=Paper=
{{Paper
|id=Vol-48/paper-7
|storemode=property
|title=The Ontology of Commonsense Knowledge
|pdfUrl=https://ceur-ws.org/Vol-48/Saba_KI2001.pdf
|volume=Vol-48
}}
==The Ontology of Commonsense Knowledge==
<pdf width="1500px">https://ceur-ws.org/Vol-48/Saba_KI2001.pdf</pdf>
<pre>
    qY‚S!tBjBkSBPS]B88BtR‚tR‚S€tBbj‚I‚S

                                   Gsj$IS7S7sAsS
                     €tBbj‚I‚SstISNstZs‚Set$t‚‚„$tSp„BZ}S
 7{YBBjSBPS]B8}Z‚„S7{$‚t{‚S=t$%‚„R$kSBPSG$tIRB„SG$tIRB„S!WSW     Tn_;S]stsIsS
                               RuBuq|R!Yd%vIRCƒ!|uS


      VAR„s{SyS$RSAkStBbSb$I‚jkSs{{‚}‚ISYsSsStZ8A‚„SBPSsR,RS$tS
      tsZ„sjSjstZs‚SZtI‚„RstI$tSwWN=DS„‚JZ$„‚SY‚SRB„s‚SBPSstIS
      „‚sRBt$tS b$YS sS %sRS s8BZtS BPS As{,„BZtIS w{B88BtR‚tR‚DS
      ,tBbj‚I‚S GY$j‚S R‚%‚„sjS ‚PPB„RS Ys%‚S A‚‚tS 8sI‚S BS AZ$jIS RZ{YS
      BtBjB$‚RSsS{BtR‚tRZRSBtSsSR{$‚t$P${S8‚YBIBjBkSPB„SBtBjB${sjS
      I‚R$tS$RSk‚SBS‚8‚„‚SytSY$RS}s}‚„Sb‚SRZ‚RSstSs}}„Bs{YSBS
      AZ$jI$tS sS {B88BtR‚tR‚S BtBjBkS PB„S jstZs‚S ZtI‚„RstI$tS
      ZR$tS jstZs‚S $R‚jPS sRS sS I‚R$tS Z$I‚S qY‚S $I‚sS $RS „BB‚IS $tS
      3„‚‚:RS {Bt{‚}$BtS BPS {B8}BR$$BtsjS R‚8st${RS stIS $RS „‚js‚IS BS
      Y‚S $I‚sS BPS k}‚S $tP‚„‚t{‚RS $tS R„BtjkTk}‚IS }Bjk8B„}Y${S
      }„B„s88$tS jstZs‚RS qY‚S 8‚YBIS }„B}BR‚IS R‚‚8RS BS w$DS
      „‚RBj%‚S Y‚S }„BAj‚8S BPS 8Zj$}j‚S $tY‚„$st{‚S w$$DS RZ‚RS stS
      ‚-}jsts$BtS PB„S }BjkR‚8kS stIS 8‚s}YB„S stIS w$$$DS }„B%$I‚S sSR‚}S
      Bbs„IRS‚RsAj$RY$tSsSRkR‚8s${Ss}}„Bs{YSBSBtBjB${sjSI‚R$tS



dSyt„BIZ{$BtS
i‚{‚tSbB„,S$tStsZ„sjSjstZs‚SZtI‚„RstI$tSwWN=DSR‚‚8RSBSA‚SRjBbjkS
‚8A„s{$tSbYsSb‚Sj$,‚SBS{sjjSY‚SZtI‚„RstI$tSsRS„‚sRBt$t:S}s„sI$8S
sRS$S$RSJZ$‚S{j‚s„SAkStBbSYsSZtI‚„RstI$tStsZ„sjSjstZs‚S$RSPB„SY‚S
8BRS }s„S sS {B88BtR‚tR‚S „‚sRBt$tS }„B{‚RRS sS Y‚S }„s8s${S j‚%‚jS PB„S
‚-s8}j‚S $tS RZ{YS sR,RS sRS „‚P‚„‚t{‚S „‚RBjZ$BtS }jstS „‚{Bt$$BtS j‚-${sjS
I$Rs8A$Zs$BtS }„‚}BR$$BtsjS }Y„sR‚S ss{Y8‚tRS ‚8}B„sjS {BY‚„‚t{‚S
stIS Y‚S „‚RBjZ$BtS BPS JZst$P$‚„S R{B}‚S s8A$Z$$‚RS 3B„S $tRst{‚S {BtR$I‚„S
Y‚S„‚RBjZ$BtSBPS<‚:S$tSY‚SPBjjBb$tUS
   S
FBYtSRYBSsS}Bj${‚8stS<‚S$88‚I$s‚jkS                                          S
sDSPj‚ISsbskS                                                                  wdDS
ADSP‚jjSIBbtS
   S
yS $RS JZ$‚S I$PP${ZjS BS $8s$t‚S YBbS {Y$jI„‚tS ‚PPB„j‚RRjkS „‚RBj%‚S RZ{YS
„‚P‚„‚t{‚RS $PS tBS AkS „‚{BZ„R‚S BS Y‚S {B88BtR‚tR‚S Ps{RS YsS k}${sjjkS
bY‚tS RYBw-kDS YBjIRS A‚b‚‚tS RB8‚S -S stIS RB8‚S kS -S $RS Y‚S 8B„‚S j$,‚jkS
RZA`‚{S BS Pj‚‚S stIS kS $RS Y‚S 8B„‚S j$,‚jkS RZA`‚{S BS PsjjS IBbtS !Y‚„S
‚-s8}j‚RSBPS{B88BtR‚tR‚S„‚sRBt$tS$tSjstZs‚SZtI‚„RstI$tS$t%Bj%‚SY‚S
„‚RBjZ$BtSBPSJZst$P$‚„SR{B}‚Ss8A$Z$$‚RS]BtR$I‚„SY‚SPBjjBb$tUS
   S
   S
‚%‚„k                                                                     S
                                                                     S
 P‚b S„sIZs‚SRZI‚t wRDSs Syq SRZA8$‚I Ss S}s}‚„ SBSV]N: S w1DS
 bB 
      
S
G‚S s„Z‚S YsS Y‚S }jsZR$A$j$kS BPS b$I‚SR{B}‚S sS w$8}jk$tSsSR$tj‚S}s}‚„DS
$t{„‚sR‚RS sRS Y‚S tZ8A‚„S BPS RZI‚tRS $t%Bj%‚IS $tS Y‚S „‚js$BtS I‚{„‚sR‚RS
Ns{,$tS sS Rkts{${S B„S sS R‚8st${S ‚-}jsts$BtS Y$RS $tP‚„‚t{‚S 8ZRS A‚S sS
PZt{$BtS BPS BZ„S {B88BtR‚tR‚S ,tBbj‚I‚S BPS YBbS Y‚S RZA8$:S „‚js$BtS
A‚b‚‚tS RZI‚tRS stIS }s}‚„R:S $RS k}${sjjkS 8st$P‚R‚IS $tS Y‚S „‚sjS bB„jIS
7}‚{$P${sjjkS Y$RS $tP‚„‚t{‚S $RS AsR‚IS BtS BZ„S {B88BtR‚tR‚S A‚j$‚PS YsS Y‚S
RZA8$S „‚js$BtS A‚b‚‚tS sS RZI‚tS stIS sS }s}‚„S $RS k}${sjjkS >d8HTBTdS
bY‚„‚S 8S $RS RB8‚S R8sjjS tZ8A‚„S B„‚B%‚„S I$PP‚„‚tS $tI$%$IZsjRS R‚‚8S BS
Ys%‚SsSRj$YjkSI$PP‚„‚tS%sjZ‚SPB„S8SbY${YS$RS{BtR$R‚tSb$YSY‚SP$tI$tRS
BPS €Z„98stS stIS s{*BtsjIS wdnDS YsS I$PP‚„‚tS $tI$%$IZsjRS R‚‚8S BS
Ys%‚SI$PP‚„‚tSR{B}‚S}„‚P‚„‚t{‚RS$tSY‚SRs8‚S‚-ZsjS{Bt‚-dS
     qY‚S ZtI‚„RstI$tS sRS „‚sRBt$t:S }s„sI$8S $RS {‚„s$tjkS tBS ‚t$„‚jkS
t‚bS $tS WN=S „‚R‚s„{YS G$Y$tS Y‚S VyS {B88Zt$kS Y$RS }s„sI$8S bsRS
$8}j${$jkS ‚8A„s{‚IS AkS sS tZ8A‚„S BPS sZYB„RS w‚S R‚‚S ]Ys„t$s,S dMES
<$„RS dMES G$j,RS dxS 7{Yst,S dM1DS =tPB„Zts‚jkS YBb‚%‚„S Y‚R‚S
s}}„Bs{Y‚RS b‚„‚S js„‚jkS AsR‚IS BtS sIS YB{S sjB„$Y8RS AZ$jS BtS B}S BPS
$tPB„8sjS ,tBbj‚I‚S „‚}„‚R‚ts$BtRS *Z‚S BS Y‚S js{,S BPS PB„8sj$kS Y‚R‚S
}„B{‚IZ„‚RS b‚„‚S YB}‚j‚RRjkS ZtR{sjsAj‚S stIS R{sjsA$j$kS bsRS PB„S Y‚S 8BRS
}s„Ss‚8}‚ISAkS}ZRY$tSY‚S}„BAj‚8SP„B8SY‚S}„B{‚IZ„‚RSBSY‚SIssS
bY${YS {BtR‚JZ‚tjkS j‚ISBSY‚S RBT{sjj‚IS ,tBbj‚I‚SABj‚t‚{,SqY‚S js{,S BPS
}„B„‚RRS $tS RBj%$tS Y‚S ,tBbj‚I‚S ABj‚t‚{,S }„BAj‚8S ‚t‚„sjjkS j‚IS VyS
„‚R‚s„{Y‚„RSBS‚$Y‚„SsAstIBtS$tP‚„‚t$sjSstIS,tBbj‚I‚TAsR‚ISs}}„Bs{Y‚RS
$tS Ps%B„S BPS 8B„‚S JZst$s$%‚S s}}„Bs{Y‚RS w‚S ]Ys„t$s,S dnDS B„S BS
PB{ZRS sj8BRS ‚-{jZR$%‚jkS BtS Y‚S I‚%‚jB}8‚tS BPS js„‚S {B88BtR‚tR‚S
,tBbj‚I‚S AsR‚RS w‚S N‚t‚S stIS pYZsS d(DS G$Y$tS j$tZ$R${RS stIS
PB„8sjS R‚8st${RS Bt‚S Y‚S BY‚„S YstIS j$j‚S B„S tBS s‚t$BtS bsRS }s$IS BS
Y‚S $RRZ‚S BPS {B88BtR‚tR‚S „‚sRBt$tS sS Y‚S }„s8s${S j‚%‚jS ytI‚‚IS Y‚S
}„‚%s$j$tS b$RIB8S wbY${YS 8$YS A‚S}s„jkSIZ‚S BS js{,SBPS }„B„‚RRS $tS VyT
AsR‚ISWN=DSbsRSYsSsStZ8A‚„SBPSWN=SsR,RS„‚JZ$„‚SY‚SRB„s‚SBPSstIS
„‚sRBt$tS b$YS sS %sRS s8BZtS BPS As{,„BZtIS ,tBbj‚I‚S w%stS *‚‚8‚„S
dEDS stS B}$t$BtS YsS j‚IS RB8‚S w‚S i‚$tYs„S dDS BS {Bt{jZI‚S YsS
}„s8s${Ss}}„Bs{Y‚RSs„‚SY$YjkSZtI‚{$IsAj‚:S
     ytSBZ„S%$‚bSABYS„‚tIRSb‚„‚S}s„jkS8$RZ$I‚ISytS}s„${Zjs„Sb‚SYBjIS
Y‚S %$‚bS YsS bY$j‚S jstZs‚S ZtI‚„RstI$tS $RS PB„S Y‚S 8BRS }s„S sS
{B88BtR‚tR‚S „‚sRBt$tS }„B{‚RRS sS Y‚S }„s8s${S j‚%‚jS Y$RS „‚sRBt$tS
}„B{‚RRS stIS Y‚S ZtI‚„jk$tS ,tBbj‚I‚S R„Z{Z„‚RS YsS $S Z$j$9‚RS8ZRS A‚S
PB„8sj$9‚IS $PS b‚S ‚%‚„S YB}‚S BS AZ$jIS R{sjsAj‚S RkR‚8RS ytS Y$RS j$YS b‚S
A‚j$‚%‚S Y‚S bB„,S BtS $t‚„s$tS jB${sjS stIS {B88BtR‚tR‚S „‚sRBt$tS $tS
jstZs‚S ZtI‚„RstI$tS w‚S Vjj‚tS dMS _‚„‚$„sS mS _Bjjs{,S ddS
sI„B9tkS mS F‚tR‚tS ddS <BAARS dMxS <BAARS ‚S sjS dnS stIS 8B„‚S
„‚{‚tjkS VRY‚„S mS NsR{s„$I‚RS dMS stIS 7sAsS mS ]B„„$%‚ZsS dDS $RS BPS
}s„s8BZtS$8}B„st{‚S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSS
dS VtS $tP‚„‚t{$tS R„s‚kS YsS 8BI‚jRS $tI$%$IZsjS }„‚P‚„‚t{‚RS $tS Y‚S „‚RBjZ$BtS BPS R{B}‚S

