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Complexity of Contextual Reasoning

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(1)UNIVERSITY OF TRENTO DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY 38050 Povo – Trento (Italy), Via Sommarive 14 http://www.dit.unitn.it. COMPLEXITY OF CONTEXTUAL REASONING Luciano Serafini and Floris Roelofsen. April 2004 Technical Report # DIT-04-027.

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(13) T<+H. `:RUWYXEM[XC8^NY` VX*6'JI RUX*6 % L('*)K+=ZN % L('-,6T<+=M[ZL XM=+ M[ZN+_R%P9+=_L ` VL `78%`(Z5XM+=X?M RUZ\RBAO5 6+=X X*65`(cK8%`S`P'NQR65`78%`IL ` VL `78%`(Z5XS+=XOM RUZ8+T+W@8(X2(` PSR/56 `(L `(Z5XU T M A % LP'*)"V 8J%8 `S`78W+X27=+ _[_Y3ZA RUL M[Z(8 XM=+ Z;PS`73 X*56 `(Z % L('-, V 8 T+W@(8 X %8 `S`%8 RUT#`27=+ _[_ X R%RD'. Wg €´\Îw{wqF_€ “Fgƒ`;_aq[|}sc„]6sg’[_I€ |ð[‘v’$\{qos„gƒc}cgrw^]6sgƒ“w{_5‘ƒ]dwucgƒòFcgƒ|}gƒqosv]As„\Î_dq[|‘°]6q ˆg‘°]6òFs„ð[c}gƒ“~ _ac}`Í]dw{w{xd 3†YðFc·ò•_d\Îqos·_d~“[gròl]dcHs„ð[c}g\Î|(]|}grs(_6~•\{q[“[\{‘ƒgƒ|"[u · ]d‘v’\Îq[“Fg"‰ ] PSRUZ5X `baX½X·€´’[\Αv’ \Î|“[gƒ|}‘ƒc\{ˆ•gr“ ˆoxß]‘ƒ_ac}cgƒ|}ò•_dq[“[\ÎqFñ~ _ac`b]d&w "½\Îq \?] [ “[gƒqF_ds„gr|b\ s’[\Î|Ƒƒ]d|g¿|}s„]dq[“l]dc}“ ò[c}_aò_a|\fs„\Î_dql]d[w $ w^]dqFñaðl]dña1g ^U_, ‚P3_b|Hsv]6sgYs„’l]6s]ò[c_dò•_a|}\{s\Î_aql]6w ~ _ac}`ið[wÎ0] ` \ÎqÙs„’FgbwÎ]dq[ñaðl]6ña<g ^U_‚’[_aw{“[|¿\Îq ‘ƒ_aqos„g ‰*s \ €JgbðFs„\{wÎ\ rgi|_ATQ‘°]6wÎwÎgr\“ _a+@2(`(_` N A RUL,T+WY_a+H8$_d~Æs’[gÍ~ _ac}` \ kb` " €´’[grq q[_Ù]d`iˆF\Îñað[\fsQx ]dc\{|gr|€‚g€´\ÎwÎw |}\Î`;ò[w{xÙc}gr~ gƒc s_ _a+@2(`(_` NA RUL,T+WY_a+H8;]dc| A RUL,T+WY_a+H8U$  _dc`ið[wÎ]d|´s„’l]6sY]dò[ò[wfx‹s_$“[.\ '•gƒc}gƒqosY‘r_aqos„g"‰*s| `b]°xˆg¿c}gƒwÎ]6s„gr“‹ˆoxÓ|}_6TQ‘ƒ]dwÎw{gƒd“ 2L,MON%KY`!L,W-_`78" (PƒFgƒ|g]dcgYg ‰5ò[cgr||\{_aq[|_d~s’[gY~ _ac6` k "Hh $ \ N k>e N fhgPghg(f \ È kie kÈ j \ ki` €´’[grcg \ N fhghgPg(f \ È f \l] [á]6q[m“ e N fhghghgf e È f ` ]dcg~ _ac}`ið[w^]6|ƒ ”S_ds„gs„’[]6s  j ؓ[_*gƒ| q[_6sW“[grq[_dsgi\Î`;ò[wÎ\{‘°]6s\Î_aq " €J7g l w{wðF|ng (oJb~ _dcs„’F\Î|Sò[ð[cò_a|}%g $" ŽWw{|_ÍqF_ds„g¿s„’l]6sW_að[c k n.

