Managing Ontological Constraints Abstract

YannisKalfoglouyannisk@dai.ed.ac.uk

DavidRobertsondr@dai.ed.ac.uk

SchoolofArtificialIntelligence,

InstituteforRepresentationandReasoning,

DivisionofInformatics,UniversityofEdinburgh,

80SouthBridge,Edinburgh,EH11HN,Scotland

Abstract

Weexploretheuseofontologicalconstraintsinanewway:deployingtheminasoftwaresystem’sformalevaluation.Wepresentaformalismforontologicalconstraintsandelaborateonametainterpretationtechniqueinthefieldofontologies.Ontologicalconstraintsoftenneedenhancementstocaptureapplication-specificdiscrepancies.Weproposeaneditingsystemthatprovidesguidanceinbuildingthoseconstraintsandweexplainhowthishelpsustodetectconceptualerrorsthatre-flectamisuseofontologicalconstructs.Wede-scribeamultilayerarchitectureforperformingsuchchecksandwedemonstrateitsusageviaanexamplecase.Wespeculateonthepotentialim-pactoftheapproachforthesystem’sdesignpro-cess.

1Introduction

IntheAIontologicalcommunitymostworkisfocusedonthetwoissuesthatontologiesclaimtodeliver:know-ledgesharingandreuse.Intherecentyears,developmentsinthefieldhavebeenfastandnewwaysofdeveloping,browsingandeditingontologieshaveemerged.However,theobserveddearthofapplicationsreportedin[Usc98]isahardrealityandontologicalengineersareworkinghard

Aswedescribelaterinthepaperexistingontologicalax-iomsneedtobeenhancedtocapturedomain-specificdis-crepancies.Thispracticeisoftenencounteredwhenwemovefromtoplevelontologiesdowntodomainspecificontologieswheretheorderofspecificityincreases.

Thispaperisorganisedasfollows:insection2wepresentaformalisationforontologicalconstraintsalongwithametainterpretationtechniquethatmakesitpossibletocheckwhethergoalsthatsucceedintheproofsviol-atethoseconstraints.Wepresentaflexiblemultilayerap-proachtofacilitatethissortofchecksandinsection3weelaborateontoolsthathelpustoconstructontologicalcon-straints.Wediscussbenefitsoftheapproachanddemon-strateabriefuseofthemultilayerarchitectureinsections4and5respectively.Insection6wegivepointerstorelatedwork.

2Formalisingontologicalconstraints

Inthissectionwepresentaformalisationforontologicalconstraintsandhowwechosetorepresenttheminaspe-cificerrorformat.Insection2.1weelaborateonagenericinferencemechanismwhichismadeexplicitthroughmeta-interpretationandwepresentanerrorcheckingmechanismtailoredtotheparticularontologicalconstraints.Insec-tion2.2weshowhowwerealisethistheoreticalmodelinamultilayerapproachthatcombinestheinferencemechan-ismalongwiththeerrorcheckingandgivesusadditionaladvantageswhichwediscussinthesequel.Theontologicalconstraintsadoptthefollowingnotation:

whereisaunitgoalandareallvari-ablesin,andisaconditioncomposedoflogicalconnectives()and/orunitgoals.Theconditionmustbecomposedofvalidontologicalconstructsanditmustbetruewhentheunitgoalistrue.

Weareinterestedinproofsoverexistentiallyquantifiedgoals,sotheformulaistransformedintoanormalformwherethe‘’operatorbelowconnectstheoriginal(left)tothetransformedversion(right):

Wethenidentifythepredicatederivedfromthelefthandsideoftheoriginalimplicationofformulaandlosetheexistentialquantifierandouternegationsincetheseexpres-sionswillbeusedtotestforerrorsongoalsintheproof.Hence,therightpartofformulawillbe:

(D)Figure1:TheMultilayerarchitecture.Therightpartshowstheapproachasawhole,whereastheleftpartisamagnific-ationofalayer.

architectureatfigure1whereweincludeattheleftpartamagnificationofonelayer.Adescriptionofalayerfollows:Specificationconstructionstartsbyadoptingthesyntaxandsemanticsoftheontology.WeuseHornClausesasaspecificationconstructionformalismwiththenormalPro-logexecutionmodel.Thisallowsustointerpretthespe-cificationdeclarativelybasedontheunderpinningcompu-tationallogicwhiletheproceduralinterpretationmakesitpossibletocheckthecorrectnessofthespecificationauto-maticallybyusingthemeta-interpretermechanism.