  s8A$Z$$‚RSsSY‚S}„s8s${Sj‚%‚jSYsRSA‚‚tSRZ‚R‚IS$tSw7sAsSstIS]B„„$%‚sZS1((dDS
    Z{YS BPS Y$RS bB„,S $RS I$„‚{‚IS Bbs„IRS PB„8Zjs$tS {B88BtR‚tR‚S
$tP‚„‚t{$tSR„s‚$‚RSBS„‚RBj%‚SsStZ8A‚„SBPSs8A$Z$$‚RSsSY‚S}„s8s${S
j‚%‚jSVjYBZYS$SYsRSA‚‚tSRYBbtSwR‚‚S7sAsSmS]B„„$%‚sZS1((dDSYsSY‚R‚S
$tP‚„‚t{‚RSIBStBSsjbskRS„‚JZ$„‚SY‚SRB„s‚SBPSstIS„‚sRBt$tSb$YSsS%sRS
s8BZtS BPS As{,„BZtIS ,tBbj‚I‚S $S $RS {j‚s„S YsS sS tZ8A‚„S BPS sR,RS IBS
„‚JZ$„‚S RZ{YS sS ,tBbj‚I‚AsR‚S ytI‚‚IS RZARst$sjS ‚PPB„S YsRS A‚‚tS 8sI‚S
Bbs„IRS AZ$jI$tS BtBjB$‚RS BPS {B88BtR‚tR‚S ,tBbj‚I‚S w‚S N‚tsS mS
pYZsS d(S sY‚RYS mS W$„‚tAZ„S dxS 7BbsS dxDS stIS sS tZ8A‚„S BPS
}„B8$R$tS „‚tIRS YsS sI%B{s‚S BtBjB${sjS I‚R$tS AsR‚IS BtS RBZtIS
j$tZ$R${S stIS jB${sjS PBZtIs$BtRS Ys%‚S Rs„‚IS BS ‚8‚„‚S $tS „‚{‚tS k‚s„RS
w‚SpZs„$tBSmSG‚jkS1(((S_ZR‚`B%R,kS1((dDS<Bb‚%‚„SsSRkR‚8s${S
stISBA`‚{$%‚Ss}}„Bs{YSBSBtBjB${sjSI‚R$tS$RSR$jjSjs{,$tSytS}s„${Zjs„S
b‚S A‚j$‚%‚S YsS stS BtBjBkS PB„S {B88BtR‚tR‚S ,tBbj‚I‚S 8ZRS A‚S
I$R{B%‚„‚IS „sY‚„S YstS $t%‚t‚IS stIS YZRS $S $RS tBS RZPP${$‚tS BS ‚RsAj$RYS
RB8‚S }„$t{$}j‚RS PB„S BtBjB${sjS I‚R$tS AZS YsS sS R„s‚kS AkS bY${YS sS
{B88BtR‚tR‚S BtBjBkS 8$YS A‚S RkR‚8s${sjjkS stIS BA`‚{$%‚jkS
I‚R$t‚IS8ZRSA‚SI‚%‚jB}‚ISytSY$RS}s}‚„Sb‚S}„B}BR‚SRZ{YSsSR„s‚kS


1SNstZs‚S=R‚SsRSpZ$I‚SBS!tBjB${sjS*‚R$tS
!Z„SAsR${SR„s‚kSPB„SI‚R$t$tSstSBtBjBkSBPS{B88BtR‚tR‚S,tBbj‚I‚S$RS
„BB‚IS$tS3„‚‚:RS{Bt{‚}$BtSBPS]B8}BR$$Btsj$kSSV{{B„I$tSBS3„‚‚SwR‚‚S
*Z88‚SdMdS}}S;TDSY‚SR‚tR‚SBPSstkS$%‚tSR‚t‚t{‚S$RSI‚„$%‚ISP„B8S
BZ„S }„‚%$BZRS ,tBbj‚I‚S BPS Y‚S R‚tR‚RS BPS Y‚S bB„IRS YsS {B8}BR‚S $S
B‚Y‚„S b$YSBZ„SBAR‚„%s$BtS BPS Y‚SbskS $tSbY${YSY‚kSs„‚S{B8A$t‚IS$tS
YsS R‚t‚t{‚S qY‚S {B„t‚„RBt‚S BPS Y$RS }s„sI$8S YBb‚%‚„S $RS stS
BAR‚„%s$BtS YsS YsRS tBS A‚‚tS PZjjkS s}}„‚{$s‚IS „‚s„I$tS Y‚S8stt‚„S $tS
bY${YSbB„IRSs„‚SRZ}}BR‚ISBSs{JZ$„‚SsSR‚tR‚SytS}s„${Zjs„SY‚S}„$t{$}j‚SBPS
]B8}BR$$Btsj$kS$RS„BB‚IS$tSY‚SY‚R$RSYsS"BZ„SZtI‚„RstI$tSBPS>YBR‚HS
bB„IRS {BtR$RRS $tS BZ„S „sR}S BPS Y‚S bskS $tS bY${YS Y‚kS 8skS P$Z„‚S $tS
R‚t‚t{‚RS$tS‚t‚„sjSstISYBbS$tS‚t‚„sjSY‚kS{B8A$t‚SBSI‚‚„8$t‚SY‚S
„ZYT{BtI$$BtRSBPSYBR‚SR‚t‚t{‚R"Sw*Z88‚SdMdS}}SxDSS
     qY$RS R$8}j‚S $I‚sS PB„8RS Y‚S AsR$RS BPS BZ„S R„s‚kS $tS I‚R$t$tS stS
BtBjBkS PB„S {B88BtR‚tR‚S ,tBbj‚I‚US bYsS jstZs‚S sjjBbRS Bt‚S BS RskS
sABZS sS {Bt{‚}S ‚jjRSZRSsSjBSsABZSY‚S{Bt{‚}SZtI‚„S{BtR$I‚„s$BtSytS
BY‚„SbB„IRSY‚S8‚st$tRSBPSbB„IRSw$‚SY‚S{Bt{‚}RDS{stSA‚SI$R{B%‚„‚IS
P„B8SY‚S 8stt‚„S $tSbY${YSY‚SbB„IRSs„‚SZR‚IS$tS‚%‚„kIskSjstZs‚SVRS
  s‚8stS wdxDS YsRS RZ‚R‚IS jstZs‚S $RS Y‚S A‚RT,tBbtS Y‚B„kS BtS
‚%‚„kIskS ,tBbj‚I‚S VRRZ8$tS YsS jstZs‚S „‚Pj‚{RS YBZYS Y‚„‚PB„‚S
stsjk9$tS}s‚„tRSBPS‚%‚„kIskSjstZs‚SZR‚:SRYBZjIS}„B%$I‚SZR‚PZjS{jZ‚RS
BS Y‚S R„Z{Z„‚S BPS {B88BtR‚tR‚S ,tBbj‚I‚S VRS sS 8B$%s$tS ‚-s8}j‚S
{BtR$I‚„SY‚StBZtRSsAj‚SstIS‚j‚}YstSstISY‚SsI`‚{$%‚RSR8s„SstISjs„‚S
BZS BPS bY${YS PBZ„S Rkts{${sjjkS b‚jjS PB„8‚IS stIS R‚8st${sjjkS %sj$IS
sI`‚{$%‚TtBZtS {B8A$ts$BtRS {stS A‚S 8sI‚S !t‚S BPS Y‚R‚S {B8A$ts$BtRS
ts8‚jkSR8s„SsAj‚S$RSk}${sjjkS„‚`‚{‚ISBtS}„s8s${S„BZtIRSsRS$S$RSsS
BIIRSb$YSBZ„S{B88BtR‚tR‚S%$‚bSBPSbYsSsAj‚RSs„‚1SytS}s„${Zjs„SbY$j‚S
$S$RSR‚tR$Aj‚SBSRskSjs„‚S‚j‚}YstSstISjs„‚SsAj‚SsSsAj‚S$RStBSY‚S,$tISBPS
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSS
1S3B„SY‚S8B8‚tSb‚Ss„‚StBS{Bt{‚„t‚ISb$YS8‚s}YB„SS
BA`‚{S PB„S bY${YS R8s„S s}}j$‚RS qY$RS stsjkR$RS „‚RZjRS $tS Y‚S P„s8‚tS
Y$‚„s„{YkSRYBbtS$tSP$Z„‚S$tSdSA‚jBbSWB‚SYsSY$RS,$tISBPSstsjkR$RS$RStBS
8Z{YS I$PP‚„‚tS P„B8S Y‚S k}‚S $tP‚„‚t{$tS }„B{‚RRS YsS B{{Z„RS $tS R„BtjkS
k}‚IS}Bjk8B„}Y${S}„B„s88$tSjstZs‚RnSS
   S
   S
   S                          − luƒ +
   S
   S                                 {l}Xuv  uBl }
   S
   S
   S                                       −R9uƒ +
   S
                            {uBl }                  {l}Xuv }
   S
           3$Z„‚SdSVSR$8}j‚SstsjkR$RSBPSPBZ„SsI`‚{$%‚TtBZtS{B8A$ts$BtRS
   S
3B„S ‚-s8}j‚S {BtR$I‚„S Y‚Sj$tZ$R${S}s‚„tRS stISY‚S {B„„‚R}BtI$tSk}‚S
$tP‚„‚t{‚RSRYBbtS$tSsAj‚SdS3„B8S-SLSnSPB„S‚-s8}j‚SBt‚S{stS$tP‚„SYsS-S
$RSsSvY9BƒSR$t{‚StZ8A‚„RSs„‚SY‚S",$tIRSBPSY$tR"SYsS{stSA‚SsII‚ISBS
nS ytS ‚t‚„sjS Y‚S 8BRS ‚t‚„${S k}‚S }BRR$Aj‚S S $RS $tP‚„„‚IS w$‚S Y‚R‚S
B}‚„s$BtRSs„‚SsRRZ8‚ISBSA‚S}Bjk8B„}Y${DSS
S
                                                                                   S
         N$tZ$R${S      qk}‚S
         _s‚„tytP‚„‚t{‚S
S
         -SLSnS S         -S$RSvY9BƒS
         ƒ'ƒRw-DS      -S$RSsSRJYv|S
         %vRƒw-kDSSSS-S$RSstSCBb|SkS$RSRJYv|SBPS-SBA`‚{RS
         XuIw-DSSSSSSSSSS-S$RSsSRJYv|S
         'vw-DS-S$RSvY9BƒS