(14) wÎ]dq[ñaðl]6ñag´“[_5gr|Jq[_6s\ÎqF‘ƒwÎðF“[gg ‰5ò[cgr||\{_aq[|w{\6g" \ k>`$8]dq[“ " \ k>`k $ \ ki`Ù\Î| ‘ƒ]dwÎw{gƒ“Øs’[g PSRUZ8%` W5`(Z;PS`]dq[“ \ N k e FN f \ È k e È ]dcg‘°]dw{wÎgƒ“ VL `(T+M-8%`78i_d~ ˆFc\ΓFñagc}ð[wÎg " *Y$ n gW€´c\fs„ g

(15)   "=$J]dq[“  "=$ ~ _ac8s„’[gW‘ƒ_aq[|}gotð[grq[‘ƒg]dq[“Ís’[g|}grs´_d~3]dw{w ò[c}gƒ`;\Î|}gƒ|Æ_d~·]ˆFc\ΓFñagYcð[w{g 5Xlc}gƒ|ògƒ‘"s„\feagƒwfxa é ##"%$¿íè (èî ê èé3ì !'&)("! ê +*rçèé•êIë  -ê ,/.Eîrê°ë 1032 VL RSV5R/8(M[X?M RUZ +=_T+WY_ XOM  ë ·!é ê ½è& PSRUZ5X `baX 8(c/8(X `(T54 – ^b_ _7698 f%:<;>= RHE=`(L18%`(XRBA!M[ZN=M PS`78 [ PSRUZ8(M-8(X*8:RBAl+<8%`(X2RBA VL RSV5RHL 8(M[XOM RUZ +=_m_a+=ZYK=W+%KY`78 – ^b— _ — _7698<+=ZN+<8%`(X2RBAW2L,MON%KY` L(WY_`78 :!; ' OQqÙs„’[\{|Yòl]dògƒcrXE€‚gb]d||}ð[`b?g [‹s„_ӈ•g "½]6s!`b_d|},s $W‘r_að[qosv]6ˆ[wÎg;]dq[“ :<; s„_ӈIg )[q[\{sgd ”S_ds„g‹s„’l]6sbs„’[gØw^]6s}s„grcÍ]d|}|ð[`;òFs\Î_aq1“F_5gr|Íq[_ds]dò[ò[wfx s„_  RÆV*|̀´\{s&’ 8%P765`(T<+=X?M P ˆ[c}\Γ[ñdgÍcðFwÎgƒ|rX(|ð[‘v’]d|ò[c_Ie6]dˆ[\{wÎ\{sQxTY]dq[“ `iðFw{s„\©T:]dñdgƒqosˆgƒw{\Îg"~Æ|}x*|}sgƒ`;6| <=C ÙPƒ[g otð[gr|}s„\{_aq߀´’[g"s„’[grc_að[cic}gƒ|ðFw{s„|`Í]°x ˆ•gñdgƒq[grc„]dw{\ ƒgr“ s„_ᑃ]dòFsð[cgÍs’[gƒ|}g$‘°]d|}gƒ|]d| €‚gƒw{w²\Î|Æ|ðF@ˆ ?}gƒ‘"ss_~ ðFc}s„’Fgƒc´\Îqoeagr|}s\Îño]6s\Î_aq.  ì  "!½Bë A QR65` %#CED X*6+=X A RUL(T<+=_ MGFU`78^X*65`O8(M[X?W+=XOM RUZ M[Z `ba>+=T&V_` *APSRUZ8(M-8(X*8 RBAIX 5 R

(16) PSRUZ5X `baX*8bhn+=ZN$Š>3 NY`78%P(L,M 2(` N2c ^  ^ " J– I f  — $ +=ZN^ y H ^ " J– I f f  — $73 N H L `78 V5`SP(XOM*E=`(_ c '&QR65`6PSRUZ8(X?L +=M[Z5X X*6+=X % L('-,gT+W@8(X

(17) 8%`S`K+$27+=_[_1M A % L('*) 8%`S`78RUZ;`73 M-8. A RUL,T<+=_ MGFU` N 2cX*65` A RU_[_RH5M[ZYK2L,MON%KY`!L,W-_`9K h!k IML  j Š+k IL L  0²grsONd _ ˆ•gÙs„’Fg ‘rw^]d|}|Ø_d~‘ƒwÎ]d||}\Α°]6wY\Îqos„grcò[c}grsv]As„\Î_dq[|Ó_d~ ^b_Q ώq>\{qtsgƒc}ò[cg"sv]6s\Î_aq  ] NdS_ \{|‘°]dw{wÎgƒ“]@_R%P9=+ _ T#RNY`(_S_d~^b,_ OQqos„grcò[c}grsv]As„\Î_dq[|_d~Wgrqos„\Îc}g  RÆV5|b]dcg ‘ƒ]dwÎw{gƒ“QP76=+ M[Z"8 (Pƒ[g"x‹]dcgY‘r_aq[|}scð[‘"s„gr“Ø~ c_d`Ï|g"s„|S_d~w{_5‘ƒ]dw.`;_*“[gƒw{|ƒ [ M-8c+ %8 ` W `(Z;PS` – F_ — _768P3  ë·é! ê½èéPAP" çRQEì@éS0T2 P76=+ M[ZU RH=E `(L +J%8 `(XRBA M[ZN=M PS`78I 5 56 `(L `>`9Y+ P7V6 7_ WXNd!_ M-8 +0%8 `(X RBA _R%P9=+ _T#RNY`(_Y>8 RBAl^b_ V' 6M-8 \ L PSRUZ(8 M-(8 X `(Z5X&M YA F_ M-8 Z;RUZ;`(T&VXOc [ ' Z(XEM-8 V5RUM[Z5X L 5 M-%8 ` M A \] 7 _ \_^ hA RULW=+ _[_ \ ] M[ `U%8 `(X L 5 M-%8 `:RUXC56 `(LF5 M-%8 `P' Ž‘v’[]d\Îq‘ƒ]dq$ˆgWs„’[_dð[ña’os´_d~3]d|Æ]|grs´_6~

