Estimating the quality of data in relational databases(4)

3SoundnessandCompletenessasMeasuresofData

Quality

Wede netwomeasuresofdataqualitythataregeneralenoughtoencompassmostexistingmeasuresandaspectsofdataquality[5,19].Thebasicideasunderlyingthesemeasureswere rststatedin[7].Inthatpapertheauthorsuggestedthatdeclarationsoftheportionsofthedatabasethatareknowntobeperfectmodelsoftherealworld(andtherebytheportionsthatarepossiblyimperfect)beincludedinthede nitionofeachdatabase.Withthisinformation,thedatabasesystemcanqualifytheaccuracyoftheanswersitissuesinresponsetoqueries:eachanswerisaccompaniedbystatementsthatde netheportionsoftheanswerthatareguaranteedtobeperfect.Thisapproachusesviewstospecifytheportionsofthedatabaseortheportionsofanswersthatareperfectmodelsoftherealworld.

Morespeci cally,thisapproachinterpretsinformationquality,whichittermsintegrity,asacombinationofsoundnessandcompleteness.Adatabaseviewissoundifitincludesonlyinformationthatoccursintherealworld;adatabaseviewiscompleteifitincludesalltheinformationthatoccursintherealworld.Hence,adatabaseviewhasintegrity,ifitincludesthewholetruth(completeness)andnothingbutthetruth(soundness).Aprototypedatabasesystemthatisbasedontheseideasisdescribedin[10].Theseideaswerefurtherdevelopedin[9]andaresummarizedbelow.

GivenadatabaseschemeD,weassumetheexistenceofahypotheticaldatabaseinstanced0thatcapturesperfectlythatportionoftherealworldthatismodeledbyD(theidealortruedatabase).Inaddition,weassumeoneormoreactualinstancesdi(i≥1).Theactualinstancesareconsideredapproximationsoftheidealinstanced0.

GivenaviewV,wedenotebyv0itsextensionintheidealdatabased0(theidealortrueextensiontoV)andwedenotebyviitsextensionintheactualdatabasedi.Again,theextensionsviareapproximationsoftheidealextensionv0.

ConsiderviewV,itsidealextensionv0,andanapproximationv.Ifv v0,thenvisacompleteextension.Ifv v0,thenvisasoundextension.Obviously,anextensionwhichissoundandcompleteistheidealextension.

Withthesede nitions,eachviewextensioniseithercompleteorincomplete,andeithersoundornonsound.Wenowre nethesede nitionsbyassigningeachextensionavaluethatdenoteshowwellitapproximatestheidealextension.Weshalltermthisvaluethegoodnessoftheextension.Werequirethatthegoodnessofeachextensionbeavaluebetween0and1,thatthegoodnessoftheidealextensionbe1,andthatthegoodnessofextensionsthatareentirelydisjointfromtheidealextensionbe0.Formally,agoodnessmeasureisafunctiongonthesetofallpossibleextensionsthatsatis es

v:g(v)∈[0,1]

v:v∩v0= = g(v)=0

g(v0)=1