo\a[Qb&gctnS[Q`he+gc_^Og5m~ky~\ikweu\^[]bcjQ\ik}N]S?yp|S>dghj|k}SZp|`cenN\^[o=`c_acSr/jQS?tn\aS?kOgc[]yHgc[]k}ªStk?=ªSpS_a\aScSZeuNQSm¦d`ctutnS>k}{`c[]yen`
=Stum¢y~\^«S?tnS?[=e{|ghtgcy~\abcRk`hON/j]RTgc[~§¹RTg=dNQ\a[QSd`cRTRjQ[Q\idgeu\^`=[l¡T[¥Fgcd£e>leuNQS¦y~\^«S?tnS?[]dSdgc[p|S¦d_agctn\^¤]S?yj]kn\^[]beuNQS
\a[/enS[|k}\a`c[LS©oenS?[]kn\^`=[y~j]gc_^\^ewmc¡
g5/\ab=ghen\a`c[\aRT{Q_^\aS?kªg[]`hen\a`c[H`h{Q_igcdScogh[]y¦`hgtuS_igeu\^`=[¦pSewªSS[H{Q_ag=dS>kFSc¡b]¡ac¤]_aSk}m~k}enSR y~\atuS?d£eu`ctu\^S>k/gh[]y¦_^\a[8E~k
`=tk}jQpy~\atnS>d£eu`ctum tnS?_aghen\a`c[]k£¡MONQtu`cj]bcN¢[|g5/\ab=ghen\a`c[llgj]knSt Rg5m¢g=k E `ctenN]S¦d`c[/euS[/e `hg{]_ag=dSc`ctgckE`=t tnS?_aghenS?y
{Q_igcdS?k?¡ MONQS&gcpQ\a_^\^ewmCen`CgckE`ctZtnS?_aghenS?y {Q_ag=dS>kf\aRT{Q_^\aS?kZeuN]ge gh[|k}ªStk+\a[ euNQS[|g5/\ab=ghen\a`c[~§¹p]g=k}S>y{|ghtgcy~\abcR pS_a`c[QbHen`
euNQS kngcR&S_agc[Qbcj|ghbcSZgckªr/jQStu\^S>k¡[HenStuRkª`hleuNQS\a[/enS?[]k}\a`c[/L5S©oeuS[]kn\^`=[Hy~j]gc_^\^ewmc~g&r/jQStum\akOgc[_A('%]Qgc[]yHgc[]knS?tuk
gctnST'1('28%%`=tOenNQSd`c[/enS?[=e{]gct}e>Qgh[]yRA$'2%`=tOenNQS tuS_igeuS?y¦{]_ag=dS?k?¡
[ =Stumd?gcknj]gh_enS?tnRk?ªSd`c[]kn\iy~St[]g5o\^b/gen\a`c[C\^enN{|`/knkn\^p]_^mTa}[Q`¦tu`=gcy~§DRgh{Oc|\7¡Sc¡a|[]`RD-`=Stu/\aS `h1euNQS
d`cjQ[/entumc¡¥zS_igeuS?y {]_ag=dS?k`ctuR k}\aRT{Q_^m¥euNQS_igh[|yQknd?gh{Stu`cR g b=\^=S[ {Q_igcdSHgck&k}N]`[ p/m g awo\aS{`c\a[=e\^[]yQ\ad?gen`=tdc£¡
Nf`S?cSt>o`cjQt{]tn`={|`/kngc_\ikd`=RT{]geu\^pQ_aS\euNgh[omTEo\^[|y`c=`-Eo[Q`_aS?yQbcStn`=R enNQS j|k}S?t?¡
¨ \^enN r/jQS?tnmo\a[Qb]Qgc[]k}ªStkOghtuSS©oenS?[]k}\a`c[|kO`c[Q_amc¡jI kn\aRqjQ_igeu\^`=[`c*[]g5o\ab=ghen\a`c[H\ik+k}en\a_^_{|`/knkn\^p]_^S=QpQj~e+`=tudS?kªeuNQS j]knSt
eu`q\a[~StN]ged`cjQ_iyTpSg pSenenStOr/jQStumtu`cR enN]SfjQ[]kugeu\ak}Fgcden`=tnm&gh[]knS?t1en`g {QtuSo\^`=j]k;r/jQS?tnm/9/\7¡Sc¡ac\a[~Stªgh[¦\a[/enS?[]k}\a`c[
tu`cRgh[¦S©oenS[|k}\a`c[l¡MONQ\ik\ikyQ\^K¦dj]_eªp|S>dghj|k}SeuNQStuSf\ik;[]`qk}\aRT{Q_aSftuS_igen\a`c[TpSewªSS?[Hg ghtu\aghen\a`c[T\a[enNQSZr/jQStumc/gh[]yTeuNQS