(18) } gƒò[\{|}sgƒ`;\ΑW|Hsv]6sgƒ| [ X[g°]6‘v’‹‘r_acc}gƒ|}ò•_aqF“[\Îq[ñ s_ ]ّƒgrc}sv]6\Îq‘ƒ_aqos„g ‰*s "½_dcb]6ñagƒqos,$ «Pƒ[gÓ~½]d‘"s;s’l]6sa 7W_ ‘r_aqosv]d\{q[|`b_ac}g$s„’l]dq_aq[g w{_5‘ƒ]dwu`b_*“[gƒw]d`;_að[qos|Js„_ ^b._ ˆ•gr\Îq[ñi\{qos„gƒc}ò[cg"sv]dˆFwÎgW\{qÍ`;_acgSs„’l]6q_aq[gðFq[\otð[gS€]°xa . 5V _FX|}grs}TC€´\Î|}gá‘v’l]d\ÎqF|$‘ƒ_ac}cgƒ|}ò•_dq[“ s_ òl]dcHs„\^]6w&tq[_I€´wÎgr“[ñag=!ò_a\ÎqosHT,€´\Î|}g‘v’l]d\{q[|s„_ ‘r_a`bòFwÎgrsg tq[_I€´wÎgƒ“Fñagd  ì  "!½Bë bcC RUZ8(MONY`(L8X*65`8(M[XOW+=X?M RUZJNY` VM P(X ` N+M[Zed1M K=W-L ` * ' I RUX*6K+%KY`(Z5X*8J6+DE=` PSRUT&V_`(X `b.UZ;RH52_` N%KY`73 PSRUL,L `78 V5RUZN=M[ZYK X R+EV5RUM[Z5X L 5M-8%` P76+=M[Z –o–oJ– I f  f –oJ– I f f f S —o— —o—o— ' g.

(19) . Mr. 2. \{ñað[cgYŠ-k(Pƒ[g¿òl]dc}s\^]dw{w{x;’[\{“[“[gƒq‹`b]dña\Αˆ•_°‰ Mr.1. ` P9+=Z M[T<+%K=M[Z;`+ 8%PS`(Z +=L,M R65RH5 `E=`(L73GM[Z 5 6YM P76 % L('*)<+=ZN % L('-, V 8

(20) E%M `5 8+=L `&L `L / 8(XOL,M P(X ` N X R X*65`+L,M KH6YX 6+=_ AO+=ZN6X*65`I_`CA,X L T#R/8(X 8%`SP(X?M RUZARBA:X*65`X2(Rea43J+H8INY` VM P(X ` N M[Z d1M K=WYL ` * ' R 5 3<2(RU*X 6 % (L '*)N+=ZN % (L '-, 6+DE=`

(21) RUZ5_ c6V +=L,XOM +=_c.UZ;RH52_` N%KY``XC65`(M[L

(22) RD28%`(LFEH+=X?M RUZ8  H <T +=Xc 2(` M[Z5X `(L VL `(X ` N#M[Z N=M  `(L `(Z5X 5 +=/c 8P'<QR6Y-M 8!-M 8 L ` `SP(X ` KN 2c*X 65` 8%`(X L 5-M 8%`:7P 6+=M[Z K. a– –JI f S — f – I f f —o— 3 –o–I f f f f — f –I f f f  — f –I f f S — f –JI f f  —a— Pƒ[gWgƒò[\{|}s„gr`b\{‘W|Hsv]6sgƒ|Js’l]6sÆ]i‘v’[]d\Îq‘r_aq[|}\Î|}s|_d~E‘r_aq[‘ƒgrcq RUZ;`+=ZNIX*65`8P+=T#`W|\fs„ð5T ]6s\Î_aq. (Pƒ[gƒc}gr~ _ac}gdX]dcˆF\{s„c]dc}xÍ|g"s„|W_6~w{_5‘ƒ]dwÐ`;_5“[grwÎ|Æ`b]°xq[_ds]dwf€]°x*|S‘ƒ_aq[|Hs„\fs„ðFsg] }|}gƒq[|}\Έ[w{gP‘v’l]d\Îq. Pƒ[gJ|_a`;gr€´’l]Ase6]dñaðFgJ‘ƒ_dq[‘ƒgròFs„\{_aq_d~ }|grq[|\{ˆ[\Îw{\{sQxi\{|‘ƒ]dòFsð[cgr“ ˆoxs’[g!`b_ac}g~ _ac`b]dw•q[_ds„\{_aqÓ_d1~ }ˆ[c\{“[ñagYc}ð[wÎgY‘r_a`bòFwÎ\^]6q[‘ƒ(g |ògƒ‘ƒ\ )lgƒ“‹ˆgƒwÎ_I€!  ë·é! ê½èéPbP" çè  "! ìlé aëØìlé ,.ìFê ½î ì E ! ê .E0 `(X l2(`+P76+=M[Z3R` + A RULFL T+WY_a+gRHE=`(L ^b_M3k+=ZN N+=Z `(_`(T#`(Z5X RBAX*65`X8%`(X RBA2L,MON%KY` L,W-_`78 RBA + T+WY_ XOM*L . . .

