ࡱ> nm),A*"H PNG  IHDR 7W PLTEtRNS AbKGDH cmPPJCmp0712OmIDATxˎ8`^g1{S@8_0j?Y߱Ū߿5+VFX 2`e4h+VFX 2`e4h+VFX 2`e4hq`gw{8w]gf̆Uvj8lc@>jtMc7`[V=ߛ /W@w7&}u 9L⎘ڰ Gn8̀u>{<ဆ,>AUN5kh!nQ=&}=dv>>>"??:~3:{6hu=a}0@ 2*:Y3^6̀䁪,wӈ»,{'Gl}h0u 8{jI!@s7@ ?pb`:]6@.>?#5Upg3C@/㉘*e{+@Y{8.t0 _1`?pv!YczEe[ǟd 3=?a@os&HF{t|c-&(·\N}vR?\]=]v@{!} @8{-sQ*Ճe9adFr;ea5eќ/l3_gk'z?s!O͂b=tG2=͍q@ p2!t瀎>×:;. H$0ݘإPA _k|ǧNG֫8} =pkА5ૼ|G`ay*o4 @3eɋFhɚ:䡀].;y`'}.念#8fV.33cuL@0A)j>pt|,e_\8F H_έ5@:AauH0<=8 sZ@ߑsY7 [a5`(De6Q ys;~J [LdHO$T/{,|̄3B 0x0@(`p:Qh0=_@O@_ ?g#W p_Wa4e-#ހV|S'%Ly^ɾnz'e!=;uaOfwY,Č8ӅtS? Ct|s k{:pǡ8b FWƀ^pO-͂eO0 }-΀N; 3E(/h)oQvIW, 8.Ϡdkyiɂ?)w,޽溾_!kVFX 2`e4h+VFJ5@5`e4h+VFX 2`e4h <; ^6;wD xIA;K~2;7|x!xཇGZ@sv/wCx}@sv7cox} hKA~ + Er48 Мѽ(۞EYVaX.犁{Sȇ9;Ŏu̎O65N|vOw]}J~b%`h׍}}|Zc- =O +V΀,r{X;  P]ހ7}+coFTVFXdşkȬ,?[ˏ8Ы]ibNrG4 @:ܧWg~']2C:𞀞4*yi\(_8) i9x;t1֜5HaZlPՓTXzXhȼ~< YFR, T=sU>[4V&ʪ >E6*)mT^No!`nD-z,! ;`$km ZdؚLd@tG1T+0)\O)Bz/xb+@ `E2}˂t@ nE\S9]ޥ"v@Tg4cE ż /,|b$zsEy"'.%e3(+,xte3{:&6z-vYZzZ<3 OE yJY5g @+Iʢ Fi $ ,V (*;c< @*uC X7;5QpYgqb5S=Fp(2iu)"ݝr\NmkN'q2|Bip=b8J@xf,4"E~ha=ohQp@/ʞ ^n)ˆaS V*;?`(tZ@+Vz~o@FﶀUj,@QH\^u x U6%LQH'өʤyx$YFuA%`dD+w[Z*p5K= l%S*c]:@SF/;.3u,v#=PD3Z,4U3Q]N6PcһrYN s iT:pЗ:Pi 93Z% lR. U} J9 jz$0+^I%;? Nv*`MZ ھ,= d0z ؇#Y2ݒ[jSZS"Py+i+j#P/L=tJ #'B@4 0 @m h`6)?~J\O:zw@M\\OEn|;o7 Xׁi `i_hQTYJ@m54(e!:u= k >[ذZwʌ,,>9~# 8XP,u1j"ˈ?e[u0R{W\50d!~L;d]ieb~Akz~FLeQ" 8D>P cMJwdtL^#9'm]F-t=,Km[ـ9Y2} `s5F %{N)qL tӱmZA^KoRЂE$E^x>դ$`V@M0>P>T3` 0yIu `PJe^<@ש4yz98Jm!: m ΂[31y##:2r34@4&%Y Y`[ 8}&,ڟa-t(MB-+Tԙi.s"f`; z=ZGjYPEjpKGjwFY@~fw@8OG-XA>R9IrFb&>(#  1>Q/ٵb .HҵTиgy hfQ GAW\Z{=OdѿYdI,`yg>ɗ]7e5NωX 2`e4h+VFX 2`e4h+VFX 2`e4h+VFX 2`e4h+V@}I7IENDB`F4R *Z*tJσ6JFIFddDuckydAdobeddd  !1 "A2#Qa3$qBC&R4% !1AQ"a2q#Bb3RrCScs$4ᓳDTd' ?MMMMMpc1`)Jc)JPLaF_`p>ߒ[OK:K}Rl9TP iG)' 0SCn|h u<=~.? TGCH7R*14[#:n1د6wۋx:[G\ m|e{[b0m\kd/# 'PO#pM̲K6&g  S;tT^#('$|_>dO1a>W^r+g lih^Ǡ)o\~=θw+FJ#QX5f]gom!v6h%`D @D&ר#U z`FrKˢ2`NVIڃ͋D]cx@6)Cq Xol֯{8l]UGē@?+bp]'}ઠՉ _y#<sr^ȵ =~B#ʡzyE#\=i쬜5j KYMg,a؄L1W&8UUP8x㬎uv^qH:K˘QQkMҩjQToLiRt>XU , ٓNX Q+ \;vqm[wAUsCY_9#K.:)࿴P%(*\W@h5 ً\퇧&W+4:dHY!D 7melyO/%v ()FnᲀW0Sd.IB@C@[!nʮM ACxA L_$]`QG>*Tp `A?|A8vNGd9ۭk!BLTuQ`El˜EHߧq.ᦗ#\6ۢd.@i|}0:M WHDZ0rվ٩11am.%Yb},ɬ\G $c o;H:h:Kpħ!JbIimYfIу+)R Au"h'Ux]J2B=#KƬAL5.T0e^]*$܋E19`PI_B*PplyOenL2p.[hUCxTH~;ߞsqXY71CiiJpPҨF#L(rB5UP!rr!