            qsAj‚SdSN$tZ$R${S}s‚„tRSstISY‚S{B„„‚R}BtI$tSk}‚S$tP‚„‚t{‚RS
S
3B„S ‚-s8}j‚S sjjS YsS {stS A‚S $tP‚„„‚IS P„B8S „‚%‚„R‚w-DS $RS YsS -S $RS Y‚S
‚t‚„${S k}‚S RJYv|S bY${YS {BZjIS A‚S sS l%RS sS Rƒ%vS wsS R‚JZ‚t{‚S BPS
|Xuƒu|ƒRDS sS '|CƒS ‚{S WB‚S sjRBS YsS $tS sII$$BtS BS s{$BtRS
w8‚YBIRDS }„B}‚„$‚RS w„ZYT%sjZ‚IS PZt{$BtRDS {stS sjRBS A‚S ZR‚IS BS $tP‚„S
Y‚Sk}‚SBPSstSBA`‚{S3B„S‚-s8}j‚SP„B8S‚%‚tw-DSBt‚S{stS$tP‚„SYsS-S$RSsS
vY9BƒSR$t{‚Sj$RRSR‚JZ‚t{‚RS‚{Ss„‚StBSY‚S,$tIRSBPSBA`‚{RSbY${YS{stS
A‚S I‚R{„$A‚IS AkS Y‚S }„‚I${s‚S ‚%‚tS ytS ‚t‚„sjS $%‚tS sS IB8s$tS wsS R‚S BPS
{Bt{‚}RDS ] = {{d !!! { 8 } S stIS sS R‚S BPS s{$BtRS wstIS }„B}‚„$‚RDS
_ = {}d !!! } t } S sS }„‚I${s‚S s}}w}{DS bY‚„‚S { ∈ ] S stIS } ∈ _ S {stS A‚S
I‚P$t‚ISRZ{YSYsSY‚Ss{$BtSwB„S}„B}‚„kDS}Ss}}j$‚RSBSwB„S8s,‚RSR‚tR‚SBPDS
BA`‚{RS BPS k}‚S {S 3B„S ‚s{YS }„B}‚„kS } ∈ _ S sS R‚S ] } = {{ | s}}w} {D} S
I‚tB$tS sjjS {Bt{‚}RS {S PB„S bY${YS Y‚S }„B}‚„kS }S $RS s}}j${sAj‚S {stS A‚S
‚t‚„s‚IS VS {Bt{‚}S Y$‚„s„{YkS $RS Y‚tS RkR‚8s${sjjkS I$R{B%‚„‚IS AkS
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSS SSSSSSSSSSS
nS qY$RS $RS „‚8$t$R{‚tS BPS wBtsZ‚S d(DUS .yS „‚`‚{S Y‚S {Bt‚t$BtS YsS Y‚„‚S $RS stS

  $8}B„stSY‚B„‚${sjSI$PP‚„‚t{‚SA‚b‚‚tSPB„8sjSstIStsZ„sjSjstZs‚R"S
stsjk9$tS Y‚S RZAR‚S „‚js$BtRY$}S s8BtS Y‚S %s„$BZRS R‚RS ‚t‚„s‚IS qBS
$jjZR„s‚S YBbS Y$RS k}‚S BPS stsjkR$RS {BZjIS wRkR‚8s${sjjkDS k$‚jIS sS k}‚S
Y$‚„s„{YkS {BtR$I‚„S sS R‚S BPS {Bt{‚}RS ]S stIS sS R‚S _S BPS }„B}‚„$‚RS wB„S
s{$BtRDSYsS8skSB„S8skStBSA‚SR‚tR$AjkSs}}j$‚ISBS{Bt{‚}RS$tS]US
S
] = {l%R Rƒ%v R} SS
_ = {9}m  99Bƒ$Q  R%: u%l XuI  ƒ'ƒR  C>}}ƒ`uR } SS
S
7YBbtS$tSP$Z„‚S1SA‚jBbS$RSsStZ8A‚„SBPSR‚RSYsSs„‚S‚t‚„s‚ISAkSs}}w}{DS
wP$Z„‚S 1sDS stIS Y‚S {Bt{‚}S Y$‚„s„{YkS $8}j$‚IS AkS Y‚S RZAR‚S „‚js$BtRY$}S
s8BtSY‚R‚SR‚RSwP$Z„‚S1ADSWB‚SYsS‚s{YSwZt$JZ‚DSR‚S{B„„‚R}BtIRSBSsS
{jsRRS$tSY‚SY$‚„s„{YkSeJZsjSR‚RSw‚S ] u%l SstIS ] XuI DS{B„„‚R}BtISBSY‚S
Rs8‚S {jsRRS VS {jsRRS {BZjIS A‚S $%‚tS stkS 8‚st$tPZjS jsA‚jS YsS $tZ$$%‚jkS
„‚}„‚R‚tRSsjjSY‚S{Bt{‚}RS$tSY‚S{jsRRS3B„S‚-s8}j‚S$tSP$Z„‚S1ASRJYv|S
$RSZR‚ISBS{Bjj‚{$%‚jkS„‚P‚„SBSR‚RSR„$tRSstISj$RRS
S
S                                          − 9}m +
S ] ƒ'ƒR = {l%R Rƒ%v}             − 99Bƒ$Q +
                                            − R%: +
S ] u%l = {l%R Rƒ%v}                                RJYv|
S ]
S     XuI = {l%R Rƒ%v}                               + u%l −
S ] R%: = {l%R R Rƒ%v}                            + XuI −
                                                        + ƒ'ƒR −
S ] 99Bƒ$Q = {l%R R Rƒ%v}      CƒIƒISwj$RRD            YvCƒIƒISwR‚RD
S
S   ] 9}m = {l%R R Rƒ%v}
S ] C>}}ƒ`uR = {Rƒ%v}             + C>}}ƒ`uR  −
S                              Rƒ%v
                 wsDSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSwADS
     S
3$Z„‚S1S7‚RS‚t‚„s‚ISAkSs}}w}{DSstISY‚SY$‚„s„{Y${sjSR„Z{Z„‚S$8}j$‚ISAkSY‚8S
S
S
]j‚s„jkS Y‚„‚S s„‚S sS tZ8A‚„S BPS „Zj‚RS YsS {stS A‚S ‚RsAj$RY‚IS P„B8S Y‚S
{Bt{‚}S Y$‚„s„{YkS RYBbtS $tS P$Z„‚S 1S 3B„S ‚-s8}j‚S Bt‚S {stS Rs‚S Y‚S
PBjjBb$tUS
S
w∀{Dws}}w„‚%‚„R‚{DS⊃Ss}}wR$9‚{DDS                                                wnDS
w∃{Dws}}wR$9‚{DS∧S¬s}}w„‚%‚„R‚{DDS                                               w;DS
w∀{Dws}}ws$j{DS≡Ss}}wY‚sI{DDS                                                   wxDS
   S
<‚„‚SwnDSRs‚RSYsSbY‚t‚%‚„S$S8s,‚RSR‚tR‚SBS„‚%‚„R‚SstSBA`‚{S{SY‚tS$S
sjRBS 8s,‚RSR‚tR‚SBSsR,SPB„S Y‚S R$9‚SBPS{SqY$RS‚RR‚t$sjjkS8‚stRSYsSstS
BA`‚{SBSbY${YSY‚SR$9‚SB}‚„s$BtS{stSA‚Ss}}j$‚IS8ZRSA‚SsS}s„‚tSBPSstS
BA`‚{S BS bY${YS Y‚S „‚%‚„R‚S B}‚„s$BtS {stS A‚S s}}j$‚IS w;DS BtS Y‚S BY‚„S
YstIS Rs‚RS YsS Y‚„‚S s„‚S BA`‚{RS PB„S bY${YS Y‚S R$9‚S B}‚„s$BtS s}}j$‚RS
AZSPB„SbY${YSY‚S„‚%‚„R‚SB}‚„s$BtSIB‚RStBSs}}jkS3$tsjjkSwxDSRs‚RSYsS
bY‚t‚%‚„S $S 8s,‚RS R‚tR‚S BS sR,S PB„S Y‚S Y‚sIS BPS stS BA`‚{S Y‚tS $S sjRBS
8s,‚RSR‚tR‚SBSsR,SPB„S$RSs$jSstIS%${‚S%‚„RsSqYZRSbY$j‚SY‚„‚S8ZRSA‚SsS
j‚sRS Bt‚S }„B}‚„kS YsS I‚P$t‚RS sS {Bt{‚}S Y‚„‚S {BZjIS A‚S 8stkS wb‚S b$jjS
Ys%‚S 8B„‚S BS RskS sABZS Y$RS A‚jBbDS 3$tsjjkS $S 8ZRS A‚S tB‚IS YsS $tS
}‚„PB„8$tSY$RSstsjkR$RSb‚SYs%‚SsRRZ8‚ISYsSY‚S}„‚I${s‚Ss}}w}{DS$RSsS
  BBj‚stT%sjZ‚IS PZt{$BtS bY${YS YsRS Y‚S {BtR‚JZ‚t{‚S YsS Y‚S k}‚S
Y$‚„s„{YkS $RS sS R„${S A$ts„kS „‚‚S ytS Ps{S Y$RS $RS Bt‚S BPS Y‚S 8s$tS
{Ys„s{‚„$R${RS BPS BZ„S 8‚YBIS stIS YsRS j‚IS BS bBS $8}B„stS „‚RZjRUS w$DS
8Zj$}j‚S $tY‚„$st{‚S $RS {B8}j‚‚jkS s%B$I‚IS stIS w$$DS AkS tBS sjjBb$tS stkS
s8A$Z$kS $tS Y‚S $t‚„}„‚s$BtS BPS s}}w}{DS j‚-${sjS s8A$Z$kS }BjkR‚8kS
stIS 8‚s}YB„S s„‚S ‚-}j${$jkS „‚}„‚R‚t‚IS $tS Y‚S Y$‚„s„{YkS qY$RS b$jjS A‚S
I$R{ZRR‚ISA‚jBbS