(23) . . :<; N ' )@' R\H \ ki` M A  \H ` M[Zd+6P(_a+H878(M P9+=_ 8%`(Z8%` A RULW+=_[_ _R%P9+=_;T#RNY`(_Y8  ] 7_B' ` 8P+=cX*6+=XE O8P+=X?M-8 7` 8 \ k@` ' ,i' PSRUT&V_ M `78 5M[X*6  M A `(M[X*65`(LU -\H

(24)   "=$RULU  \ k A RUL 8%RUT#` \ k ] M "  = $P' #. PSRUT&V_ M `78k5M[X*6 M A!M[X2PSRUT&V_ M `785M[X*6

(25) `E=`(L,cR ] ' ' 8P+=X?M-8 `78 \ kZ` M[Z@PSRUT&V_ M +=Z;:<PS; `W5M[X*6 :!; M A 8P+=X?M-8 `78 \ kZ`;+=ZNJ:<PS; RUT&V_ M `78 5M[X*6 :!; '. XC6+=X 8P+=X?M-8 `78 \ k>` M[Z PSRUT&V_ M +=Z;PS`

(26) 5M[X*6  '*Z A XC65`(L `&M-8k+=Z \ L PSRUZ8(M-8(X `(Z5X P76+=M[Z : 3 5 1 ` P 8 = +  c C X  6 = + X i k ` M 1 8 P 8 = + O X M  8  @ +  2 _`!M[Z  N  ' \ :<;. PSRUZ5X `baX (8 c/8(X `(T. Pƒ[g¿‘ƒ_dqtsg"‰*s„ð[]dw|]6s„\{|b)u]6ˆ[\Îw{\{sQxbò[c_aˆFwÎgƒ`‹X[s„’FgƒqÐXu\Î|Æs_b|}grsswÎg!€´’[grs’[gƒcS_ac´q[_dsW]|grs _d~w^]6ˆ•grwÎgƒ“~ _dc`ið[wÎ]d| \Î|Æ|„]As„\Î| )u]dˆ[w{gY\Îq‹]`ið[wfs„\fT,‘ƒ_aqosg"‰*s´|}x*|}sgƒ5 ` N  h +=ZNÓ>Š 3 NY`78%P(L,M 2(` N2cK^ " –  — $  ì  "!½ë C RUZ8(MONY`(LX+=Z %#CED 5M[XC6APSRUZ5X `baXC8bd +=ZN ^ " – — $G3ELS`78 V5`SP(XOM*E=`(_ c/3 +=ZN?8(W2 `SP(X X RXC65` A RU_[_RH5M[ZYKX2L,MON%KY`!L,W-_`789K h k j :Š k ! h k@  j :Š k ! n . . . . . . .

(27) QR65`UA RUL,T+WY_a+iŠ+k@ -M 818P+=XOM-8. . . ` N M[Z

(28) X*6YM-88(c (8 X `(T 2 c X*65` A UR _[_RH5M[ZYK>P76+=M[Z. K. o– –  — f –  —o— 3 –o– —o— Pƒ[\{|g"‰F]d`;ò[wÎg$c}g lgr‘rs|;s’l]6s`ið[wfs„\©TQ‘ƒ_dqtsg"‰*s|Hx5|Hs„gr`b|;‘°]dq q[_6sˆ•gÓgƒqF‘ƒ_*“[gƒ“\Îqos„_ ò[c}_aò_a|\fs„\Î_dql]dw(wÎ_dña\Α6X|}\Î`;ò[w{xوox \Îq[“[g ‰5\Îq[ñòFc_aò_a|\fs„\{_aq[| Ù|ðF‘v’ ]6qßgƒq[‘r_5“F\Îq[ñ_6~ s’[g¿]dˆ•_Iedg¿|Hx*|}s„gr` €J_aðFwΓӈ•g!\{q[‘ƒ_aqF|\Î|Hs„grqtsƒ OQqÓs„’[g~ _aw{wÎ_I€´\ÎqFñ€‚g¿€´\{wÎwcgr~ grcÆs„_s„’[gY|}grsS_d~ˆ[c\{“[ñagc}ð[wÎgr|Æ_d~  V‹]6| :<; Xl]dqF“ s_s’[g!|g"s_6~‘r_aqos„g"‰*s|W\Îqoed_aw{edgƒ“‹ˆtxÍ~ _ac`iðFw^]d|\{q ]d| · . . . . . . . . 

(29) 

(30)   . . >G.  . . 