d`ctutnS>k}{`c[]yQ\^[Qbq5gctn\igeu\^`=[¦\a[¦enN]SZgc[]k}ªSt>¡MONQSfS©o{Stu\aS[]dSZknNQ`+k1euN]geªFgcd\^[]b&gr=j]Stum&N]`=knSfS©oeuS[]kn\^`=[¦\ikeu`o`gck}e?~g
j]knStfRTg5mHentum¦eu`¦tnS¤][QS \^e?pQj~e+euNQStuS?knjQ_^en\a[QbS©oenS?[]kn\^`=[\a_a_`heuS[CpSS\^enNQS?tgc_^RT`=k}efgck+5g=kwefg=kOenN]S `ctuRTSt+`=tRqj]dN
eu`/`knRgh_a_7¡[enN]S¤|tuk}ed?gcknSceuNQS&r/jQS?tnm_igcdE~kZ`hq-'2% \D¡S=¡^([ojQRp|S?t`htuS_aSgc[=eZ\euSRk\a[¢euNQSgh[]knS?tZyQ\^o\iy~S?y
pomen`hegh_[/j]RqpStf`c1\euSRkf\a[CenN]Sgh[|k}ªSt££QN]StuS?gck+\^[CeuNQSknS?d`c[]yCdg=k}S=QeuNQSr/jQS?tnm"'A\D¡Sc¡a|[ojQRp|S?tf`h1tuS_aSgh[/e
\^enS?RTk+\^[enN]Sgh[]knS?ty~\^o\iy~S?ypom¦[ojQRp|S?t`htnS?_^S?5gc[/eO\^enS?RkO\^[enN]Sk}m~k}enSR¦ª\ikªen`o`_a` ¡
WZ`~y~\a[Seqgh_D¡ 5717:*=Zgh[|yx\^[]yQ\^b 5717/cN]g5=S&knNQ`[enN]ghe)CQ`=tnRgh_6J`=[]dS?{~eYI+[]gc_^m~kn\ak\ak gCb=`/`~y¥dgc[]y~\iyQgeuST`ct
tuS?d`c[]d\^_a\aghen\a[Qb[]g5o\ab=ghen\a`c[gh[]yHr=j]Stum/\a[Qb|¡¨¥Sf`=_^_a` enNQ\ikª`c{Q\a[Q\a`c[l/pQj~eOªS+p|S?_^\aS=S+euN]gedgctnS+Rj]k}epS+eug1EcS?[en`RTg1EcS
`=tnRgh_*d`=[=euS©oeukZgckd_a`=knS en`HenNQS&y~S?kudtu\a{~en\a`c[_igh[Qb=j]ghb=S?k`c1enNQSS[]y~§Dj]knStk?|gh[|ySN]g5cS {]tn`={|`/k}S>yxl`cb=\ad?gh_PJ`=[]dS?{~e
If[]gh_am~k}\ik FxhJUIªNQS?tnSZ`ctuRgh_(y~S>kndtn\a{~en\a`c[|kªgctnS_a`cb=\ad?gh_|`ctuRqjQ_igckª\a[]kweuS?g=yH`c*pS\a[Qbk}SeukO`c*genentu\^p]j~enS>k 7oS>d£en\a`c[ UQ¡355£¡
jQt b=`=gc_*\a[enNQ\ikknS?d£eu\^`=[\ikeu`CknNQ`N]` g`ctuR `hO[]g5o\ab=geu\^`=[gc[]yr/jQS?tnmo\a[QbCdgh[¥pS¦y~S¤][]S?y(*k}`enN|geqgj]knSt
NQ`ME/[]`+kO[QS\^enNQS?t+euNQSqd`=[/enS[/e+`c1gx`cb=\ad?gh_l[~`=tnRghen\a`c[ om~kweuSRC][]`cteuNQS_a`cbc\id`h\^eukfyQS?kudtu\^{~eu\^`=[]k?]dgc[[]g5o\^b/genS
\a[H\^eOgc[]y¦y~\ikud`cS?t1enN]S{]gct}ek`c(enNQSd`=[/enS[/ekgc[]yTenN]S{]gct}ek;`clenNQSZ_a`cbc\idOeuN]geghtuS+tuS_aSgh[/eeu`qNQ\ikªr=j]S?k}e?¡+`cenSenN]gheOg
RT`ctuSZS©~{|S?t}eªj]knStORg5mEo[Q` pSenenS?t+gh[]yRg5m[]g5o\ab=ghenS+RT`ctuSyQ\^tuS?den_amTen`&NQ\akªb=`=gh_D/pQj~e+k}\a[]dSZgc_^RT`=k}eS?cS?tnmop`oyQm&N|gck