nSNstZs‚SstIS]B88BtR‚tR‚S€tBbj‚I‚S
qY‚SbB„,SI‚R{„$A‚ISY‚„‚SbsRS8B$%s‚ISAkSY‚SPBjjBb$tSbBSsRRZ8}$BtRUS
w$DS Y‚S }„B{‚RRS BPS jstZs‚S ZtI‚„RstI$tS $RS PB„S Y‚S 8BRS }s„S sS
{B88BtR‚tR‚S „‚sRBt$tS }„B{‚RRS sS Y‚S }„s8s${S j‚%‚jS stIS w$$DS R$t{‚S
{Y$jI„‚tS 8sR‚„S R}B,‚tS jstZs‚S sS sS %‚„kS kBZtS s‚S {Y$jI„‚tS 8ZRS A‚S
}‚„PB„8$tS {B88BtR‚tR‚S „‚sRBt$tS sS Y‚S }„s8s${S j‚%‚jS stIS
{BtR‚JZ‚tjkS Y‚kS 8ZRS }BRR‚RS sjjS Y‚S {B88BtR‚tR‚S ,tBbj‚I‚S„‚JZ$„‚IS
BS ZtI‚„RstIS R}B,‚tS jstZs‚;S ytS BY‚„S bB„IRS b‚S s„‚S sRRZ8$tS YsS
I‚{$I$tS BtS sS }s„${Zjs„S s}}w%{DS RYBZjIS tBS A‚S {Bt„B%‚„R$sjS stIS YsS
{Y$jI„‚tS {stS ‚sR$jkS stIS {BtR$R‚tjkS stRb‚„S R$8}j‚S JZ‚R$BtRS RZ{YS sRS IBS
‚j‚}YstRSPjkSIBS8BZts$tRSsj,SIBSABB,RS„ZtS‚{SWB‚SYsS$tSstRb‚„$tS
Y‚R‚SJZ‚R$BtRS$S$RS{j‚s„SYsSBt‚SYsRSBSA‚S{B{BtR{$BZRSBPS8‚s}YB„S3B„S
‚-s8}j‚S bY$j‚SsAj‚RS }‚B}j‚SstIS P‚‚j$tRS{stSA‚S R„BtSw$‚S$S$RSJZ$‚S
8‚st$tPZjS BS RskS R„BtS sAj‚S R„BtS }‚„RBtS R„BtS P‚‚j$tDS $S $RS {j‚s„S
YsSY‚SR‚tR‚RSBPSR„BtS$tSY‚R‚SY„‚‚S{sR‚RSs„‚SJZ$‚SI$R$t{SytSPs{SY‚S
%s„$BZRS8‚s}YB„${sjSI‚„$%s$BtRSBPSsSj‚-‚8‚Ss„‚S‚%‚tZsjjkSI$R{B%‚„‚ISAkS
Y‚S}„B{‚RRSb‚SI‚R{„$A‚SY‚„‚SsRSb$jjSA‚{B8‚S‚%$I‚tS$tSY‚St‚-SR‚{$BtRS
qY‚S }B$tS Y‚„‚S $RS YsS sjjS YsS 8s‚„RS $t$$sjjkS $RS BS {BtR$I‚„S }BR$tS
JZ‚„$‚RS RZ{YS sRS s}}wR8s„‚j‚}YstDS BS sS P$%‚Tk‚s„S BjIS 3Z„Y‚„8B„‚S $tS
sR,$tS RZ{YS sS JZ‚„kS b‚S s„‚StBSsR,$tSbY‚Y‚„SB„StBS ‚%‚„kS ‚j‚}YstS $RS
R8s„S tB„S YBbS R8s„S ‚j‚}YstRS {stS A‚S AZS bY‚Y‚„S B„S tBS $S $RS
8‚st$tPZjS BS RskS R8s„S ‚j‚}Yst:S G‚S A‚j$‚%‚S YsS RZ{YS JZ‚„$‚RS s„‚S
A$ts„kT%sjZ‚ISytSBY‚„SbB„IRSbY$j‚SsSY‚SJZst$s$%‚SwB„SsSIssTj‚%‚jDS$S
{BZjISA‚SsS8s‚„SBPSI‚„‚‚SsRSBSYBbSR8s„SsSR}‚{$P${S‚j‚}YstS8$YSA‚S
PB„S‚-s8}j‚SY‚SJZsj$s$%‚SJZ‚R$BtSBPSbY‚Y‚„SB„StBS$S$RS8‚st$tPZjSBS
RskS R8s„S ‚j‚}Yst:S $RS tBS sS 8s‚„S BPS I‚„‚‚xS G$YS Y$RS $tS 8$tIS BZ„S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
;SyS8skS%‚„kSb‚jjSA‚SY‚S{sR‚SYsS"‚%‚„kY$tSb‚S,tBbSb‚Sj‚s„t‚IS$tS,$tI‚„s„‚t"S
xSG‚Sb$jjStBSIb‚jjSBtSY$RS$RRZ‚SBBS8Z{YSY‚„‚S‚-{‚}SBSRskSYsSsRSej,stSwdnDSYsRS

  {Bt%$t{$tjkS s„Z‚IS BS s%B$IS {‚„s$tS {Bt„sI${$BtRS jB${sjS „‚sRBt$tS 8ZRS sS RB8‚S

  j‚%‚jS {Bjjs}R‚S BS sS A$ts„kS jB${S GY$j‚S ej,st:RS s„Z8‚tS R‚‚8‚IS BS A‚S RZR{‚}$Aj‚S BS

  RB8‚S {„$${$R8S w‚S *ZAB$RS ‚S sjS wd;DDS Y‚„‚S s„‚S 8B„‚S {Bt%$t{$tS s„Z8‚tRS

  RZ}}B„$tSY‚SRs8‚S„‚RZjS3B„S‚-s8}j‚S{BtR$I‚„SY‚SPBjjBb$tUSS

  S

      wdDS FBYtSj$,‚RS‚%‚„kSPs8BZRSs{„‚RRS

      w1DS N$9S$RSsSPs8BZRSs{„‚RRS

      wnDS FBYtSj$,‚RSN$9S

  S

  ]j‚s„jkSwdDSstISw1DSRYBZjIS‚ts$jSwnDS„‚s„Ij‚RRSBPSYBbSPs8BZRSN$9Ss{ZsjjkS$RS=R$tS
AsR${Ss}}„Bs{YSBSI$R{B%‚„$tSY‚SBtBjBkSBPS{B88BtR‚tR‚S,tBbj‚I‚S{stS
A‚SRZ88s„$9‚ISsRSPBjjBbRUS
      S

Œ 7‚j‚{SsSR‚SBPSsI`‚{$%‚RSstIS%‚„ARSz = {% d !!! % 8 } SS
Œ 7‚j‚{SsSR‚SBPStBZtRS ] = {{d !!! { t } S
Œ p‚t‚„s‚SR‚RS ] = {{ ∈ ] | s}}w%  { D}Sd ≤ $ ≤ 8 SPB„S‚%‚„kS % ∈ z S
                            $                        $                                      $

Œ VtsjkR‚SY‚SRZAR‚S„‚js$BtRY$}SA‚b‚‚tSsjjSR‚RS ] $ ∈ {] d !!!] 8 } S
S


VRS stS $t$$sjS ‚-s8}j‚S {BtR$I‚„S Y‚S R‚S BPS %‚„ARS zS )S {9C'S dul/S ƒYvS
ul/S ƒuRCv}S stIS Y‚S R‚S BPS tBZtRS ]S )S {ku%CvulS #%ƒIS jl}XuvS
6Xuƒ/SVv%9ulSV9Bu}S kS„‚}‚s‚IjkSs}}jk$tSs}}w%{DSY‚SPBjjBb$tSR‚RS
s„‚S‚t‚„s‚IUS
S
] 9C' = {ku%Cvul Vv%9ul #%ƒI jl}Xuv 6Xuƒ/ V9Bu } S
] ul/ = {ku%Cvul} S
] ƒuRCv = {ku%Cvul} S
] X%v/ = {Vv%9ul} S
] dul/ = {ku%Cvul #%ƒI jl}Xuv} S
] ƒYv = {ku%Cvul  #%ƒI jl}Xuv} S
S
3$„RSb‚StB‚SYsSbY$j‚SRB8‚SI‚{$R$BtRS{BZjIS‚{Yt${sjjk:SA‚SJZ‚R$Bt‚IS
wRskSAkSsSA$BjB$RDSBZ„SR„s‚kSbsRSBSR$8}jkS{BtR$I‚„SY‚SJZ‚R$BtSP„B8S
Y‚S}B$tSBPS%$‚bSBPS{B88BtR‚tR‚SytSI‚{$I$tSBtSsS}s„${Zjs„Ss}}w%{DSb‚S
{BtR$I‚„‚IS Y‚S JZ‚„kS }B$R‚IS BS sS P$%‚Tk‚s„S BjIUS IBS ‚j‚}YstRS PjkSIBSY‚kS
„ZtSIBSY‚kSsj,S‚{S+Z‚R$BtsAj‚SR$Zs$BtRSb‚„‚SR$8}jkS$tB„‚ISqY$RS
$t$$sjS}„B{‚RRS„‚RZj‚IS$tSY‚SY$‚„s„{YkSRYBbtS$tSP$Z„‚SnSA‚jBbS7B8‚SBPS
Y‚S R‚RS $tI${s$tS}BR$$%‚Sj‚PSstIS„$YSs„$AZ‚RSs„‚S$%‚tS$tSP$Z„‚S;S
A‚jBbS WB‚S YsS RB8‚S }Bb‚„PZjS $tP‚„‚t$sjS }s‚„tRS YsS {stS A‚S ZR‚IS $tS
jstZs‚S }„B{‚RR$tS s„‚S $8}j${$S $tS Y‚S R„Z{Z„‚S RYBbtS $tS P$Z„‚S nS 3B„S
‚-s8}j‚S bYsS IB‚RStBSY$t,S IB‚RS tBS YZ„Sw N DSbYsS bsj,RSsjRBS„ZtRS
w NM DSstkY$tSYsSj$%‚RS‚%Bj%‚RSw Nn SstIS N; DS‚{S