(31) . Ž )lc}|}s\Îq[|}\Îña’os´cgrño]dc}“[\Îq[ñs„’Fg‘r_a`bòFwÎg"‰5\fsQx_d~‘ƒ_aqos„g ‰*s„ðl]dw1fih9jÙ`Í]°xӈg¿_dˆFsv]d\{q[gƒ“ ˆox$\{qtedgƒ|Hs„\Îña]6s„\{q[ñ\{s„|Ægrq[‘ƒ_*“[\{q[ñ\Îqos„_`;_5“l]6w p È |]6s„\{|b)u]dˆF\ÎwÎ\fsQxa OQq‹s’[\Î|´|gr‘rs\Î_aqӀJg |}’[_I€s’l]6s]dqox ‘r_aqos„g ‰5sðl]dw‚|„]6s\Î|b)l]dˆ[\Îw{\{sQxáòFc_aˆ[w{gƒ` `b]°x ˆgÍc}gƒ“[ðF‘ƒgƒ“ßs_Øs’l]6si_6~ |]6s„\{|}~ x*\Îq[ñb|_a`;g~ _dc`ið[wÎ];\{q p È X€´’[_a|g`b_*“l]dw²“[gròFs„’á\{|]6s`;_a|}sWg otðl]dw3s„_Í_dq[gd Pƒ[\{|´ò[c_aˆFwÎgƒ` \Î|€‚gƒw{wfT tq[_I€´qÓs„_ˆg”pTQ‘ƒ_d`bò[w{grsg <[iX @ n g¿“Feg )lq[g]is„c]dq[|wÎ]6s„\{_aq " g $ ´_d~w^]dˆgƒw{gƒ“~ _ac}`ið[wÎ]d|\Îqos_;`;_*“l]dw.~ _ac}`ið[wÎ]d| k . _acƈ[c}\Γ[ñdgYcð[w{gƒ|€‚g’l]°edg=k. . " \ kie;$. H. _Ce. N NF fhghgPgPf g\ È " k>\ È e lÈ kie j È $ \ kio e;$ " \ Hkie;$ N N ghghg Ž dTQ‘r_aq[|}\Î|}sgƒq[‘"xӑƒ_aqF|}s„c]d\ÎqosS\Î|Ƒƒ]dòFsð[cgr“؈oxk "GaT,‘ƒ_aqFS| $ H Q3ëtèuíë  # QR65`(L `M-8+0.UL(MV. ` T#RNY`(_p H 4 f Uf = 8(W P76gX*6+=X2p f A RUL8%RUT#` ] +=ZNK " \ ik e " \ kie $ . . . . . .  H M Al+=ZN RUZ5_ cM A X*65`(L ` 5M[*X 6 :!; '.  . . " \ ki;e $   " L PSRUZb8 $   "=$  !_ " 6$# 6&% 6+*, ')(  M-8 + bL PSRUZ8(M-8(X `(Z5X2P76+=M[Z- .CX*6+=XU8P+=X?M-8 `78 /. . . \H . M[ZgPSRUT&V_ M +=Z;PS`.

(32) w0 R1. R3 R2 R2. R2. R3. Î\ ñað[c}g!k*k(Ž |‘v’[gr`Í]As„\Α!tc\{ò9dg!`;_5“Fgƒw.~ _ac S   " $ n gi|}’[_I€ ’F_€ s„_͑ƒ_aq[|Hs„c}ð[‘rs ~ c_d` pß !0²grs

(33) ˆgs„’Fgi\Îqos„grcHT ò[c}grs„]6s„\{_aqÓ_d~ ^b_]d||}_5‘r\^]6sgƒ“$s„_b]i€J_dcwΓ [~ _ac´]dqox [uXlwÎg"s 

(34) \ _Eˆ•g s’[g!cgƒ|Hs„c}\Αrs\Î_aq$_7_669~S8 

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(54) w{_5‘ƒ]dwJ`;_5“Fgƒw_d~ _ |]6s„\{|b)lgr|U² X8]dq[“ ]dqoxßs„c}ðFs„’ e6]dwÎðFg\.' _ \Î| gr`bòFsQxd O,s´\Î|Æg°]6|}x$s„_|}gƒg!s„’l]6s |]6s„\{|b)lgr| S  . .   . . G.  . OQqs„’[\{| |gƒ‘"s„\{_aqÐXo€Jg]dò[òFw{xis’[g´cgƒ|}ð[w{s|‚òFcgƒ|}gƒqos„gr“|_¿~½]dc·s„_¿\Î`;ò[c}_edgƑƒð[c}cgrqtsJ‘ƒ_a`T ò[w{g"‰5\{sQxˆ_að[q[“[|~ _ac  ‘°R]dc}s’oix l |8ò[c_aò_a|}\{s„\{_aql]dwow{_aña\{‘‚_d~‘r_aqos„g"‰*sƒ ·Pƒ[gƈgƒ|}s c}gƒ|}ð[w{s |}_b~½]dc´\Î|´“[ðFgs„_  ]d|}|„]d‘r‘ƒ\ <=C Hg“Fgƒ|‘rc\{ˆ•gr“];s„]dˆ[w{g°]dð5‰tT,ˆl]d|gr“ “[gr‘ƒ\{|\Î_dqØò[c}_5‘rg"T “[ðFcgdXa€´’F\Αv’“[g"s„gƒc}`b\{q[gƒ||„]6s\Îb| )l]dˆ[\Îw{\{sQx!_d~]WEp 03Rß~ _ac`ð[w^] ` \Îqiq[_dq5TQ“[g"s„grc`;\Îq[\{|}s„\{‘ s\Î`;g  "\ ` \ ,$" p 03R ~ _ac}`ið[w^X] `\{qos„_]bw^]dˆgƒw{gƒ“Ó~ _ac`iðFw^]  k ` ]dqF“á]b`iðFw{s„\©T n gs„c]dq[|}w^]6sg]1 ‘r_aqos„g"‰*s´|Hx5|Hs„gr`  RÆmV " `$"Xl|}_is„’l]6s ` \Î||]6s„\{b| )u]dˆFwÎgW\{qÓ1p 0R .\ 'ki` \Î|J|]6s„\{b| )u]6ˆ[wÎg \{q  RÆmV " `$"  ðFc}s„’Fgƒc`;_ac}gdX€‚g|}’[_I€s’l]6s“[grsgƒc`;\ÎqF\Îq[ñ‹€´’[grs’[gƒci_dcq[_ds #kU` hŠ.