Theontologicalconstructswillnotbetheonlypartsofthespecification.Infact,itisnormallyimpracticaltocon-structanexecutablespecificationbyusingonlytheonto-logy’sconstructs.Otherconstructsarenormallyaddedtocustomisethespecificationfortheparticulardomainofap-plication.Thesewillnotbenefitfromthemeta-interpretererrorcheckingmechanismbutcanbecheckedinthenor-malway.

Ontologicalaxiomsareusedtoverifythecorrectuseofontologicalconstructsinthespecification.Theirroleistoensurethatthecorrectinterpretationsofontologicalconstructswillbegiven.Thiscanbedoneautomatic-allywiththemeta-interpreterandaswedescribedinsec-tion1.1therecanbeextra,applicationspecificontologicalconstraintsthatareconstructedwiththeuseofsupportingtools,liketheeditorwedescribeinsection3.

Thespecificationalongwiththeontologicalconstraintsisinterpretedbythemeta-interpreter.Wheneverastate-mentinthespecificationdoesnotsatisfytheontologicalconstraintsanerrorisreported.

Therightpartoffigure1showsourapproachinamul-tilayerperspective.Thisallowsustocheckthecorrect-nessofontologicalconstraintsthemselves.Whethertheyareprovidedbyontologicalengineersintheformofon-tologicalaxiomsorareapplicationspecificerrorcondi-tionstheymaybeerroneouslydefined.Thiscouldleadtoanerroneouserrordiagnosiswithpernicioussideeffects.However,ourproofsthaterrorexistaredoneusingthesamemechanismasforspecifications,makingitpossibletodefineconstraintsonerrorontologies.Theadvantageofthisapproachisthatwecanusethesamecoremechanism,themeta-interpreterprogram,tocheckspecificationsandtheirontologicalconstraintssimultaneously.Ultimately,thislayercheckingcanbeextendedtoanarbitrarynum-beroflayersupwards,untilnomorelayerscanbedefined.Abriefexampleofthemultilayerapproachisgiveninsec-tion5,whileherewedrawtheattentionofthereadertotheformatweadopttorepresentspecificationstatementsinanalogywiththeclause/2builtinpredicatedescribedinsection2.1.Theonlydifferenceisthatweaddonemoreargumenttotheclausetoindicatetheindexofalayer.Theformatisasfollows:

specification(Index,(AB))

Thesameadditionhasbeenmadetotheerrordescriptionformatgiveninsection1.1.

3Buildingontologicalconstraints

Theexistingsetofontologicalconstraintscanbeaugmen-tedbyaddingextraconstraints.Asimilarapproachwas

Y.Kalfoglou,D.Robertson5-4

introducedin[UCH98],wheretheauthorsreportthattheyhadtoaddextraontologicalaxiomsintheirspecifica-tionformulationinordertoprovesomeconceptsthatweretreatedasprimitivesintheunderpinningontology.Wehaveelaboratefurtheronthenotionofdefiningextra,applica-tionspecificontologicalconstraintswhichresultsinacus-tomisedaxiomatisation.Webelievethattheusershouldbeprovidedwithsupportinutilisingbothkindsofconstraints,existingandnewonestailoredtotheparticularapplication.Whateverthechoice,theconstructsusedintheconstraintsshouldconformtotheontologyvocabularyandbeconsist-entwiththeexistingconstraints.Howevertheapplicationspecificconstraintscanuseextraconstructswhicharenotpartoftheunderpinningontology.