;S€tBbj‚I‚TN‚%‚jUS ‚$tSNB{,‚ISBSsS_„B}‚„kS
B$%s$tS BZ„S s}}„Bs{YS BS I$R{B%‚„$tS wsRS B}}BR‚IS BS $t%‚t$tDS Y‚S
R„Z{Z„‚S BPS {B88BtR‚tR‚S ,tBbj‚I‚S $RS Y‚S $I‚sS YsS {B88BtS jstZs‚S
8ZRS„‚Pj‚{S {B88BtR‚tR‚S stIS YZRSI$PP‚„‚t{‚RSstISR$8$js„$$‚RSA‚b‚‚tS
{Bt{‚}RS8ZRSA‚S„‚Pj‚{‚IS$tSBZ„S‚%‚„kIskS{Bt%‚„Rs$BtSq‚{Yt${sjjkSY‚S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
    stkS JZst$s$%‚S 8BI‚jS wRZ{YS sRS PZ99kS jB${DS Y$RS $tZ$$%‚S ‚ts$j8‚tS {sttBS A‚S

    }„BIZ{‚ISwb‚S j‚s%‚SY‚SI‚s$jRSBPSPB„8Zjs$tSY$RS$tSPZ99kS jB${SsRSstS‚-‚„{$R‚DSqY‚S

    }„BAj‚8S Y‚„‚S $RS YsS sS Y‚S JZsj$s$%‚S j‚%‚jS Y‚S „ZYT%sjZ‚S BPS         Ps8BZRw-DS 8ZRS
    {Bjjs}R‚S BS ‚$Y‚„S „Z‚S B„S PsjR‚S R$t{‚S sS YsS j‚%‚jS sjjS YsS 8s‚„RS $RS bY‚Y‚„S B„S tBS

    N$9S$RSPs8BZRStBSYBbSPs8BZRSRY‚Ss{ZsjjkS$RS
{js$8S b‚S s„‚S 8s,$tSY‚„‚S{stSA‚SRs‚ISsRSPBjjBbRUS‚%‚„kS{Bt{‚}SsSY‚S
,tBbj‚I‚TS wB„S {B88BtR‚tR‚TDS j‚%‚jS 8ZRS :Bbt:S RB8‚S Zt$JZ‚S }„B}‚„kS
stIS Y$RS 8ZRS sjRBS A‚S j$tZ$R${sjjkS „‚Pj‚{‚IS AkS RB8‚S %‚„AS B„S sI`‚{$%‚S
qY$RS8$YSA‚SR$8$js„SBSbYsS3BIB„SwdMS}Sd1EDS8‚stSAkS"Ys%$tSsS
{Bt{‚}S$RSA‚$tS jB{,‚IS BS sS }„B}‚„k"S ytSPs{S $SR‚‚8RSYsSY$RS$RSBt‚S
bskS BS ‚RS Y‚S I‚8s„{s$BtS j$t‚S A‚b‚‚tS {B88BtR‚tR‚S stIS IB8s$tS
R}‚{$P${S ,tBbj‚I‚S ytS }s„${Zjs„S $S R‚‚8RS YsS IB8s$tTR}‚{$P${S {Bt{‚}RS
s„‚S YBR‚S {Bt{‚}RS YsS s„‚S tBS Zt$JZ‚jkS jB{,‚IS BS stkS bB„IS $tS Y‚S
jstZs‚S
S                                                                        sX%v
S
                                                                           + Nd −
S                                                      aXmR%|ulsX %v      −id +     VBRƒu|sX %v
S
S                                                           + N1 −
S                                          5Cƒ9u%Cv        −i1 +       6YBRuv|
S
                                              + Nn −
S
S                     WuYƒul5Cƒ 9u%Cv −in +              uvuI5Cƒ 9u%Cv
S                            + N; −                                + Nx −
S          M%'%vsX%v R −i ; +       yvVv%9u Vƒ%Qu|R          − x +      `CvRƒY|% CvR
S
S              + NE −
S aluvR       −iE +     Vv%9ulM%Q
S                             + N −
S            %|ƒC$ƒR        − i +     Vv%9ulR
S
S                                           + NM −
S                          MI           −i M +     WCvMI
S
                          + N −
S                         −i +
             G%vI                  WCvG%vI
S
S                                      + Nd( −
S                       ku%Cvul       −id( +        yƒƒu%Cvul
S
S                          + Ndd −
S           `X%lI          −idd +       VIYl
S
3$Z„‚S nS VtS sIZjS $RS sS }YkR${sjS j$%$tS Y$tS YsS $RS PB„8‚IS yS ‚%Bj%‚RS $S „BbRS $S
I‚%‚jB}RS8B%‚RS$S{stSbsj,S„ZtSY‚s„SR‚‚Ssj,SY$t,S„‚sRBtS‚{        S
  S
+ N1 − = {I‚%‚jB} PB„8}                + Nn − = {‚%Bj%‚}
+ N; − = {j$%‚ I$‚ AB„t „Bb}        + NE − = {A„st{Y}
− iE + = {8B%‚}                         − i + = {Rj‚‚} „‚R ‚s I$‚R Aj‚‚I  YZ„ Y$t,} S
+ NM − = {R$ `Z8} bsj, „Zt}         − i + = {„Bs„  {„k}
+ Nd( − = {sj,}                        − idd + = {„‚sRBt}
S
                                               S
                               3$Z„‚S;S7‚RSRYBbtS$tSP$Z„‚SnS
S
qBS$jjZR„s‚SY$RS}B$tSPZ„Y‚„Sj‚SZRSstsjkR‚SsSP„s8‚tSBPSY‚SY$‚„s„{YkS
RYBbtS $tS P$Z„‚S nS $tS RB8‚S I‚s$jS qY‚S {Bt{‚}S M%'%vsX%vS Bt‚S {stS
s„Z‚S$RSY‚S{Bt{‚}SPB„SbY${YSBt‚S{stSRskSY‚SPBjjBb$tUS
S
s}}wM%'%vsX%vrƒCdD
s}}wM%'%vsX%v-'lC}D
s}}wM%'%vsX%vM%'D
s}}wM%'%vsX%v-%DS
S
   qYsS $RS j$%$tS Y$tRS „BbS I‚%‚jB}S j$%‚S stIS I$‚S wY‚S {Bt{‚}S
M%'%vsX%vS $RS s{ZsjjkS :jB{,‚I:SBSR‚%‚„sjSBY‚„S }„B}‚„$‚RSstISYZRS BS
R‚%‚„sjSBY‚„S%‚„ARSstISsI`‚{$%‚RDSGYsS$RS$8}B„stSBStB‚SY‚„‚S$RSYsS
$tS B„I‚„S BS {jsRR$PkS M%'%vsX%vS PZ„Y‚„S Bt‚S 8ZRS P$tIS RB8‚S {Bt{‚}ZsjS
I$PP‚„‚t{‚SA‚b‚‚tSsjjSj$%$tSY$tRSsSI$PP‚„‚t{‚SbY${YS8ZRSA‚SRB8‚YBbS
„‚Pj‚{‚IS$tSjstZs‚SVRS$SYs}}‚tRSY‚SbB„IS:8B%‚:S{BZjISA‚SZR‚ISBtSsjjS
j$%$tS Y$tRS ‚-{‚}S }jstRS !t‚S {BZjIS Y‚„‚PB„‚S RZ‚RS sS {jsRR$P${s$BtS
AsR‚ISBtSYsS%‚„ASsRSRYBbtS$tSP$Z„‚SnS
     qYZRSsjjSj$%$tSY$tRSs„‚S‚$Y‚„S}jstTj$,‚SY$tRSwaluvRDSbY${YSs„‚S
Y‚S$88BA$j‚Sj$%$tSB„st$R8RSB„Sst$8sjTj$,‚SY$tRSwVv%9ulM%QDSbY${YS
s„‚S Y‚S 8BA$j‚S j$%$tS B„st$R8RS G‚S s„‚S tBbS ss$tS Ps{‚IS b$YS Y‚S Rs8‚S
R$Zs$BtSts8‚jkSPZ„Y‚„S{jsRR$P${s$BtSBPSaluvRSstISVv%9ulM%QSqY$RS$tS
Z„tS „‚JZ$„‚RS ZRS BS P$tIS RB8‚S {Bt{‚}ZsjS I$PP‚„‚t{‚S A‚b‚‚tS }B‚t$sjS
RZAk}‚RSBPSY‚R‚SbBS{Bt{‚}RSbY${YS8ZRS„stRjs‚S$tBSsSI$PP‚„‚t{‚S$tS
B„I$ts„kSjstZs‚SqY$RS}„B{‚RRS$RS„‚}‚s‚ISZt$jStBSPZ„Y‚„S{jsRR$P${s$BtS
AsR‚ISBtSj$tZ$R${SI$PP‚„‚t{‚RS$RS}BRR$Aj‚SytSP$Z„‚SnSPB„S‚-s8}j‚SG%vIS
bY${YS $RS Y‚S {jsRRS BPS st$8sjRS YsS s„‚S j‚‚IS stIS Ys%‚S b$tRS bsRS
$t„BIZ{‚ISAsR‚ISBtSY‚S}„B}‚„kSBPSPjk$tSsSI$PP‚„‚t{‚SYsS„stRjs‚RS$tS
jstZs‚S BS Y‚S j‚-‚8‚S :Pjk:S GY$j‚S sS A$BjB$RS {stS j$RS tZ8‚„BZRS
I$PP‚„‚t{‚RS A‚b‚‚tS sjjS A$„IRS YsS PjkS {jsRR$P${s$BtS BtS RZ{YS „BZtIRS $RS
IB8s$tTR}‚{$P${SstISIB‚RStBSA‚jBtSBSY‚S,tBbj‚I‚SwB„S{B88BtR‚tR‚DS
j‚%‚jS R$t{‚S Y‚„‚S IB‚RS tBS R‚‚8S BS A‚S sS j$tZ$R${S I$PP‚„‚t{‚S A‚b‚‚tS sjjS
A$„IRS YsS PjkS qY$RS 8ZRS A‚S Y‚„‚PB„‚S Y‚S ,tBbj‚I‚Tj‚%‚jS stIS stkS
PZ„Y‚„S {jsRR$P${s$BtS A‚kBtIS Y$RS j‚%‚jS $RS AsR‚IS BtS IB8s$tTR}‚{$P${S
,tBbj‚I‚S


