item dIDpIDitemEx6issafeandmoreexpressivethanEx5HerepIDanddIDuniquelyidentifyeachpaymentanddeliveryThekeypIDenablesexpressingdistinctcommitmentsforthesamepriceitempairFurthereverydelivere ID: 333812
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Tracking.Tointeracteffectively,anagentshouldbeabletotrackthestatesofthecommitmentsinwhichitisin-volved.Doingsoisessentialforaccountability.Forexample,aresourceownerwouldtrackwhichresourcesitofferedtosharewithwhomanduntilwhen.Apa-tientwouldtrackwhichrecordsahospitalshouldshare,archive,ordestroy.Currentapproachesprovideinade-quatesupportfortrackingcommitmentinstances.Modelingguidance.First-ordercommitmentsmayfailtocapturewhattheirmodelersintended.Forinstance,vari-ablesmaybeinappropriatelyquantiÞed,whichcouldmeanthatcommitmentinstancesareimpossibletodis-charge.Or,speciÞcationofdeadlinesmaybesuchthatcommitmentinstancesareneverviolatedortheyneverex-pire,bothofwhichwouldbeundesirableinmanysettings. !item( dIDpID,item)))Ex.6issafeandmoreexpressivethanEx.5.HerepIDanddIDuniquelyidentifyeachpaymentanddelivery.ThekeypIDenablesexpressingdistinctcommitmentsforthesameprice-itempair.Further,everydeliveredeventreferstoapaideventviapID,whichidentiÞesthepaymentthedeliv-eryisfor:pIDisaforeignkeyindelivered.Thus,pIDiden-tiÞesthecommitment;anoccurrenceofdeliveredwiththatpIDdischargesthatcommitment.Ex.6demonstratestwodesirableproperties:properuseofquantiÞers(forsafety),anduseofkeystoidentifycommitments.Acommitmentmaybedischargedeveniftheantecedenthasnotbeenbroughtabout(YolumandSingh2002b).Forexample,amerchantcandischargeitscommitmentbyde-liveringbeforepaymentoccurs.ThecommitmentinEx.6rulesoutthispossibilityastheconsequentisdependentontheantecedentforinformation(bindingsforpIDanditem).Doesacommitmentbeingsafeentailthatacommitmentin-stancemustnotbedischargedbeforeitisdetached?Such !oID!price!item!pID"dID(C(o!ered(oID,item,price)#paid(pID,oID,price),delivered(dID, !oID!price!item!pID"dID(C(o!ered(oID,price,item)#paid(pID,oID,price),delivered(dID,,item)))Ex.9expressesthatthemerchantcommitstodelivertheitemonlyifthepaymentwereatleast90%ofthequotedprice.Further,Ex.9alsousesexpressionsfordeadline:thecommitmentexpireswithintendaysofmakingtheofferandisviolatedifmorethanÞvedayspasssincepayment(oDateandpDatearethetimestampsofo!eredandpaid).Ex.9!oID!price!item!oDate!pID!pDate"dID(C(o!ered(oID, %Expr|Expr&Expr|Exprwhere! ,andsoon.Oursemanticscomputesatimestampforcompositeevents.Timeinter-valsforanevent([Time,Time]inTable1)areinterpretedstrictly:theeventisrequiredtooccurafter(includingat)thelefttimepointbutbeforetherighttimepointoftheinterval.Whenthesamedebtorandcreditorapplyuniformlyinaformulation,weomitthemforbrevity.Thatis,wewritecommitment(c,r,u)insteadofcommitment(x,y,c,r,u).3.2SemanticsAninformationschemaisanonemptysetofevents,eachmodeledasarelationwithasuperkeyandadistinguishedtimestampcolumn.Baseeventsarematerializedrelations.Lifecycleeventsarecomputedviathesemanticsbelow.AmodelMofaninformationschemaspeciÞes,foreacheventschemaE,anextensionofthatschema