Withthisaiminmindwehavebuildtwoeditingtoolsthatfacilitatetheconstructionofontologicalconstraintsandprovidebuiltinchecksforconflictsandsubsumptionoccurrence.Wewillelaborateondesignchoicesanduseofthesetoolsviatwoshortexamplecases:aconstructionofagenericconstraintborrowedfromtheProcessInterchangeFormat(PIF)ontologyandaconstructionofanapplica-tionspecificconstraintborrowedfromourwork([Kal99a])intheAIRCRAFTontologyapplication.

Inthecaseofbuildingagenericconstrainttheusercandefineunary,binaryandternaryrelationsthatholdoveron-tologicalconceptsandchooselogicalconnectivestolinkthem.Thecollectionofconceptsfromtheontologyaswellasthedistributionofvariablesthatwillbesharedamongtheliteralsisdoneautomatically,theuseronlyhastoselecttheconceptshewantstouse.Theresultofeditinganax-iomofthecorePIF,whichisgivenbelowintextualform:“Thebeforerelationholdsonlybetweentimepoints”isasfollowsinFOPCnotation:

Ifweareinterestedinusingtheconstraintasanaxiomthenatthisstagewearereadytoaddittotheexistingontologyaxiomatisationafteraconflictandsubsumptioncheckingisdone.Thesortofconflictcheckweapplyde-clarestwoaxiomsasbeingcontradictorytoeachotherifafteramatchingoftheirheadshavebeensuccessful,theirsubgoalshavethesamesymbolsbutstillarenotunifiableafterhavingtheirvariablestemporarilybounded.Thesub-sumptioncheckwillensurethatfortwoaxiomsthattheirheadsmatch,wewon’tletamoregenericonetosub-sumeanexistingdetailedone.Thisisalimitedformofsubsumptioncheckthatwillpreventspecificinformationlosscausedbyagenericaxiom.Forexample,assumethe

target_typeguidancestoresmissiontargetweaponweaponguidanceTypeordnanceaircraftaircraftmissionType

max_rangemax_speedhorsepowerengine_manufacturerflyingObjectnumberflyingObjectnumberpropellorEnginenumbernameengineISA taxonomy declarations:

(format: ISA )

aircraftweaponpropellor engine

ISAISAISA

flyingObjectordnanceengine

Figure2:AselectionofrelationsfromtheAIRCRAFTontology.Therelationsarerepresentedasrectangularboxeswiththeconceptsthatholdoverstemmingfromthem.WealsoincludeasubsetoftheISAtaxonomydeclarationstionstoresaswell.Therearenomorerelationstoberetrievedbasedontheparticularconcept,sothemechan-ismwillproceedtoretrievepotentialrelationsbasedonassociatedkeywords.Thosewillbetheremainingcon-ceptsfromtherelationsthatalreadyhavebeenretrieved:target,guidanceTypeandaircraft.Thesameprocessisap-pliedforeachofthenewconceptswhichwillresultintheretrievalofthreemorerelations:mission,max

.Anynewconceptsthatwillaccompany

thenewrelations(i.e.number)willnotberegardedasnewkeywordstotrysincethiswillresultinretrievalofrela-tionsdissociatedwiththeoriginalkeyword.Therefore,atthispointthealgorithmterminatessincetherearenomorerelationstoretrievenorthereareconceptsfromtheoriginalretrievedrelationssetthathaven’tbeencheckedyet.

Oncethecandidaterelationshavebeenretrievedtheuserselectstheoneshewantstoincludeintheconstraint.Inourcase,thosewere:storesandtarget

type.Therecanbeanaugment-ationoftheconstraintwithextrapredicateorrelationswithrespecttothisvariable,butinourcase,thiswasboundedtotheconstant‘Naval-Unit’.

Thefinalstepistolinktheconstraintliteralswithlo-gicalconnectives().Afteraconflictandsubsump-tioncheckingisdonetheconstraintisreadytoaddintheconstraintsbaseandtransformedautomaticallyintheerrorconditionspecificformat.WegivethembelowinFOPCnotationandinerrorconditionformat:inFOPC:

Figure3:Ascreenshotthatshowsthestepofdefiningtheheadoftheconstrainttobebuiltalongwiththetypeofvariablesthatwillbeusedinit.

Figure4:Ascreenshotthatshowsthestepofinstantiatingvariablesintheconstraint’srelations.