xS_BjkR‚8kSstIS‚s}YB„S
ytS BZ„S s}}„Bs{YS Y‚S B{{Z„„‚t{‚S BPS sS %‚„A\sI`‚{$%‚S sS stkS }js{‚S stIS sS
stkS j‚%‚jS $tS Y‚S Y$‚„s„{YkS sjbskRS „‚P‚„RS BS sS Zt$JZ‚S R‚tR‚S BPS YsS
%‚„A\sI`‚{$%‚SqY‚„‚PB„‚SBt‚S‚-}‚{RSR$8$js„SR‚tR‚RSBPSsSj‚-‚8‚SBSs}}jkS
BS{Bt{‚}RSsjBtSY‚SRs8‚S}sYSsjA‚$SsSI$PP‚„‚tSj‚%‚jRS$tSY‚SY$‚„s„{YkS
ytS}s„${Zjs„SBt‚SbBZjIS‚-}‚{SYsSY$YjkSs8A$ZBZRS%‚„ARSBSs}}jkSBS
{Bt{‚}RSY$Y‚„TZ}S$tSY‚SY$‚„s„{YkSbY‚„‚S%s„$BZRSR$8$js„SR‚tR‚RSBPSsS%‚„AS
%SRYBZjIS‚tITZ}Ss}}jk$tSsS%s„$BZRSj‚%‚jRSA‚jBbS%SS
     ]BtR$I‚„SPB„S‚-s8}j‚SQCƒ9 stISQCƒ9YluS$tSY‚SR‚tR‚SBPSPB„8$tSstIS
PB„8Zjs$tS $I‚sRS 7$t{‚S BZ„S 8‚YBIS $RS AsR‚IS BtS Y‚S $I‚sS BPS ZR$tS RZ{YS
%‚„ARSBSI$R{B%‚„SY‚StsZ„‚SBPS{Bt{‚}RSQCƒ9 stISQCƒ9YluS8ZRSABYS
s}}jkS BS ideasS WB‚S YsS $PS ‚%‚„kY$tS YsS {stS A‚S :PB„8‚I:S {stS A‚S
:PB„8Zjs‚I:SstIS%${‚S%‚„RsSY‚tSY‚R‚SbBS%‚„ARSbBZjISA‚SRktBtk8BZRS
<Bb‚%‚„S $tS Y$RS {sR‚S Y$RS $RS tBS RBS R$t{‚S Y‚„‚S s„‚S Y$tRS YsS {stS A‚S
PB„8‚IS AZS tBS PB„8Zjs‚IS 3B„S ‚-s8}j‚S {BtR$I‚„S Y‚S R8sjjS P„s8‚tS
RYBbtS $tS P$Z„‚S xS bY‚„‚S $S $RS RYBbtS YsS :I‚%‚jB}$t:S S :PB„8Zjs$t:S
:PB„8$t:S‚{Ss„‚SsjjSR}‚{$P${SbskRSBPS:8s,$t:Sw$tSBY‚„SbB„IRSBt‚SR‚tR‚S
BPS :8s,‚:S $RS :I‚%‚jB}:DS WB‚S Y‚S ‚%‚tZsjS R}j$S YBb‚%‚„S ytS }s„${Zjs„S
bY$j‚Sb‚S9u/SQCƒ9SstISI'lC}SABYS%IuRSstISQl%vRS%IuRSs„‚S
QCƒ9YluISbY$j‚SQl%vRSs„‚SQCRƒIS
   S
   S                                        − 9u/ +
   S                                                     `
   S                                                  + QCƒ9 −
   S
   S
   S                                       + I'lC} −
   S                       {%IuR  Ql%vR }
   S
   S                           + QCRƒ −
   S                       − QCƒ9Ylu +
   S               Ql%vR                   %IuR
                                         S
                       3$Z„‚SxSVtS‚-}jsts$BtSBPS}BjkR‚8kS
S
GY$j‚S Y‚S B{{Z„„‚t{‚S BPS R$8$js„S R‚tR‚RS BPS %‚„ARS sS %s„$BZRS j‚%‚jRS $tS Y‚S
Y$‚„s„{YkS$tI${s‚RS}BjkR‚8kSY‚SB{{Z„„‚t{‚SBPSY‚SRs8‚S%‚„ASwY‚SRs8‚S
j‚-‚8‚DS sS R„Z{Z„sjjkS $RB8B„}Y${S }js{‚RS $tS Y‚S Y$‚„s„{YkS $tI${s‚RS
8‚s}YB„${sjSI‚„$%s$BtRS]BtR$I‚„SY‚SPBjjBb$tUS
S
s}}wƒYvMIsX%vDS                                                            wEDS
s}}wƒYvu|X%vDS                                                                wDS
s}}wƒYv6XCdDS                                                                   wMDS
S
wEDSY„BZYSwMDSRs‚SYsSb‚S{stSR}‚s,SBPSsSj‚‚ISY$tSsS8s{Y$t‚SstISsS
RYBbS „Ztt$tS ]j‚s„jkS YBb‚%‚„S Y‚R‚S ‚-s8}j‚RS $t%Bj%‚S Y„‚‚S I$PP‚„‚tS
R‚tR‚RSBPSY‚S%‚„ASƒYvSyS{BZjISA‚Ss„Z‚ISYsSY‚SR‚tR‚RSBPSƒYvSYsSs„‚S
$8}j$‚IS AkS wDS stIS wMDS {B„„‚R}BtIS BS sS 8‚s}YB„${sjS I‚„$%s$BtS BPS Y‚S
s{ZsjS „Ztt$tS BPS tsZ„sjS ,$tIRS Y‚S R‚tR‚S $8}j$‚IS AkS wEDS yS $RS sjRBS
$t‚„‚R$tS BS tB‚S YsS Y‚R‚S 8‚s}YB„${sjS I‚„$%s$BtRS B{{Z„S sS %s„$BZRS
j‚%‚jRUS P$„RS P„B8S tsZ„sjS ,$tIRS BS s„$Ps{RS stIS Y‚tS P„B8S }YkR${sjS BS
sAR„s{SB„‚B%‚„SY‚S8sRR\{BZtSI$R$t{$BtSBtSY‚S}YkR${sjSR$I‚SR‚‚8RS
BSYs%‚SsS8$„„B„S$8s‚SBPSsS8sRR\{BZtSBtSY‚SsAR„s{SR$I‚S3B„S‚-s8}j‚S
tB‚S Y‚S PBjjBb$tS R$8$js„$kS A‚b‚‚tS duƒS w}YkR${sjS RZARst{‚DS stIS
%vQCƒ9u%CvSwsAR„s{SRZARst{‚DUS
S
Œ duƒ\%vQCƒ9u%CvSPjBbRS{stSA‚SI$%‚„‚ISP$j‚„‚IS}„B{‚RR‚IS‚{S
Œ b‚S{stSA‚SPjBBI‚ISAkSB„SI„BbtS$tSduƒ\%vQCƒ9u%CvS
Œ sSj$j‚SA$SBPSbs‚„\$tPB„8s$BtS$RSwR$jjDSbs‚„\$tPB„8s$BtS
S
!t‚S$t‚„‚R$tSsR}‚{SBPSY‚R‚SP$tI$tRS$RSBSPZ„Y‚„S$t%‚R$s‚SY‚S‚-s{S
tsZ„‚S BPS Y$RS 8‚s}YB„${sjS 8s}}$tS stIS bY‚Y‚„S Y‚S 8s}S $RS {BtR$R‚tS
Y„BZYBZS YsS $RS bY‚Y‚„S Rs8‚Tj‚%‚jS Y$‚„s„{Y$‚RS s„‚S R„Z{Z„sjjkS
$RB8B„}Y${SsRSY‚S{sR‚Ss}}‚s„RSBSA‚SRBSPs„SwR‚‚SP$Z„‚SEDES
   S      Vv%9ul                                   u|X%v
   S
   S       − ƒYv +                                   − ƒYv +
   S
   S          MIM%'% vsX%v                          GXlIu| X%v
   S
   S
                      + Qlm −                                    + Qlm −
   S
   S
  G%vIM
   S         IM%'%vsX %v                   G%vIGX lIu|X%v
                                        S
              3$Z„‚SESyRB8B„}Y${SR„Z{Z„‚RS‚-}js$t$tS8‚s}YB„RS


ESW‚s$BtSy88ZsAj‚S3‚sZ„‚RSstIS7Z„}„$R‚S
qY‚S8BI‚jS}„B}BR‚ISY‚„‚SsjjBbRSZRSBSYs%‚SsS%‚„kS$t‚„‚R$tS8BI‚jSBPSY‚S
t‚s$BtSqBS$jjZR„s‚S{BtR$I‚„SY‚SPBjjBb$tS}„B}BR$$BtRS$8}j$‚ISAkSY‚S
{Bt{‚}SY$‚„s„{YkS$%‚tS$tSP$Z„‚SnSts8‚jkSYsS‚t‚„sjjkSst$8sjRS8B%‚S
stIS}‚B}j‚Ssj,US
S
s}}wC'Vv%9ulDS                                                                 wDS
s}}wsul/ku%CvulDS                                                             wd(DS
S
GYsS$RS$t‚„‚R$tSBS{BtR$I‚„SY‚„‚S$RSYBbSBt‚S$t‚„}„‚RSY‚St‚s$BtSBPS
RZ{YS }„B}BR$$BtRS ytS }s„${Zjs„S Y‚„‚S s„‚S bBS }BRR$Aj‚S stRb‚„RS BS Y‚S
JZ‚„kS¬s}}wC'2DS$‚SBSY‚SJZ‚„kS"bYsSBA`‚{RSIBStBS8B%‚2"S!t‚S
{stS R$8}jkS }„B%$I‚S w>S TS Vv%9ulDS sRS stS stRb‚„S bY‚„‚S >S $RS Y‚S R‚S BPS sjjS
{Bt{‚}RS $tS Y‚S Zt$%‚„R‚S BPS I$R{BZ„R‚S qY$RS $RS Y‚S R‚S BPS sjjS {Bt{‚}RS
‚-{jZI$tS YBR‚S PB„S bY${YS s}}wC'Vv%9ulDS YBjIRS qYZRS }jstRS stIS sjjS
tBtTj$%$tS Y$tRS IBS tBS 8B%‚S wR‚‚S P$Z„‚S S A‚jBbDS qY$RS $RS R„BtS
t‚s$BtSR$t{‚S$SR$8}jkS„‚Z„tRSY‚S{B8}j‚8‚tSb$YS„‚R}‚{SBSY‚S‚t$„‚S
R„Z{Z„‚S<Bb‚%‚„Sb‚Ss„Z‚SYsSY‚„‚S$RSsSRZAj‚SI$PP‚„‚t{‚SA‚b‚‚tSY‚S
PBjjBb$tSJZ‚„$‚RUS
   S
*BS8BZts$tRSsj,2S                                                             wddDS
*BS‚j‚}YstRSsj,2S                                                             wd1DS
S
VjYBZYS sS „s$BtsjS s‚tS bBZjIS stRb‚„S "tB"S $tS ABYS {sR‚RS Bt‚S 8$YS
$8s$t‚SsS{Y$jIS„‚}jk$tS"tsYS8BZts$tRSIBStBSsj,"S$tS„‚R}BtR‚SBSwddDS
qY$RS 8ZRS A‚S PZt{$BtS BPS Y‚S PBjjBb$tUS ‚j‚}YstRS PsjjS I$„‚{jkS ZtI‚„S Y‚S
t‚s$%‚S }Bjs„$kS BPS ul/S bY$j‚S Y$RS }„B}‚„kS $RS tBS ‚%‚tS s}}j${sAj‚S BS
8BZts$tRS wR‚‚S P$Z„‚S S A‚jBbDS 3„B8S sS p„${‚stS }B$tS BPS %$‚bS $S R‚‚8RS
YsS "‚j‚}YstRS IBS tBS sj,"S $RS RB8‚bYsS 8B„‚S 8‚st$tPZjS YstS
"8BZts$tRS IBS tBS sj,"S qY$RS RZAj‚S I$PP‚„‚t{‚S $tS Y‚S bBS {sR‚RS BPS
t‚s$BtS $RS {„Z{$sjS $tS }‚„PB„8$tS {B88BtR‚tR‚S „‚sRBt$tS $tS jstZs‚S
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
ES]BtR‚„%s$%‚jkSY‚S8s}}$tS8$YSA‚SsSYB8B8B„}Y$R8SstIStBSstS$RB8B„}Y$R8S
ZtI‚„RstI$tSqY$RS$RSsjRBS„‚js‚ISBSY‚StB$BtSBPSY‚S$88ZsA$j$kSBPSsS
P‚sZ„‚S w7jB8stS ‚S sjS dMDS bY${YS $RS YBZYS BS „‚Pj‚{S Y‚S I‚„‚‚S BS
bY${YSsS{Bt{‚}SI‚}‚tIRSBtSsS{‚„s$tSP‚sZ„‚SwB„S{Bt%‚„R‚jkSYBbS{‚t„sjS
$RSsS{‚„s$tSP‚sZ„‚SBSY‚SI‚P$t$$BtSBPSsS{Bt{‚}DS3B„S‚-s8}j‚SPB„SRB8‚S
}‚„RBtS }S ¬iZtw}DS $RS s„ZsAjkS j‚RRS RZ„}„$R$tS YstS ¬Gsj,w}DS bY${YS $tS
Z„tS$RSj‚RRSRZ„}„$R$tSYstS¬B%‚w}DSqYsS$RS$S$RS8Z{YSYs„I‚„SBSsRRZ8‚S
Y‚S$88BA$j$kSBPSsS}‚„RBtSYsSBSsRRZ8‚SYsSsS{‚„s$tS}‚„RBtS8$YStBS
A‚SsAj‚SBSbsj,SB„S„ZtSytSBZ„S8BI‚jSRZ{YS8‚sRZ„‚RSw$t{jZI$tSsS8‚sRZ„‚S
BPSRZ„}„$R‚DS{BZjISA‚S‚sR$jkS{B8}Z‚IS
S
S                                          sX%v
S
S
S                          aXmR%|ulsX %v          VBRƒu|sX %v
S
S
S                      M%'%vsX%v                               ¬ sj, w- D
S          ¬ sj, w- D
S
S                                  WCvG%vI
S
S                                    + ul/ −        ¬ sj, w- D
S
S                         ƒu%Cvul            %ƒƒu%Cvul
S
S
                                     S
           3$Z„‚SSBZts$tRS‚j‚}YstRSstIS}B‚8RSIBStBSsj,S