(55) \{|¿|]6s„\{|b)u]6ˆ[wÎg\Îq  RÆVm" `$Y‘°]dq ˆ•g;“[_aq[g;\Îq q[_aq*TQ“[g"s„gƒc}`b\{q[\Î|Hs„\{‘ò•_awfx*q[_a`;\^]dw3s„\Î`;g  " \ ` \ y $ n g;òFc_*‘ƒgƒgr“ ]6|~ _awÎw{_€´|r  _acgƒ]d‘v’ qFgƒ|}s\Îq[ñ‹òl]6s}s„grcqAM-8(X " ( NFfhghghg M-8(X " ( È f  $ ghghg $ \{q `‚XwÎg"s  RÆmV "M`$´‘ƒ_aqos„]d\Îq ]b‘ƒ_dqtsg"‰*swÎ]dˆgƒwÎgr“‹€´\fs„’‹s„’[g|gotð[grq[‘ƒg ( N ghghg ( È 0²grs s’[gwÎ]dq[ñaðl]6ñag!_d~(‘ƒ_dqtsg"‰*s ( N ghghg ( È ‘r_aq[|\{|}sW_d~ ]dw{wÐs„’[g]6s„_a`;\Α!ò[c}_aò_a|\fs„\Î_dq[|´\ÎqBSX ò[w{ð[|·]q[gr€«]6s„_d`b\{‘8òFc_aò_a|\fs„\{_aq~ _ac3g°]6‘v’~ _dc`ið[wÎ]S_6~ls„’[gJ~ _dc` M-8(X " ( f $3_*‘ƒ‘rð[cc}\Îq[ñ \{q S (ŽsSw^]d|Hs°X[eg otð[\Îò  RÆmV " `$J€´\{s„’$s’[gY~ _awÎw{_€´\{q[ñiˆ[c}\Γ[ñdgYcð[w{gƒ|"(N k .  k5M-8(X " (  $ (> f  k5M-8(X " (  $ j ( (. ( k f  k@ M-8(X " ( M-8(X?"  $ $ j ( (  (>k@2M-8(X " f  $ f f  k@ M-8(X " ( ( f M-8(X " f  $ $ j (  (>k5M-8(X " f  $. (  (>k. j. €´’[grcg ( H ( N ghghg ( È c}gr~ grc|s_]dqox¿‘ƒ_dqtsg"‰*s(_d~  RÆVm"M`G$"Xd€´’[_d|gJwÎ]dq[ñað[]dñag8‘ƒ_aqosv]6\Îq[| M-8(X " ( f  $J_ac M-8(X " ( f M-8(X " f $ $"  ì  "!½ëcC RUZ8(MONY`(L

(56) ` H  L M-8(X " ( f oC" M-8(X " f  T $ o M-8(X "  f $ $b$P' % CED ` PSRUZ8(M-8(X*8+RBA A RUW-L+PSRUZ5X `baX*8/_a+@2(`(_` N XC65`I`(T&VXOc<8%` W5`(Z;PS` /3 ( 3 ( 3 +=ZN ( 'KQR65` . . . . . . . . . _a+=ZYK=W+%KY`:RBA 3"^

(57) 3 PSRUZ5XS+=M[Z8!X 5 R VL RSV5R/8(M[X?M RUZ873M+=ZN M-8(X " ( f  o " M-8(X " M-8(X "  f  $ $b$ `R^$#PSRUZ5XS+=M[Z88X 5 R8VL RSV5R/8(M[XOM RUZ3  +=ZN+M-8(X " f E> $`^$ H ^ ^$  H ^  'XQR65l` 2L,MON%KY`!L,WY_`78+RBA % CED ` X+=L ` +H818(XS+=X ` NK+@2(RHE=`P '. . . Q3ëtèuíë. – — . . "  A/b/0. ` -M 8