4Benefitsoftheapproach

Theuseofontologicalconstraintsweproposehasseveralbenefitsforthesystem’sdesignprocess.Wesummarisebelowthemostimportantofthemalongwithpointerstodocumentedwork:

augmentationofspecificationswithformallydefinedconstructsdrawnfromtheunderpinningontology.Wearguethattheseconstructsmightbereusedinothersimilarapplicationswhichmayresultinacost-effectivesolutionforthedesignprocess.In[Kal99a]weexplorethefeasibilityofthisapproachviaanexamplecaseinthedomainofACP(AirCam-paignPlanning)realisedthroughtheAIRCRAFTontology([VRMS99]);

useofontologicalconstraintstodetectconceptualer-rorsinspecificationsthatuseontologicalconstructs.Thishasapotentialimpacttotheearlyphasesofsoft-waredesignsinceitmakesitpossibletodetecterrorsthatwerepreviouslyuncaught.Moreover,theseon-tologicalconstraintsmightbereusedtodetectsimilarkindoferrorsinotherapplications.In[Kal99b]wepresentanapplicationofthisapproachinthedomainofecologicalmodelling;

themultilayerarchitecturemightbeusedtoeasethemappingofontologiesandspotmismatchesofcon-

ceptsandrelationsinanarbitrarynumberoflayers.Thismaybeusefulwhenappliedtomethodologiesthatimposealayeredontologydesignapproach(see,forexample,[van98]).

5Useofmulti-layerarchitecture

Wewilldemonstratebrieflyamotivatingexampleontheuseofthemulti-layerarchitectureborrowedfromthePHYSSYSontology.Theontology,whichisisdocumentedin[BAT97],isaformalontologybaseduponsystemdy-namicstheoryaspracticedinengineeringmodelling,sim-ulationanddesign.Itexpressesdifferentconceptualview-pointsonaphysicalsystemandconsistsofthreeengin-eeringontologiesformalisingtheseviewpoints.Inourex-amplecasewedealwithoneoftheseontologies,thecom-ponentontology.

Thecomponentontologyisconstructedfrommere-ology,topologyandsystemstheory.Toquote[BAT97]:

“Inaseparateontologyofmereologyapart-of-relationisdefinedthatformallyspecifiesthein-tuitiveengineeringnotionofsystemordevicede-composition.Thismereologicalontologyisthenimportedintoasecondseparateontologywhichintroducestopologicalconnectionsthatconnectmereologicalindividuals.Thistopologicalon-tologyprovidesaformalspecificationofwhat

Y.Kalfoglou,D.Robertson5-7

Figure5:Thecomponentviewofaphysicalsystem:Itshowsthetopologyforanairpump.Sub-componentsaredrawninsidetheareadefinedbytheirsuper-component.Thesmallsolidblocksaretheinterfacesthroughwhichcomponentsareconnected.

theintuitivenotionofanetworklayoutactuallymeansandwhatitspropertiesare.Theontologyofsystemstheoryincludesthetopologicalonto-logyanddefinesconceptslike(openorclosed)systems,systemboundary,etc.,ontopofit.”Todemonstrateacomponentviewpointbasedonthecomponentontology,weillustrateinfigure5(borrowedfrom[BAT97])astructural-topologicaldiagramforaphys-icalsystem,likeanairpump.

TheprinciplesunderlyingtheconstructionandusageofthePHYSSYSontologyarebeyondthescopeofthispaper;wepointtheinterestedreaderto[BBWA96]forfurtherde-tails.Inthesequel,weelaborateontheapplicationofthemulti-layeredarchitecturetoeachofthethreeontologiesincludedinthecomponentontology:mereology,topologyandsystemstheory.