Si‚sRBt$tSb$YS]B88BtR‚tR‚S€tBbj‚I‚S
GYsS b‚S s„‚S RZ‚R$tS $tS Y$RS }s}‚„S $RS sS }„B{‚RRS YsS bBZjIS YB}‚PZjjkS
j‚sIS BS Y‚S I$R{B%‚„kS BPS Y‚S BtBjBkS BPS {B88BtR‚tR‚S ,tBbj‚I‚S qY$RS
sjBt‚S bBZjIS {j‚s„jkS IBS j$j‚S BS AZ$jI$tS tsZ„sjS jstZs‚S ZtI‚„RstI$tS
RkR‚8RS Ztj‚RRS stS $tP‚„‚t{$tS R„s‚kS YsS Z$j$9‚RS Y$RS BtBjBkS $RS
}„B}‚„jkSPB„8Zjs‚ISGY$j‚SY‚SBtBjBkS}„B%$I‚RSY‚SRktY‚${S,tBbj‚I‚S
YsSstSWN=SRkR‚8S8$YSt‚‚ISstSWN=SRkR‚8S8ZRS{j‚s„jkSZR‚SJZ$‚SsS
A$SBPSstsjk${S,tBbj‚I‚SVSk}${sjS‚-s8}j‚SbBZjISA‚SY‚SPBjjBb$tUS
S
w∀} {d  { 1 Dws}}w} {d D ∧ $Rsw{ d  { 1 D ⊃ s}}w} {d DD S              wdnDS
S
qYsS$RSstkS}„B}‚„kSYsSs}}j$‚RSBSsS{Bt{‚}Ss}}j$‚RSBSsjjS$RSRZAk}‚RS
]j‚s„jkSY‚„‚Ss„‚StZ8‚„BZRSBY‚„SRZ{YS„Zj‚RSYsS{BZjISA‚SsII‚ISVtBY‚„S
$8}B„stSBAR‚„%s$BtSY‚„‚S$RSYsSY‚SRkR‚8SYsSb$jjS‚%‚tZsjjkS‚8‚„‚S
b$jjS k$‚jIS sS 8Z{YS „${Y‚„S k}‚S R„Z{Z„‚S YstS Y‚S wPjsDS k}‚S RkR‚8RS
k}${sjjkS sRRZ8‚IS $tS PB„8sjS R‚8st${RS w‚S BtsZ‚S dnDS 3B„S
‚-s8}j‚S PB„8S Y‚S Y$‚„s„{YkS $tS P$Z„‚S nS Bt‚S {stS {j‚s„jkS ‚RsAj$RYS Y‚S
PBjjBb$tUS
Gul/ U w‚ MIsX%v →  D S                                                     wd;DS

 Gƒ% U w‚ =Y9uv → w‚ `Cvv →  DD S                                            wdxDS
S
qYsS $RS :b„$‚:S $RS tBS R$8}jkS sS „‚js$BtS A‚b‚‚tS bBS ‚t$$‚RS AZS sS
„‚js$BtSA‚b‚‚tSbBSR}‚{$P${Sk}‚RSBPS‚t$$‚RSWB‚SY‚S$8}B„st{‚SBPSY$RS
R‚}SwBPS{B8A$t$tSPB„8sjSR‚8st${RSb$YSsS„${YSk}‚SY$‚„s„{YkDSYBb‚%‚„S
3B„S ‚-s8}j‚S wdxDS Rs‚RS YsS b„$‚w-kDS $RS b‚jjTk}‚IS sRS jBtS sRS
%Ruw-=Y9uvDSstIS%Ruwk`CvvDSytS‚t‚„sjS
S
b‚jjqk}‚I w'w‚DD ≡IP k}‚w' w‚8 →  DD ∧ k}‚w‚ s D ∧ %Ruws 8 D
b‚jjqk}‚I w'w‚d ‚1 DD ≡IP k}‚w' w‚8 → w‚t →  DDD ∧ k}‚w‚d s D ∧ k}‚w‚1  AD
SSSSS∧ %Ruws 8D ∧ %RuwA tD
S
B„‚S$8}B„stjkSYBb‚%‚„SY‚S{B8A$ts$BtSBPSsS„${YSk}‚SY$‚„s„{YkSstIS
sS„$B„BZRSR‚8st${RSRYBZjISRY‚ISRB8‚Sj$YSBtSY‚SR‚8st${RSBPS{B8}BZtIS
tB8$tsjRS3B„S$tRst{‚Sk}‚S$tPB„8s$BtS8$YS‚-}js$tSbYkS„‚8B%$tSY‚S
8$IIj‚StBZtSPB„8SwdEDS{Yst‚RSY‚SRZA`‚{S{BtR$I‚„sAjkSbY$j‚SY‚SRs8‚S$RS
tBS„Z‚S$tSwdDS
S
]B8}Z‚„SABB,SRsj‚S                                                     wdEDS
ytPB„8s$BtS8sts‚8‚tSRkR‚8S                                          wdDS
S
7Z{YS„Zj‚RSs„‚S$8}B„stS$tSsS%s„$‚kSBPSjstZs‚S}„B{‚RR$tSsR,RSstIS$tS
}s„${Zjs„S$tSB}${TAsR‚IS$tPB„8s$BtS„‚„$‚%sjSVS{B8}BR$$BtsjSR‚8st${RS
YsS ‚-}jB$RS sS „${YS k}‚S Y$‚„s„{YkS RYBZjIS Y‚„‚PB„‚S Ps{$j$s‚S Y‚S
I‚%‚jB}8‚tSBPSsS8‚st$tSsj‚A„sSPB„S‚-s8}j‚SBS‚-}js$tSbYkSPs,‚SZtS$RS
tBSw‚-s{jkDSsSZtSbY‚„‚sRS$8}B„‚ISZtS$RS%‚„kS8Z{YSsSZtSqY‚R‚Ss„‚S
}„‚{$R‚jkSY‚S,$tIRSBPS$RRZ‚RSYsSYs%‚S}„B8}‚ISY$RSbB„,SstIS8Z{YSBPS
Y$RS$RS{Z„„‚tjkSZtI‚„SI‚%‚jB}8‚tS