`( >R t#Oa #f/bjf} x`͢Y$ýd[ [ȹPH6 jdA\mUxK:>$|BQŰOYk,vSz75 9'@p^S}bc  妳&bz)IPnJ`ȡJ`/,Rr1$I#qUe=#cQC61k| KLͤHfǁDV]IVIvnkDs/ #1"-c@)䅾liR7* xt|mn{qM[sY-=~Z񞆽Hyp~z`B*F:Z{#U4vG̎WlapʡݷNb$ޝ#l ܺ9v2=ocO(> $?R> tl팓WKb?2o(hc1Rzo*<(Pq":҂jkKU G:֊WNYdo A8*2p|&pȑrJH 2 ;n"Ā> `LX̽{>M'J,+jv5Qi ap>wREȣ!T1.b۷w8}sZKx㒸B;e4lnhB<RPeH MLK3e@ V 2wm O(-M0=_1y8>3_b[6o^&R@G9xeC޹v|E/ 9(˝An%JN)C|]aV_iI E5ҍ| l,NA'JVhb SH+@+7/T8{1\f:b!RU O$1e"rTΠlr7(;۷="Zhm/RvT5ܟwxK&;XKͲ̻cX4(0sSxWoS:QDo9&oəJ)(=)E)"Ainx6Ư˜$JVbwtٷ) Aھs^sٹ9 En$v &&I(#G')|7-ZI3+FDj:\ |٤^N Q83 }u'M X7 ? ϴT5|ݧ"&Z^E :.S:"u]µ o̧w{ܲ )hh *H&_4R>#Gcƿ>?MK2N\27H&_Le$Ty" TASE'륮'$8ɪ-GOF&cjS@TDM5W'F !|"R3[7vքE>#϶Xfu^LRG%72}!pͧ~s[|=z?U}FMS~-eǣ/OnuZR[zvJֿ uޯ.␃&C[ Q09ٴ`Pt][n%L?7?\Oo>KO#~ICϝ#\j8w #+H] He`#@t?glaigcm=PrXZ~1%:EE#C1ʼ8?j2]JTOS'mpxy&gl2ca}8Uf+R1q?*Ƭ?jz2Zbl$DH2rAMd7X)J;c(;mw^Ș2:XxG)e.;%sL$2:VSЂ44ŕz)66YҽB8z.^B!nNs(#=ڮ?3.f,] A;/'H?<}Ha]G =JP75`鍤#ػbN1uZ?j/ZAMf9"ܷX%1S;i=Y`f&B AADi(UpC+T=>`=Gs0ct d!PP聽4[t3Y9VQ.P֣wdyoo1ȕxό'( pL'o{Xp"X~ h*hPU!TXD5)>F45O->|Ǩ}WKW:CQ2?dU|*ztָ_7_jR7M?5|)xiz}iRʎBٕXK- PN&嗌I-t0!C͈p,= P{Ys};:wfլ竦Z-ܞk-5nN9G|)&sWe- **Md 3NN,mczEH44tnI ~mLd Z# J1&BP8`埽2g(l][[p΢U#2jvDB&9$2Hp@B'^,28% C)SP I:x߽= |/no_\TOs-ÂԖAԠ (Eo>l^doJ`EAgvfDM}pS}v2UZWАVWa U#M)^}d;!L_,Xz*֓];]i zￆ#h c9e,A/Uwʦ G]% v `I ;my5So"2H¿Fc{/'Y D³DmSN1tbĀZ";;\gI2S [ʞayOD:jQLHc$`038Nm 6*I"ES`V^Z04v/&qy9 B[i4đ3WcYHgތߏ(87wz@ؘFWI ΔnY=**(ro]6[rW1cQi#f׮ض Nq,2icB!OPB=c|vid3U u7ljާMʝv69M  x qZ"ש?cjOYw_gX6JbE4I^V:KSSS[dgZ.룸~OۏYN|5%w=oy0?7?aK~/T"sdD2ߧj\T5eG?KuF]ճúD蘠S7p 9Gɦ[}q6W:hG(|?aeks6h֫h )VR ~uѦzv^h*fJpe퉚Fݶ@@C )L]8=R\r"]"$X HJB Y/mO$Q\$v(RI02D * iu*(.ہ0lj塙V&(71D, բ FBs$<`&b) Rw~!֋x b $)ZP~y'v~QT3Vh2 [㹎 D:r7jTdd3(@n$þvϵqLSCᘻ3I@If*'YOW5555{Wu>ϽN7UYmߍ>Ѣ/ˮ9[:FEu,H v7$Nbtl^o0|uSnas]J d6LL@V{VһOe@khSSSG{ڷځ*c?g$bhĚ{9BfYYj`Y1;WHB'P@߲Yn_&cTB(FM>VRA4isLpQJgyFtA#nx's ţK+l X{qQ\'6IqnIi6 !e{lUUe :p/n+nSnq8V{/ #E-Bƀ_1y.1gN}cK QM- Ry:_ve+I4@_n-'+]jC"=2(RL_|;Aqu1r3FjK VR*MH$x5:˵Yk?8_e ̗* (Ib2W.{Hs?K,Z1T4TNבLfͿbŔ2P9]Ha4qoŦB,C J˴-z Iś¶J+RAyHh!ӫH@Ÿq lr -S?ȺsC=^]iy*'Vvsh?k{ٛnSlx%/\ 愃!x+'HOe}e2Ifr9]cs۰sClc@2:s.6w ֩Z9Qfzp֗n(1],LE)¤wF$,&hQDKPy($@œynحRT}XiGy#|4ۦB2.Ģ$I 1pn ~ h' |/Zq"^;hzv;幉 y k!t93_O8Q1GZ٩TvZjjjh~ۤϔ]u}~ͺ'Goo}OߤOzi#u>Jt|/מyp3rn(A k|2Im_U%7!fa L7Tj"7-aWGhߨ˷{.z?;IeyKOWYm7|LZB:+*s̙c!Kz,@LV=nBovSs6 WMb>?/1%Cw,"5\n,\?Լ+h Z$jjYUx#LLP#ւP7Q w4T. ~͵ԭhkG}\-fɽbd>&yjO4sʨE1Nzɜ%6-*d>ND3.۫yx뉜:m! _GԦʙw>V/ߑw;6XhQr!RHiMZzT]ٳvc(/4Zg8JU3EE3&o]0z(((t_u^;'?%@d~^ew'&G'][ X.䩧FO0^Y'=-EchXj kcLXPS 19nwpMy įVx"/m ր&{Nځmt]+摀7) \:njVo;y g,RʮD$e i _ L^GlBOʆ0O ;v,S`9 +m+m1ߑtj6í]XkMÊ E#]"n&(v7W+{e 4) P?5٬kswII-3@'d,PQZuO\{{B;?TYyE!APy*Q )5HTlB뛙q79rM:(?I4:^3朖ljԶG!rJ~g"ۯ>?R-s=ߒz{>mgU~?