Answertuple t Movie526338SweeneyTodd2007 033 Director23456DavidBurton 033 Director23468HumphreyBurton 033 Director23488TimBurton 033 Movie359516LetsFallinLove1933 025 Mo ID: 481114
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(a)LineagefromDirectorsandMoviesoftheMusicaltuple Answertuple t Movie(526338,\SweeneyTodd",2007) 0.33 Director(23456,David,Burton) 0.33 Director(23468,Humphrey,Burton) 0.33 Director(23488,Tim,Burton) 0.33 Movie(359516,\Let'sFallinLove",1933) 0.25 Movie(565577,\TheMelodyLingersOn",1935) 0.25 Movie(6539,\Candide",1989) 0.20 Movie(173629,\Flight",1999) 0.20 Movie(389987,\ManonLescaut",1997) 0.20 (b)ResponsibilityrankingsforMusicalFigure2:RankingcausesintheIMDBexample.DisplayedaretheresultsfortheMusicaltuple,assumingthatallthetuplesintherelationsDirectorsandMoviesareendogenous.analysisbytheusertodeterminethefrequencyofatuple'sappearanceinthelineage,aswellasitsparticipationinmintermsofpossiblydi erentsizes,todetermineitsactualsignicancetotheresult.Italsoturnsoutthatall137tuplesareactualcauses(byProp.2.2),socausalitydoesnotprovideuswithanymoreinformationthanlineageinthiscase.However,rankingbyresponsibilitygivesusmuchmoreinterestinginformation,aswenowshow.ConsiderthecaseoftheanswerMusical,whoselineageismuchsmallerthanMusicandshowninFig.2a.1Wecanseeimmediatelythecausesofthesuspiciousanswer.AlthoughTimBurtondiddirectonemusical,\SweeneyTodd"(surprise!),therearetwootherdirectorswithlastnameBurton(oops!)whodirectedseveralmusicals.Whatwewouldlikefromasystemistolist\SweeneyTodd",DavidBurton,andHumphreyBurtonastopcausesforMusical:therstisasurprisingnding,thelasttwopointtoabuginthequery.Wedon'twantasystemtolistamovielike\TheMelodyLingersOn"asatopexplanation,becausethatdoesn'treallyexplaindirectlythesurprisinganswerMusical.Rankingbyresponsibilityachievespreciselythisbehavior,asshowninFig.2b.Themovie\SweeneyTodd"hasaminimumcontingencyofsizetwo,consistingofthedirectorsDavidandHumphreyBurton,becausebyremovingthesetwodirectorsfromthedatabase,\SweeneyTodd"becomescounterfactual.Inaddition,eachofthethreedirectorswithlastnameBurtonalsohasacontingencyofsizetwo,consistingoftheothertwodirectors.Thus,thesefourtuples(themovieandthethreedirectors)havethesameresponsibility,1=3,andarelistedasthetopexplanationsforwhyMusicalisreturnedbythequery.Ontheotherhand,thesmallestcontingencyforthemovie\ManonLescaut"hassizefour,2henceitsresponsibilityis1/5.TheanswerMusichasamuchlargerlineageconsistingof118tuples;rankingthembyresponsibilityprovestobeakeytechniqueinidentifyinginterestingexplanations.InthiscaseTimBurtonandhismovie\CorpseBride"appearhighestintheranking,alongwiththreemoredirectorswhosharethesamelastname:Al,Tom,andHumphrey.Discussion.Ourexampleillustratesageneralphenomenon.Tupleswithhighresponsibilitytendtobeinterestingexplanationstoqueryanswers;tupleswithlowresponsibilitytendtobeuninteresting.Thereasonforwhyatupleisinterestingmayvary:itmaybeasurprisingfactinthedata,itmaypointtoabuginthequery,oritmayrepresentanerrorinthedata.Oursimpledenitionofcausalitydoesnotdistinguishbetweentheseexplanations,butonlyranksthembythedegreeofinterestingnesstotheuser.Achallengingresearchdirectionwouldbetorenethesenotionsinordertoadaptthemtospecicpurposes.3.2DiagnosingNetworkFailuresWiththebasicintuitioninmind,wewillillustratenowaquitedi erentapplicationofcausality.Consideracomputernetworkconsistingofanumberofservers,withphysicallinksbetweentheserversstoredinatableLink(srv1,srv2).Atanygiventime,aservermaybeactiveordown,andActive(Srv)isthetableofserversthatareassumedtobeactive.Anetworkadministrator,callherAlice,isconcernedinmaintainingthenetwork'sconnectivity,whichcanbeexpressedbythefollowingDatalogprogram:Connected(x,y):-Link(x,y),Active(x),Active(y)Connected(x,y):-Connected(x,z),Link(z,y),Active(y)Connected(x,y):-Connected(y,x) 1Thelineagehas21tuples.TuplesfromtheMovie DirectorsandGenrerelationsaredepictedinFig.2aasedgesbetweentheDirectorandMovietuplesandtheMovieandanswertuples,respectively.Itisnaturaltoconsiderthelatterexogenous;iftheywereendogenous,theywouldhavethesameresponsibilityasthemovietheycorrespondto.2fMovie(\Candide"),Movie(\Flight"),Director(DavidBurton),Director(TimBurton)g.4