(58) 8P+=X?M-8 +@2_`. +@2_`!M[Z % EC D `D' + XOM-8 +@2M[_ M[X?c^RBAU`AM[Z )D =  Q3ëtèuíë  V5RU_ cUZ;RUT+M =+ _;XOM[T#`  "\ ` \ y $P' . . . M[Z .  . f–   L  =+ $cZo N f —. [C M A+=ZN>RUZ5_ c+M A ki` M-88P+=XOM-8L. C P9+=ZK2(`&PSRUT&VWYX ` N M[Z#Z;RUZL NY`(X `(L,T+M[Z5M-8(X?M P. 3‚x«s’[gƒ_dcgƒ` * ]dqox1|]6s„\{|b)u]6ˆ[\Îw{\{sQxò[c_dˆ[wÎgr` \{q pE03R ‘°]dq ˆgs„c„]6q[|HT ~_ac}`bgr “  \Îqos„_ ] |„]6s\Î| )u]dˆ[\{wÎ\{sQxò[c}_aˆ[w{gƒ` \{q  RÆV• ´Pƒ[\Î|sc„]dqF|}~ _ac}`Í]6s\Î_aq ‘ƒ]dq ˆ•g gr|}sv]6ˆ[wÎ\{|’[gr“‹\{qÓwÎ\ÎqFg°]dcJs\Î`;gd ·eagrc}xو[c}\Γ[ñagc}ð[wÎg  RÆVm"M`G$Y\{qoea_awfeagƒ|¿]6s!w{g°]d|HsY_aq[gò[c}_aò_a|\fs„\Î_dq_d~ s„’[g~ _ac}` M-8(X " ( f  $ (edgƒcHx |ð[‘v’ ò[c_aò_a|}\{s„\{_aq \Î|\{qoea_awfeagƒ“\Îq]6s`;_a|Hs~ _að[cˆ[c}\Γ[ñag$c}ð[wÎgr|ƒ ·eagrc}x |ðFˆF~ _ac`ð[w^]Ó_d~ ` _d~Js’[g~ _ac` M-8(X " (  $I"@]6q[“ q[_6s„’[\{q[ñØgrwÎ|}%g $Ycgƒ|}ð[w{s|\{q ] ò[c}_aò_a|\fs„\Î_dq _d~Æs’[gÍ~ _ac}` M-8(X " ( f  $!\Îq s’[gw^f ]6q[ñaðl]dñdgÍ_d~´g ‰[]6‘rs„wfx _dq[g‘ƒ_dqtsg"‰*s\Îq  RÆ;V "M`$ ¿PƒFgq*ðF`iˆ•grcY_d~ |ðFˆF~ _ac`ð[w^]d|W_d~ `«_d~(s„’Fgi~ _ac` M-8(X " ( f  $S\{|ˆ•_dð[q[“[gr“  "!$#&%%&')(+*!,.-0/1 !2345#6(1!!7#98:(1;"-<%(=%>;"(?%,4(1;@# (?ABC"DEBF GHCJILK1;"-MBN1GHDOGHCPIQ6(1;P%RP%$# ' ,434X%X3.K1#9% %&')(Y*!,4-/1X!2"3Z7# 6(1!!5#8@([;"-Y%(Y%]\^K?R0,Z([_^,Z;P%!(0-02"65-L,Z; S`T1UOa S T1UWV . hIk.

(59) oˆ xT\ ` \‡  c_d` s„’[gr|g_aˆ[|grc}e6]6s\Î_aq[|rXo€Jg`Í]°x‘r_aq[‘ƒw{ð[“[g´s„’l]As‚s’[gqtð[`ˆ•grc‚_d~.ˆ[c\{“[ñag c}ð[wÎgr|>\ \t\{q RÆVm"M`$Æ\Î|´ˆ_að[q[“Fgƒ“‹ˆtx "P\ ` \‡ ð[c}s’[gƒc}`b_dcgdXFˆtxӑr_aq[|Hs„cðF‘rs„\{_aqÐX s’[g´|ð[`:<; _d~s„’Fg w{gƒq[ñds’[|(_d~•s„’[gÆ~ _ac}`ið[w^]6|(g \Îqoea_awfeagr“b \{qb]6qtxˆFc\ΓFñagÆcð[w{gÆ_d~  RÆVm"M`$ \{|´]6s´`b_d|}sÆ~ _að[cr 3‚x s„’[gr_acgr` -lX·|]6s„\{b| )u]6ˆ[\Îw{\{sQxá_d~ kb` \Îq  RÆmV "M`G$‘°]dq ˆg͓Fgrs„grc`;\Îq[gr“ß\Îq s\Î`;=g k \ \ k  \ $b$  " "\ Y\  \ <: ; \ $ "A"  \ \ k>` \   _  6$# 6')( +*, _!   6  ')( . OQq s„’[g;wÎ\{ña’os!_d~Js’[gÍ]6ˆ•_Ieag;_aˆ[|}gƒcHed]As„\Î_dq[|ƒX]dq[“ dgƒgrò[\ÎqFñ\ÎqÙ`;\Îq[“Ùs„’l]As `bgrcgƒwfx r‘ _aq[|\{|}s|S_6~