~~j~S_~_ѭ}E.Kӭ?:3.&g<_vז`yw "Pjeg$۔S}4"`D\~;qݶoeO?aU#u\kxG⯭)kT22r'8їzK֟c:L ,U*(h;$qRY |J:~1ێ,SV _8o?(|k6d݉?KVP4~ǥ\@-̀7DAEc;) erC@C=>cd~Q Z k_Y{1D4R"AȃuY/)y.R0>19ArKqI˕6L#<  + ~|GQ{#Tg.ެ=8Gcy==z SJ`0fl%#l~CpJr~G9_j}bA)ҳֶ/9CMܹUߐU`ڴ5c&.NJK &t Ao?\' q9ZtBeRUH4*zhmlȻqCɬkqo=),b4 SV;GͬW(lTfHI4)Ne_5= E4U@L™D}b%%+LT?{`s]8w5v*,aI0BΫnw̌#Ob9MerME<$tAjc COafYیjba-IDmY}RGSp`A" f`eP_H=8z sl7(V?$u,dpH*eΣ^w@j91N!H#(P BJRJh{-O.R2&BwkZ׳_1 1W z"nԭAF ԂlW-`fqtlmT(gkQae51Q?<>U#Z_쏲ZDPx,r:3Q-Z gRVAPeUC"Qo1SSTGr("iOe\W 3U@1sv0X\0 HOV |k+m-5*cc2P_#F0\a|7m+rKmћI$$q?`_ž u!2j@@wIYO%ELZ)>j]|OPu>n8*{\͹YbovA vjP/ض霅Qqյ J Ee\ baY> LB ##Pk@~ee ݽv>{m_+DąVh ք*Is3PvgK7I~ԚU*;& xTTn;(^/|T( e~kϠM6GOn1q?|s ^$FeC;7SԨbhh|0xy5p)r7'rzw%OdK*cbv5*tc&˲eFr exYZKC f#FZ|KjOAZ^׸w3/$1FQ](E/r-Ce mQ8œS7v13e6nAaW Ǯ8WRplPw1(|#37r cF.Qgv (HV_oy/83]LR.v*  YvG˦dXR*8LAVː}xN$&;YʻzW0 DtrXFRNz(OuqZc'BH#cI`#)]<5s ⡍/ogMJ dg O* ?ŧX̕cWx E:\2NXW]d90O4Wyc,fҥ+l?"xքi%9/.UW#DUIӊappq""#fQP#fڠA J;1fcRI$_m㴴E$(]z5G 0`-9ղko*)[>HF u_ry?o2WG(jx:ч:h[.p+r}1JV(Fe:V^S{PNd``Wշ}6#KGLDk%LRHJQ\716 -eP`^A>5-&KuFۂYZ ok uQr s$W (T/Md)L00" #!"#tMӵ7D~O~//ɿ>`_x~ԓ-cso?]z<UTWOޥ)gZ~|}E^OxWv{OwokmS˿OHӯz^;G}׮gZ~>`Sfe~}ҟq}=/^;I}[u'}/~]Yk(4J H/ 0|DArialas0LLyԖ0ԖDTahomas0LLyԖ0Ԗ" DWingdings0LLyԖ0Ԗ0DSymbolgs0LLyԖ0Ԗ@DVerdanas0LLyԖ0Ԗ" B:.D @n?" dd@  @@`` |p0 9:'"?$b$m),A*"H R$R *Z*tJσ64 0AA E@3|;ʚ;ʚ;g4dddd0f;pA%pP <4ddddc20L80___PPT10 /  0` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" ddD|?" ddDg Z"  DM AX n?" dd@   @@``PR   D   ` p>ZMA::>MA:44 z(    T@@@@ 1g  _+Haga clic para cambiar el estilo de ttulo , ,M  N@@@@ c1B  kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7    l  N@@@@ CI  \*-DDD   N@@@@ C"I   ^*-DDD   Np@@@@ C%1I  ^*-DDD H  0nF! ? 3380___PPT10.p6-O *Diseo predeterminado50 PE(    N ܆ z z T=   r*  b11bb   N z z  =  t*  b11bbd  c $ ?- %  Q  N z z  9  kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7   l   T z z T   r*  b11bb  T z z    t*  b11bbH  0h  ? 3380___PPT10.`#(X @x(    Nz z z T=   p*   b11bb  N z z  =  r*   b11bb   TȔ z z T   p*   b11bb  T$ z z    r*   b11bbH  0h  ? 3380___PPT10.`%&0 `&X& $9%(    0h>0 *VALIDATION OF MAPPINGS BETWEEN DATA MODELS +(2+: + D  0`8   EGuillem Rull Technical University of Catalonia (UPC) Barcelona, Spain2 (295(  F Dd   C <A$MSR Logo 1280x403A`+P2q   0Haa% 4The Motivation Mappings are key elements for any application requiring interaction of heterogeneous data. A lot of research efforts have been done to automate the mapping creation process. However, all approaches require human feedback at some point, to solve semantic heterogeneities. It is thus necessary be able to check whether the resulting mappings satisfy the expected needs and requirements. Few work has been done in this area.