MS]Bt{jZI$tSi‚8s„,RS
ytS Y$RS }s}‚„S b‚S s„Z‚IS PB„S stIS }„‚R‚t‚IS sS t‚bS s}}„Bs{YS BS Y‚S
RkR‚8s${SI‚R$tSBPSBtBjB$‚RSBPS{B88BtR‚tR‚S,tBbj‚I‚SqY‚S8‚YBIS$RS
AsR‚IS BtS Y‚S AsR${S sRRZ8}$BtS YsS XjstZs‚S ZR‚"S {stS Z$I‚S Y‚S
{jsRR$P${s$BtS }„B{‚RRS qY$RS $I‚sS $RS $tS Z„tS „BB‚IS $tS 3„‚‚:RS }„$t{$}j‚S BPS
]B8}BR$$Btsj$kSstIS$RSR$8$js„SBSY‚S$I‚sSBPSk}‚S$tP‚„‚t{‚S$tSR„BtjkT
k}‚IS }Bjk8B„}Y${S }„B„s88$tS jstZs‚RS qY‚S ‚-}‚„$8‚tS b‚S
{BtIZ{‚ISRYBbRSY$RSs}}„Bs{YSBSA‚SJZ$‚S}„B8$R$tSsRS$SR‚‚8RSBSYs%‚S
stRb‚„‚IS sS tZ8A‚„S BPS JZ‚R$BtRS R$8Zjst‚BZRjkS ytS }s„${Zjs„S Y‚S
s}}„Bs{YSR‚‚8RSBSw$DS{B8}j‚‚jkS„‚8B%‚SY‚St‚‚ISPB„S8Zj$}j‚S$tY‚„$st{‚S
w$$DS }„B%$I‚S sS BBIS 8BI‚jS PB„S j‚-${sjS s8A$Z$kS stIS }BjkR‚8kS stIS w$$$DS
RZ‚RSsS}jsZR$Aj‚S‚-}jsts$BtSBPS8‚s}YB„S$tStsZ„sjSjstZs‚S
    Z{YS BPS bYsS b‚S }„‚R‚t‚IS Y‚„‚S $RS bB„,S $tS}„B„‚RRS 8B„‚S RBS YstS sS
P$tsjS„‚RZjSqY‚„‚PB„‚Sb‚Ss„‚Sb‚jjSsbs„‚SYsS$S8$YSA‚SJZ$‚Ss8A$$BZRS
BS‚-}‚{SY$RS}„B{‚RRSBSk$‚jISsS{B8}j‚‚S{jsRR$P${s$BtS$tSsSR„${SA$ts„kS
„‚‚S wtBS 8Zj$}j‚S $tY‚„$st{‚S stIS tBS j‚-${sjS s8A$Z$kDS S G‚S 8ZRS sjRBS
tB‚SYsSsStZ8A‚„SBPSBY‚„SsR}‚{RSBPSY$RSbB„,Sb‚„‚StBSI$R{ZRR‚ISY‚„‚S
RZ{YSsRSY‚S}s„TbYBj‚S„‚js$BtRY$}SytS}s„${Zjs„S$SR‚‚8RSYsSRB8‚SAZS
tBSsjjS%‚„ARSYsSs}}jkSBSsS{Bt{‚}Ss}}jkSBSY‚$„S}s„RS3B„S‚-s8}j‚S
„BbS$tSs}}w„Bbj‚DSstISs}}w„Bbs„8DS$RS%‚„kS8Z{YS„‚js‚ISBS„BbS$tS
s}}w„Bb}‚„RBtDSqYsS$RSbY‚tSb‚S„‚P‚„SBSsS}‚„RBtS„Bb$tSs$tS‚{S
b‚S s„‚S$tI$„‚{jkS„‚P‚„„$tSBSY‚S„Bb$tSB„Ss$tSBPSY‚S}s„RSVtBY‚„S
$8}B„stS }s„S BPS Y$RS bB„,S $RS BS sjRBS I$R{B%‚„S Y‚S tsZ„‚S BPS Y‚S
„‚js$BtRY$}SA‚b‚‚tSw‚tZ$t‚DSk}‚RSw‚S=Y9uvDSstIS„Bj‚RSYsS{Bt{‚}RS
}jskS w‚S su|XƒS 5uXƒS ‚{DS ytS Y$RS „‚s„IS sS tZ8A‚„S BPS ‚8}B„sjS
sR}‚{RS8ZRSsjRBSA‚SPB„8sj$9‚IS
     VS„‚sSI‚sjSBPSbB„,S$RSR$jjSt‚‚I‚ISBSPB„8sj$9‚SY‚S‚t$„‚Ss}}„Bs{YSsRS
b‚jjSsRSbB„,SBZSY‚S%s„$BZRS$tP‚„‚t{‚S„Zj‚RSYsSb$jjS‚%‚tZsjjkSA‚St‚‚I‚IS
$tSsStsZ„sjSjstZs‚SZtI‚„RstI$tSRkR‚8SG‚SYs%‚Ssj„‚sIkSRZ{{‚RRPZjjkS
ZR‚ISRB8‚SBPSY‚S$I‚sRS}„‚R‚t‚ISY‚„‚S$tSWN=SsR,RSRZ{YSsRSI‚%‚jB}$tSstS
‚PP${$‚tSstIS{Bt$$%‚jkS}jsZR$Aj‚S$tP‚„‚t{$tSR„s‚kSBS„‚RBj%‚SJZst$P$‚„S
R{B}‚S s8A$Z$$‚RS sS Y‚S }„s8s${S j‚%‚jS wR‚‚S 7sAsS mS ]B„„$%‚sZS 1((dDS
GY$j‚S BZ„S $88‚I$s‚S BsjS $RS BS I$R{B%‚„S Y‚S BtBjBkS BPS {B88BtR‚tR‚S
,tBbj‚I‚S BZ„S Zj$8s‚S BsjS $RS BS AZ$jIS RkR‚8RS YsS {stS ZtI‚„RstIS
R}B,‚tS jstZs‚S qY$RS sR,S YsRS }„B%‚tS BS A‚S 8B„‚S {Ysjj‚t$tS YstS YsRS
‚%‚„SA‚‚tS$8s$t‚ISqZ„$tS8$YSYs%‚SYsIS$S„$YSsjjSsjBtUSsS8s{Y$t‚S
YsS{stS{Bt%‚„R‚S$tSR}B,‚tSjstZs‚S8ZRSA‚SstS$t‚jj$‚tS8s{Y$t‚S


i‚P‚„‚t{‚RS
Allen, J. (1987), WsZ„sjS NstZs‚S =tI‚„RstI$t, Benjamin/Cummings, Menlo
   Park, CA.
Asher, N. and Lascarides, A. (1998), The Semantics & Pragmatics of
   Presupposition, FBZ„tsjSBPS7‚8st${R, dx:239-299.
Bateman, J. A. 1995. On the Relationship Between Ontology Construction and
   Natural Language: a Socio-Semiotic View. International Journal of Human-
   Computer Studies, 43: 929-944
Charniak, E. (1993), 7s$R${sjSNstZs‚SN‚s„t$t, Cambridge, MA: MIT Press.
Charniak, E. (1986), A neat theory of marker passing. In _„B{‚‚I$tRS BPS Y‚S 3$PYS
   Ws$BtsjS ]BtP‚„‚t{‚S BtS V„$P${$sjS yt‚jj$‚t{‚ , pp. 584--588, Los Altos, CA,

   Morgan Kaufmann.
Fuzzy logic vs. possibilistic logic, yeeeSe-}‚„, 9(4), pp. 15-19
Dummett, M. (1981), 3„‚‚US _Y$jBRB}YkS BPS NstZs‚, Harvard Univ. Press,
   Cambridge: MA.
Elkan, C. (1993), The Paradoxical Success of Fuzzy Logic, In _„B{‚‚I$tRS BPS Y‚S
   ddYS Ws$BtsjS ]BtP‚„‚t{‚S BtS V„$P${$sjS yt‚jj$‚t{‚S AAAI-93, pp. 698-703.

   AAAI Press.
Fodor, J. A. (1998), ]Bt{‚}RS TS bY‚„‚S {Bt$$%‚S R{$‚t{‚S b‚tS b„Bt, Oxford
   University Press: NY.
Guarino, N. and Welty, C. (2000), A Formal Ontology of Properties, In _„B{‚‚I$tRS
             Y
   BPS Y‚S d1 S ytS ]BtPS BtS €tBbj‚I‚S et$t‚‚„$tS stIS €tBbj‚I‚S sts‚8‚tS

   NW]7   , Verlag.
Hirst, G. (1986). 7‚8st${S yt‚„}„‚s$BtS stIS Y‚S i‚RBjZ$BtS BPS V8A$Z$k.
   Cambridge University Press, Cambridge
Hobbs, J. (1985), Ontological Promiscuity, In _„B{‚‚I$tRS BPS Y‚S 1n„IS VttZsjS
   ‚‚$tS BPS Y‚S VRRB{$s$BtS PB„S ]B8}Zs$BtsjS N$tZ$R${R , pp. 61-69, Chicago,

   Illinois, 1985. ACL.
Hobbs, J. R., ‚Ssj. (1993), Interpretation as Abduction, V„$P${$sjSyt‚jj$‚t{‚, En:69-
   142.
Kurtzman, H. and MacDonald, M. (1993), Resolution of Quantifier Scope
   Ambiguities, Cognition, 48, 243-279.
Lenat, D. B. and Guha, R.V. (1990), Z$jI$tS Ns„‚S €tBbj‚I‚T sR‚IS 7kR‚8RUS
   i‚}„‚R‚ts$BtSstISytP‚„‚t{‚S$tSY‚S]O]S_„B`‚{ . Addison-Wesley.

Mahesh, K. and Nirenburg, S. (1995), A Situated Ontology for Practical NLP, In
   yF]VyTxS GB„,RYB}S BtS sR${S !tBjB${sjS yRRZ‚RS $tS €tBbj‚I‚S 7Ys„$t , IJCAI-

   95, August 1995, Montreal, Canada.
Montague, R. (1973). The Proper Treatment of Quantification in Ordinary English,
   In Thomason (1974).
Montague, R. (1970), English as a Formal Language, In Thomason (1974).
Pereira, F. C. N. and Pollack, M. E. (1991), Incremental Interpretation, V„$P${$sjS
   yt‚jj$‚t{‚, x(:37-82.

Pustejovsky, J. (2001), Type Construction and the Logic of Concepts, In P. Bouillon
   and F. Busa (eds.), qY‚S7kts-SBPSGB„IS‚st$tR, Cambridge University Press.
Reinhart, T. (1997), Quantifier Scope: How Labor is Divided between QR and
   Choice Functions, N$tZ$R${RSstIS_Y$jBRB}Yk, 1((4): 335-397
Saba, W. S. and Corriveau, J.-P. (1997), A Pragmatic Treatment of Quantification
   in Natural Language, In _„B{‚‚I$tRS BPS Y‚S dS Ws$BtsjS ]BtP‚„‚t{‚S BtS
   V„$P${$sjSyt‚jj$‚t{‚ (AAAI-97), pp. 610-615, Morgan Kaufmann.

Saba, W. S. and J-P. Corriveau (2001), Plausible Reasoning and the Resolution of
   Quantifier Scope Ambiguities, 7ZI$sS NB${s (Special Issue on Commonsense
   Reasoning), E(2):1-19
Schank, R. C. (1982), *kts8${S ‚8B„kUS VS qY‚B„kS BPS N‚s„t$tS $tS ]B8}Z‚„RS stIS
   _‚B}j‚, Cambridge University Press, New York.

Sloman, AS., Love, B. and Ahn, W-K. (1998), Feature Similarity and Conceptual
   Coherence, ]Bt$$%‚S7{$‚t{‚, 11(2):189-228.
Sowa, J. F. (1995). €tBbj‚I‚S i‚}„‚R‚ts$BtUS NB${sjS _Y$jBRB}Y${sjS stIS
   ]B8}Zs$BtsjS3BZtIs$BtR. Boston, MA: PWS Publishing Company.

Thomason, R. (1974), Editor with an Introduction, 3B„8sjS _Y$jBRB}YkUS 7‚j‚{‚IS
   _s}‚„RSBPSi${Ys„ISBtsZ‚, Yale University Press.

van Deemter, K. (1996), Towards a Logic of Ambiguous Expressions, In K. van
   Deemter and S. Peters (eds.), 7‚8st${S V8A$Z$kS stIS =tI‚„R}‚{$P${s$Bt, pp.
   55-76, CSLI, Stanford, CA.
Wilks, Y. (1975), A Preferential, Pattern-Seeking, Semantics for Natural Language
   Interface, V„$P${$sjSyt‚jj$‚t{‚, E:53-74.
Zadronzy, W. and Jensen K. (1991), Semantics of Paragraphs, ]B8}Zs$BtsjS
   N$tZ$R${R, d(2):171-209.

</pre>