(60) ki`‚X[€‚g¿`b]°x$cg"€´c\fs„gs„’F\Î|Æ\Îq$sgƒc`;|´_d~b` ]6|k  " \` \y $ . . F

(61) J . (g ’l]°eag ‘v’l]dc]d‘rsgƒc}\ƒgr“¿s’[g(‘ƒ_d`bò[w{g"‰5\{sQx_d~*‘ƒ_dqtsg"‰*s„ð[]dwocgƒ]d|_aqF\Îq[ñƈl]6|gƒ“¿_aq!ò[c}_aò•_AT |}\{s„\{_aql]dw•`ið[wfs„\fT,‘ƒ_aqosg"‰*sÆ|}x*|Hs„gƒ`;|´€´\{s„’>)lqF\{s„g!|}grs„|´_d~ˆ[c}\Γ[ñagYc}ð[wÎgr|ƒ Ž )lc|HsÍ\{q[|\{ña’os;€J]d|;_aˆFs„]d\Îq[gr“ ˆoxgƒ|Hsv]dˆFwÎ\Î|}’[\ÎqFñ ]6q«gƒqF‘ƒ_*“[\Îq[ñ _d~W‘ƒ_aqos„g ‰*s„ðl]dw |]6s„\{b| )u]dˆF\ÎwÎ\fsQx\Îqos_i|„]6s\Î| )u]dˆ[\{wÎ\{sQxi\Îq`iðFw{s„\©TQ`;_5“[]d9w p È X*€´’[\Αv’$\{| tq[_I€´q$s„_iˆgY”WpT ‘r_a`bòFwÎgrsgd ”g ‰*s°XƀJg]d‘ƒ‘r_a`bòFwÎ\Î|}’[gƒ“«] `;_ac g )lq[g TQñac]d\Îq[gr“«ð[òFò•grcˆ•_dð[q[“«~ _acs„’Fg‘ƒ_a`T ò[w{g"‰5\{sQxÓ_6~(‘ƒ_aqosg"‰*s„ðl]6w|„]As„\Î| )u]dˆ[\{wÎ\fsQxˆox];“[\Îc}gƒ‘"sW\{qtedgƒ|Hs„\Îña]6s„\{_aqØ_6~(\{s||}gƒ`b]dqos„\Αƒ]dw ò[c}_aògƒc}s\Îgr|ƒ Hgƒc}gƒ\{q!€‚g8_aˆ[|grc}edgƒ“s’l]6s3`ið[wfs„\©TQ‘ƒ_dqtsg"‰*s²|Hx5|Hs„gr`b|3gƒJq ?}_Ixs’[g ˆ•_dð[q[“[gr“ `;_5“FgƒwÐò[c}_aògƒc}sQxd ŽWw{|_[X•€Jgò[c}_Ie5\{“[gƒ“ ]bsc„]d‘"sv]dˆFwÎgigrq[‘ƒ_*“[\ÎqFñ$_d~ ‘ƒ_aqosg"‰*s„ðl]6w(|„]6s\Îb| )l]dˆ[\Îw{\{sQxÓò[c}_aˆ5T w{gƒ`;|J\Îqos_iò[ð[c}gƒw{xÍò[c_dò•_a|}\{s\Î_aql]6w_dq[gƒ|r 8OQq$“F_a\Îq[ñ|_[XF€‚gYw^]6\Γbs’[gYñac}_að[q[“F€‚_abc b~ _ac ] fih9jT,ˆl]d|gr“Ø\{`bòFwÎgƒ`;gƒqos„]6s„\{_aq_d~‘ƒ_aqosg"‰*s„ðl]6w3c}g°]d|}_aq[\{q[ñ|}x*|}sgƒ`;|ƒ  \{ql]dwÎwfxaX´€Jg _aˆFs„]d\Îq[gr“ \{`bòFc_Ieagr“ ‘r_a`bòFwÎg"‰5\fsQx cgr|ð[wfs„|Ó~ _ac$s„’[g |„]6s\Î| )u]dˆ[\{wÎ\{sQx ò[c}_aˆ[ w{gƒ` \Îq  ‘IR]6c}s„’ox l |Yò[c_aò_a|}\{s„\{_aql]dw²w{_aña\{‘¿_6~(‘ƒ_aqosg"‰*s°XЈox‹s„c]dq[|wÎ]6s„\{q[ñ;\{sS\Îqos„_ s’[g!|„]6s\Îb| )l]dˆ[\Îw{\{sQx;ò[c}_aˆ[wÎgr`s„’[]6sƀJg¿’l]°eag!‘r_aq[|\{“[gƒc}gƒ“Ø\Îq$s„’[\{|Æòl]dògƒcr ðFs„ðFcg$€J_dc ߀´\Îw{wJgrq[‘ƒ_a`;òl]d|}|bg ‰5ò•grc\Î`;gƒqos\Îq[ñ€´\fs„’ˆ•_ds’ ql]6s„\feag‹]dq[“ fih9jT ˆl]6|gƒ “ ‘ƒ_aqos„g ‰*s„ðl]dwcgƒ]d|_aqF\Îq[ñ|Hx*|}s„gr`b|r WŽwÎ|_FX€‚gi]dc}g\{qtsgƒc}gƒ|}sgƒ“s_b€´’l]6sWg"‰*s„grqos _aðFcSc}gƒ|}ð[w{s|S`b]°x$ˆg¿ñdgƒq[grc„]dw{\ ƒgr“Ó|_b]d|Æs„_b]dò[ò[wfxÍs„_;`ið[wfs„\©TQ‘ƒ_dqtsg"‰*s´|}x*|Hs„gƒ`;|´€´\{s„’ |}‘v’[gƒ`b]6s„\{‘Yˆ[c\{“[ñag!cðFwÎgƒ|´]6|´€‚gƒw{wC n. hg.

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