@ 2 ($    D   04V1)0+6 tThe Research The main goal is to propose a method for testing whether a mapping satisfies some desirable properties. We will extend the CQC method which we successfully applied to the validation of database schemas. Main steps:@ 2 2 $   D;c3  0tM=@P/" oWe have proved that the four properties can be expressed in terms of query liveliness in a relational database."p 2p  p  DV  0z/60ED<4___PPT9 DIdentify relevant properties to validate. Validate mappings according to these properties in the context of relational databases. Extend the previous results to mappings between different types of models (XML, OO, etc.) Develop a tool able to, given a mapping and its models, perform tests to check the desirable properties.E% E  E D8XG  0"`g/  uMapping inference allows us to check for redundant mapping formulas. Mapping losslessness allows us to check whether some data is captured by mapping. It is a generalization of query answerability. Query answerability checks whether the exact answer of a query is preserved by mapping. Mapping satisfiability allows us to ensure that the mapping contains no contradiction. v5 v v  D>  0"` "/k- pA query is not lively if it returns an empty answer for all database instances. We can check it with the CQC method. We can define a new schema putting together the mapped models and incorporating the mapping in form of additional constraints. Then, for each property we can define a query such that its liveliness determines if the property holds or not. q5 q q  D0  0\ @/d nTwo important properties of mappings are defined in the literature: mapping inference and query answerability."o 2o  o  D2  0@P/j pWe have also proposed and formalized two additional properties: mapping satisfiability and mapping losslessness."q 2q  q  D  0 @p0  yCurrent State of the Research 2$  D  0-@P/^1 SWe are currently working on computing explanations when the properties do not hold."T 2T  T  Dl  6Ԕ"`a&l  6Ԕ"`(Fl  6Ԕ"`@012f ! 