isthepowersetofitsuniversere- modelofaninformationschemaisafunc-tionthatmapseachofits(Base)eventschemastoitsexten-sion,i.e.,amemberofitsintension.SpeciÞcally,M:ED/0+[E],.WetermM(E)theextensionofE ),project("),naturaljoin(#$),rename(%),union(&),intersection(1),Cartesianproduct(.),andcomplement(\)retaintheirusualmean-ings(ElmasriandNavathe1994).WereproducedeÞnitionsforsomeofthelesscommonones.Below,SingletonA,B={(null,...,null)}isthesingletonnullrelationwhoseat- Leftouterjoin(#$).R#$ Ethatoccurafter(includingat)cbutbefored.D2.[[E[F+c,d]]]=!t!+c!t([[E]] }isasingletonrelationwithasingleat-tributet.D9.[[ E[0,F+c]]].RisXsuchthatEoccurredtoosoon,thatis,beforef+c,wherefisthevalueofFÕstimestamp.¥SX ¥T={(d)}isasingletonrelationwithasingleat-tributet.ThedeÞnitionof[[X2E[c,F+ ,c]]].¥S=[[X]]!%t/t![[E[0,F+d]]] ¥S=[[X]]! X2Z)]].D13.[[X2(Y)Z Y2Z)]]=[[(X2Y))(X(Z)]].D15.[[created(c,r,u)]]=[[c]].Acommitmentiscreatedwhenitscreateeventoccurs.D IncontrastwithEx.10,Ex.12expressesacustomerÕscommitment.Thesameschemaunderliesbothcommit-ments.WehavethechoiceherebecausePaymentandShip-mentdonotdependuponeachother.WhichcommitmentismodeledisthemodelerÕschoice.Ex.12Listing4speciÞesthecustomerÕscommitmenttothemerchantthatiftheordereditemsareshippedwithinÞvedaysoforderplacement,thenpaymentforatleast90%of Bvalue.DeÞni-tion4usesthisnotiontocorrelateevents.DeÞnition4LetEandFbeevents.EdeterminesFiff¥thekeyofEfunctionallydeterminesthekeyofFinE,or¥thekeyofEfunctionallydeterminesthekeyofGinE,andGdetermines ifandonlyifdetached(X,X!,X!!)determinescreated(X,X!,X!!),anddischarged X,X!,X!!)isX;andthatofviolated(X,X!,X!!)isX!.Well-identiÞedcommitmentsarecrucialtocorrelatingtheeventsinvolvedasinglecommitmentinstance.Eachofthecommitmentsinthelistingsaboveiswell-identiÞed.Foranexampleofacommitmentthatisnotwell-identiÞed,con-sideranalternativeschemawherePaymentdoesnotrefer M|=discharged(X,X!,X!!).Theorem2givesasyntacticcriterionforidentifyingvac-uouscommitments,e.g.,toassistacommitmentmodeler.Theorem2Acommitmentthatisnotwell-identiÞedisvac-uous.ProofSketch.FollowsfromD16andD17.5.3Time-OrientedPropertiesIngeneral,modelerswouldnormallyprefertowritecommit-mentsthatoncecreatedareeitherdetachedordischargedoraresettoexpirewithinaÞniteamountoftime.DeÞnition9formalizesthisproperty.DeÞnition7A (X,X!,X!!)isviolablyspec-iÞediff(1)anyeventthatappearsintherighttime-pointofanyintervalspeciÞcationinX!!iseithercreated(X,X!,X!!)ordetached(X,X!,X!!),and(2)'X!!.Theorem4connectsDeÞnitions9and10.Theorem4Acommitment(X,X!,X solidation,andcompensationcanbehandledthroughasuit-abledesignofeventschemas(andtheirkeys);concessionre- Yolum,P.,andSingh,M.P.2002a.Commitmentmachines.InProceedingsofthe8thInternationalWorkshoponAgentTheories,Architectures,andLanguages(ATAL2001)