NQ\ik+knNQ`ctneud`cRT\a[Qb=k?/enNQS [Q`c§Eo[Q`_aS?yQbcSg=knknjQRT{~eu\^`=[\ikOenN]SknghS?k}eO`=[QSZen`y~`|¡
> 9"!A# %.-*/@0@ -R1j#0 *=M143
[enNQ\ikknS?d£eu\^`=[l~ªS\a_^_(\a[]kn\ak}e`c[[]g5o\^b/geu\^`=[en`o`c_ik?ogc[]y\^_a_ly~S_ig5mTenN]SZRgc[]ghb=SRTS[/eO`hg&_a`cbc\idgc_d`c[/enS©oeFSc¡b]¡aQdtuS§
ghen\a[Qb]Qj]{yQghen\a[QbT`cp~vwS>d£ekuªjQ[/eu\^_~S?d£eu\^`=[|¡
I x}H[]SS?y]kgTj]k}S?t\^[/euStnFgcdS=¡¨S \a_^_l`ctuRTgc_^\aS gTknNQS_a_§¹p]g=k}S>yH\a[/enStnFgcdScoeuNQ`cjQb=NenNQ\ik\ikO[Q`heeuNQS RT`=k}eORT`~y~S?tn[
euNQ\^[]beu`yQ`]¡qMONQ\ikZ\akZpS?d?ghj]knSªS&p|S?_^\aS=SqeuN]ge k}N]S_a_1\^[/enS?t}Fg=dS>kF_^\FEcS&\^[ l f`ct`;¢/§ QZgctnSqFghRT\^_a\ightZen`Rgh[om
`cj]k?gc[]ypS?d?ghj]knSeuNQ\akgcp]kweutug=d£eu\^`=[_^S?cS_*S©~{`=knS?k{Qtu`c{Stu_^menNQSTy~\igh_a`cb=jQSq`cr=j]Stu\^S>kgc[]y gh[|k}ªStk¡ I N]\^b=NQStn§D_aS=S_
\a[/enStnFgcdSC_^\FEcS g¥bctgh{]NQ\ad?gh_O`c[]Sª`cj]_ay NQ\iy~S\e>ONQStuS?g=k_a`ªStn§D_aS=S_ª\^[/enS?t}Fg=dS>k_^\FEcS g¤]_aS k}m~k}enS?Rªª`cjQ_iy S©~{|`/k}S
\atntuS_aSgc[=e+y~Seugc\^_ik¡QNf`S?cSt>o[Q`heuNQ\a[QbT{QtnS?cS?[=ekO`c[QSZeu`&b=\^=S gb=tugc{QNQ\idgc_\a[/enS?t}Fg=dSZen`gTxl}¡
MONQS¦knNQS?_^_ªd`cRTRgh[|yQk ghtuS&enNQ`/k}S`cªeuNQSTl f knNQS_a_7*tuS\a[=euStu{QtuSenS>y¢\a[enN]SHxl}¢tghRTSª`ctE¡T; gh\a[ dN]gh[Qb=S?k gctnS
euNQStnS?{Q_ag=dS?R&S?[/eª`cZ-?>[%p/mT`=tnRjQ_igckª`h*: tuSS?tntu\a[Qbeu`&d`c[]dS{~ekO/\igRTgc{Q{Q\a[QbVq¿QQgc[]yHenNQSj]knS`c*d`c[/enS©/euj]gh_a\aS?y
knjQp]knjQRT{~en\a`c[n<Q&¡\CQ`=tenN]S¦tnS>kwe>*d`cRTRgh[]y]k N]g5cSTS>knknS[/en\igh_a_am enN]SHkngcRTSS«S?d£ek¡MONQSd`ctutuS?kn{|`=[]y~S[|dSTp|SewS?S[ g
l + ¤]_aS k}m~k}enS?R gh[|yg&_a`cbc\idgc_(\^[Q`ctuRTghen\a`c[k}m~k}enSR \akknjQRTRghtu\^?S?y\^[euNQS`c_a_^`\a[QbeugcpQ_^S=¡
l + knNQS?_^_ x}knNQS?_^_
¤|_^S `=p~vwS?de
{|genN _a`cb=\ad?gh_`ctuRqjQ_ig
gcp]kn`c_aj~enS[]gcR&S `c*g¤]_aS `=p~vwS?deyQS?kudtu\^{~eu\^`=[
yQ\^tuS?den`ctum `=tnRjQ_ag@Ld`c[]dS{~e
tu`o`he `=tnRjQ_agCnLhd`c[|dS{Qe C P
ª`ctEo\^[]b&y~\atuS?d£eu`ctum ª`ctEo\^[QbTr/jQStumLd`c[]dS{~e