0"`!H Hf " 0"`# !Hf # 0"``% 2rf $ 0"`q`1!2, % <΄4@%O6 lExample of Mapping   D< & <Ԅ"`7I-9 Demployees(name, category, happiness-degree) categories(name, salary)>E # ED[ ' <"`:I"-< Ihappy-employees(name, happiness-degree) all-employees(name, salary)>J(( D> ( 0D='@ Hselect name, happiness-degree from employees where happiness-degree > 10XI  I D ) 0 @&sD Uoselect employees.name, salary from employees, categories where employees.category = categories.nameXp2\9   D * 0X=p':0@ 2select name, happiness-degree from happy-employees>3 3 D + 0XAp'z/C &select name, salary from all-employees>' ' D , <T"`>&}'? V  D - <\7A&}'B V  D . <A"`<@Q"= Mapping formulas:.   Drl / 6Ԕ"`q4@0!E 1 <G"`6@ 7 { Source model:.    Dr 2 <O"`9@ : { Target model:.    Dr 6 <aI0+-3I <Microsoft is a registered trademark of Microsoft Corporation== = DV 9 C .Alogoupc-901`%'H  0nF! ? 3380___PPT10.k0 ` ,(   ^  S - %     c $ 9   " H  0h  ? 3380___PPT10.`*r`.&DJF (4J H/ 0|DArialas0LL*Ԗ0Ԗ"DTahomas0LL*Ԗ0Ԗ" DWingdings0LL*Ԗ0Ԗ0DSymbolgs0LLOh+'0|R px    , 8DL,Validation of Mappings Between Data ModelsGuillem RullGuillem Rull78Microsoft PowerPoint@BnY@@@Ϝ+G(Q  (a&    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___wwwX4a&A q(qHʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___www22222222222mmmmmmmmmmⴳmۻ0Ԗ@DVerdanas0LL*Ԗ0Ԗ" B:.D @n?" dd@  @@`` |p0 9:'"?$b$m),A*"H R$R *Z*tJσ64 0AA E@3|;ʚ;ʚ;g4ddD-0XpA%pP <4ddddc20L80___PPT10 /rLeLLR (4J H/ 0|DArialas0LL Ԗ0ԖDTahomas0LL Ԗ0Ԗ" DWingdings0LL Ԗ0Ԗ0DSymbolgs0LL Ԗ0Ԗ@DVerdanas0LL Ԗ0Ԗ" B:.D @n?" dd@  @@`` |p0 9:'"?$b$m),A*"H R$R *Z*tJσ64 0AA E@3|;ʚ;ʚ;g4dd` 0XpA%pP <4ddddc20L80___PPT10 /&0 `&X& $9%(    0 0 *VALIDATION OF MAPPINGS BETWEEN DATA MODELS +(2+: + D  0ߚ    EGuillem Rull Technical University of Catalonia (UPC) Barcelona, Spain2 (295(  F Dd   C <A$MSR Logo 1280x403A+2q   0К a% 4The Motivation Mappings are key elements for any application requiring interaction of heterogeneous data. A lot of research efforts have been done to automate the mapping creation process. However, all approaches require human feedback at some point, to solve semantic heterogeneities. It is thus necessary be able to check whether the resulting mappings satisfy the expected needs and requirements. Few work has been done in this area.