extendourmethodssothateachoperationdelivers,inadditiontoagoodnessestimateofitsresult,thenecessarybasesforfutureoperations.Thisprovidesuswiththeabilitytoperformsequencesofoperations.

Alegitimatequestionatthispointiswhethertheseestimatesdependontheorderinwhichtheyarecomputed,i.e.,whethertheestimatesofthegoodnessofequivalentrelationalalgebraexpressionsarethesame.Theanswertothisquestionisthattheestimatesareindependentoftheparticularexpressionused[11].

6ConclusionsandFutureResearch

Weintroducedanewmodelfordataqualityinrelationaldatabases,whichisbasedonthedualmeasuresofsoundnessandcompleteness.Thepurposeofthismodelistoprovideanswerstoarbitraryquerieswithanestimationoftheirquality.Weachievedthisbyadoptingtheconceptofabasis,whichisapartitionofthedatabaseintoviewsthatarehomogeneouswithrespecttothegoodnessmeasures.Thesebasesareconstructedusingdatabasesamples,whosegoodnessisestablishedmanually.Oncethebasesandtheirgoodnessestimatesareinplace,thegoodnessofanswerstoarbitraryqueriesisinferredrathersimply.

Weplantodevelopthecompletesetofproceduresforcalculatingsoundnessandcom-pletenessoftheanswerstootherrelationalalgebraoperations;i.e.,addproceduresforunion,di erence,andintersectionofviews.Oneofourmajorgoalsistousethesemethodstoesti-matethegoodnessofanswerstoqueriesagainstmultidatabases,wherethesamequerycouldbeanswereddi erentlybydi erentdatabases,andgoodnessinformationcanhelpresolvesuchinconsistencies.

Wehavealreadydiscussedtheadvantageofconsideringthecorrectnessofindividualattributesoverthecorrectnessofentiretuples.Still,anindividualvalueiseithercorrectorincorrect,and,whenincorrect,wedonotconsidertheproximityofastoredvaluetothetruevalue.Thisdirection,whichiscloselyrelatedtoseveraluncertaintymodelingtechniques,meritsfurtherinvestigation.

Becauseofthecostofestablishinggoodnessestimations,wehavenotedthatourmeth-odsaremostsuitableforstaticinformation.Whentheinformationisdynamic,itwouldbeadvisabletotimestamptheestimationsatthetimethattheywereobtainedandattachthesetimestampstoallqualityinferences.Onemayalsoconsidertheautomaticattenua-tionofqualityestimationsastimeprogresses.Thisdirectionisstilloutsideourimmediateobjectives.