Asimpleapproachtogoodnessistoconsidertheintersectionoftheextensions;thatis,thetuplesthatappearinbothvandv0.Let|v|denotethenumberoftuplesinv.Then

|v∩v0|

|v|

expressestheproportionofthedatabaseextensionthatappearsinthetrueextension.Hence,itisameasureofthesoundnessofv.Similarly,

|v∩v0|

|v0|

expressestheproportionofthetrueextensionthatappearsinthedatabaseextension.Hence,itisameasureofthecompletenessofv.

Itiseasytoverifythatsoundnessandcompletenesssatisfyalltherequirementsofagood-nessmeasure.1Soundnessandcompletenessaresimilartoprecisionandrecallininformationretrieval[15].

Adisadvantageofthesemeasuresisthatadatabasetupleisassumedtobesound(andcontributetothesoundnessmeasure)onlyifitidenticaltoatupleoftheidealdatabase(sim-ilarlyinthecaseofcompleteness).Thus,atuplethatiscorrectinallbutoneattribute,andatuplethatisincorrectinallitsattributesaretreatedidentically.Anessentialre nementofthesemeasuresistoconsiderthegoodnessofindividualattributes.

AssumeaviewVhasattributesA0,A1,...,An,whereA0isthekey.2WedecomposeVintonkey-attributepairs(A0,Ai)(i=1,...,n),ingdecom-posedextensionsinthepreviously-de nedmeasuresimprovestheirusefulnessconsiderably,andweshallassumedecomposedextensionsthroughout.

Soundnessandcompletenesscanalsobeapproachedbymeansofprobabilitytheory[11].Forexample,thede nitionofsoundnesscanbeinterpretedastheprobabilityofdrawingacorrectpairfromagivenextension.Probabilisticinterpretationsgivenewinsightintothenotionsofsoundnessandcompletenessandalsohelpustoconnectthisresearchwithalargebodyofworkonuncertaintymanagementininformationsystems[8].

Thedataqualitymeasuresthathavebeenmentionedmostfrequentlyasessentialareaccuracy,completeness,currentness,andconsistency[5,18].Itispossibletorelatethesequalitymeasurestoourowngoodnessmeasures[11].

Whenvisempty,soundnessis0/0.Ifv0isalsoemptythensoundnessisde nedtobe1;otherwiseitisde nedtobe0.Similarlyforcompleteness,whenv0isempty.

2Weconsideratupleasarepresentationoftherealworldentityidenti edbyakeyattribute;thenonkeyattributesthencapturethepropertiesofthisentity.Forsimplicity,weassumethatkeysconsistofasingleattribute.1