@ 2 ($    D   0 1)0+6 tThe Research The main goal is to propose a method for testing whether a mapping satisfies some desirable properties. We will extend the CQC method which we successfully applied to the validation of database schemas. Main steps:@ 2 2 $   D;c3  0 =p/" oWe have proved that the four properties can be expressed in terms of query liveliness in a relational database."p 2p  p  DV  0$ /60ED<4___PPT9 DIdentify relevant properties to validate. Validate mappings according to these properties in the context of relational databases. Extend the previous results to mappings between different types of models (XML, OO, etc.) Develop a tool able to, given a mapping and its models, perform tests to check the desirable properties.E% E  E D8XG  0 "`g /  uMapping inference allows us to check for redundant mapping formulas. Mapping losslessness allows us to check whether some data is captured by mapping. It is a generalization of query answerability. Query answerability checks whether the exact answer of a query is preserved by mapping. Mapping satisfiability allows us to ensure that the mapping contains no contradiction. v5 v v  D>  0 "` " /k- pA query is not lively if it returns an empty answer for all database instances. We can check it with the CQC method. We can define a new schema putting together the mapped models and incorporating the mapping in form of additional constraints. Then, for each property we can define a query such that its liveliness determines if the property holds or not. q5 q q  D0  0  p0d nTwo important properties of mappings are defined in the literature: mapping inference and query answerability."o 2o  o  D2  0 p/j pWe have also proposed and formalized two additional properties: mapping satisfiability and mapping losslessness."q 2q  q  D  0  p0  yCurrent State of the Research 2$  D  0 -p/^1 SWe are currently working on computing explanations when the properties do not hold."T 2T  T  Dl  6Ԕ"`a&l  6Ԕ"`(Fl  6Ԕ"`p012f ! 0  !"#$%'()*+,-./0123456789:;<=>?@ABCDEFGHIKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{|}~tRoot EntrydO)Њ+@PicturesKCurrent User DSummaryInformation(JRPowerPoint Document(&eDocumentSummaryInformation8*Ԗ0Ԗ@DVerdanas0LL*Ԗ0Ԗ" B:.D @n?" dd@  @@`` |p0 9:'"?$b$m),A*"H R$R *Z*tJσ64 0AA E@3|;ʚ;ʚ;g4ddD-0XpA%pP <4ddddc20L80___PPT10 /rFnFUL (4J H/ 0|DArialas0LL*Ԗ0Ԗ"DTahomas0LL*Ԗ0Ԗ" DWingdings0LL*Ԗ0Ԗ0DSymbolgs0LL*Ԗ ՜.+,D՜.+,T   ( 0 Personalizado(Technical University of Catalonia (UPC)e4 ArialTahoma WingdingsSymbolVerdanaDiseo predeterminadoDiapositiva 1 Fuentes usadasPlantilla de diseoTtulos de diapositivaD 4<$_A Guillem RullGuillem RullVersion"`!H Hf " 0"`# !Hf # 0"`%P2rf $ 0"`q1Q2, % <h- 4p&O6 lExample of Mapping   D< & <. "`7y.9 Demployees(name, category, happiness-degree) categories(name, salary)>E # ED[ ' <> "`:yR-< Ihappy-employees(name, happiness-degree) all-employees(name, salary)>J(( D> ( 0M =F'@ Hselect name, happiness-degree from employees where happiness-degree > 10XI  I D ) 0Q @'sD Uoselect employees.name, salary from employees, categories where employees.category = categories.nameXp2\9   D * 0( ='j0@ 2select name, happiness-degree from happy-employees>3 3 D + 0D A'/C &select name, salary from all-employees>' ' D , <x"`>&'? V  D - <yA&'B V  D . <w"`  0 "` "P0k- pA query is not lively if it returns an empty answer for all database instances. We can check it with the CQC method. We can define a new schema putting together the mapped models and incorporating the mapping in form of additional constraints. Then, for each property we can define a query such that its liveliness determines if the property holds or not. q5 q q  D0  0  @0d nTwo important properties of mappings are defined in the literature: mapping inference and query answerability."o 2o  o  D2  0 /j pWe have also proposed and formalized two additional properties: mapping satisfiability and mapping losslessness."q 2q  q  D  0  0  yCurrent State of the Research 2$  D  0 -/^1 SWe are currently working on computing explanations when the properties do not hold."T 2T  T  Dl  6Ԕ"`a&l  6Ԕ"`(Fl  6Ԕ"`012f ! 0"`!H Hf " 0"`# !Hf # 0"`%2rf $ 0"`q12, % <h- 4H&O6 lExample of Mapping   D< & <. "`70.9 Demployees(name, category, happiness-degree) categories(name, salary)>E # ED[ ' <> "`:-< Ihappy-employees(name, happiness-degree) all-employees(name, salary)>J(( D> ( 0M =v'@ Hselect name, happiness-degree from employees where happiness-degree > 10XI  I D ) 0Q @@'sD Uoselect employees.name, salary from employees, categories where employees.category = categories.nameXp2\9   D * 0( ='0@ 2select name, happiness-degree from happy-employees>3 3 D + 0D A'/C &select name, salary from all-employees>' ' D , <x"`>&'? V  D - <yA&'B V  D . <w"`<"= Mapping formulas:.   Drl / 6Ԕ"`q40!E 1 <ž "`6K!7 { Source model:.    Dr 2 <ɞ "`93!: { Target model:.    Dr 6 <ٞ I0+-3I <Microsoft is a registered trademark of Microsoft Corporation== = DV 9 C .Alogoupc-901%(H  0nF! ? 3380___PPT10.krw:S2 (4J H/ 0|DArialas0LL$&a Ԗ0ԖDTahomas0LL$&a Ԗ0Ԗ" DWingdings0LL$&a Ԗ0Ԗ0DSymbolgs0LL$&a Ԗ0Ԗ@DVerdanas0LL$&a Ԗ0Ԗ" B:.D @n?" dd@  @@`` |p0 9:'"?$b$m),A*"H R$R *Z*tJσ64 0AA E@3|;ʚ;ʚ;g4dd(a 0XpA%pP <4ddddc20L80___PPT10 /rnJ1