Alltheontologieswereimplemented,originally,inOn-tolinguausingtheOntologyserver([FFPR96]).Wetrans-latedthemtothetargetlanguageweuse:inProlog.Al-thoughwecouldusetheautomatictranslationprovidedbytheserverwechosetodothismanually.Thismadeiteasiertotranslateselectivepartsoftheontologieswhilepre-servingthesyntacticeleganceoftheresultingHornclauses.In[Bri99]theauthorelaboratesontheOntolinguasyntaxtoPrologtranslationissue.5.1Mereology-Layer2

Thetoplayerofthearchitecture,layer2,consistsofthemereologyontology.Itprovidesdefinitionsformereolo-gicalrelationstospecifydecompositionandthepropertiesthatanydecompositionshouldhave.WerewriteOntolin-guastatementsoftheform:as:forspe-cificationstatementsandasontologicalaxiomswhichmustnotbeviolated.Thesecanberewrittenaserrorconditions,aswedescribedinanearliersection(2),ofthe

form:.Anexcerptofthemereologyonto-logyisgivenbelowinthespecificationformatweadopt:

specification(2,(individual(X)equal(X,X))).specification(2,(properof(X,Z)part

partof(X,Y)

properof(Y,Z))).

specification(2,(directof(X,Y)properof(X,Y)

(properof(Z,Y)properof(X,Z)))).

specification(2,(disjoint(X,Y)(equal(X,Y)

(properof(Z,X)properof(Z,Y))))).

specification(2,(simple

part,X))).

Thedeclarativereadingoftheseclausesisthefollow-ing:thefirstclauserealisesthenotionofmereologically

individual.AnindividualXisamereologicalindividualwhenequal(X,X)holds.Therelationequal(X,Y)defineswhichindividualsareconsideredtobemereolo-gicallyequalanditusuallyholdsforequal(X,X).Thesecondandthirdclauserepresenttheproperofrelation.Whenanindividual,X,ispartofindividualZthentheproperofrelationholds.Inthethirdclausetherecursivedefinitionofproperofreal-isesthetransitivityproperty.Weusethepart

part

individual/1predicatestatesthatanindividualXisregardedasasimpleindividualwhenithasnodecomposition.

Apartfromthesespecificationstatementswecanalso

Y.Kalfoglou,D.Robertson5-8

writedown,directlyfromtheOntolinguasyntax,errorcon-ditionswithrespecttothespecificationgivenabove:

error(3,individual(X),equal(X,X)).error(3,properof(X,Y),properof(Y,X)).error(3,directof(X,Y),(properof(X,Y)

(properof(Z,Y)properof(X,Z)))).

error(3,disjoint(X,Y),(equal(X,Y)

(properof(Z,X)properof(Z,Y)))).

error(3,simple

part,X))).

Noticethattheindividual,directof,

disjointandsimple

of/2withre-specttoinstancesoftheairpumpsystem.5.2Topology-Layer1

Atlayer1ofthearchitectureweplacethetopologyon-tology.Thisontologyprovidesthemeanstoexpressthatindividualsareconnected.Axiomsensurethatonlysoundconnectionscanbemade.WeapplythesameprinciplestotransformtheOntolinguasyntaxinthespecificationformat:

specification(1,(connection(C)connects(C,X,Y))).specification(1,(connects(C,X,Y)(connect(C,X,Y)

connect(C,Y,X)))).

ThefirstclausestatesthataconnectionCconnectstwoindividualsXandY.Theconnects/3predicaterealisesthesymmetricalpropertythatholdsfortheconnectsrela-tion.Itusesthepredicateconnect/3toexpressinstanceswithrespecttotheairpumpsysteminfigure5.Theseare:

specification(1,(connect(valve1reservoir,

valve1,reservoir)true)).

specification(1,(connect(reservoirvalve2,

reservoir,valve2)true)).

specification(1,(connect(bellowsreservoir,

bellows,reservoir)true)).

specification(1,(connect(leverbellows,

lever,bellows)true)).

specification(1,(connect(coilMagnetlever,

coilMagnet,lever)true)).

specification(1,(connect(airSupplyvalve1,

airSupply,valve1)true)).

specification(1,(connect(airSupplyvalve1,

Y.Kalfoglou,D.RobertsonairSupply,pump)true)).

specification(1,(connect(powerSupplycoilMagnet,

powerSupply,coilMagnet)true)).

specification(1,(connect(powerSupplycoilMagnet,

powerSupply,pump)true)).

specification(1,(connect(airLoadvalve2,

airLoad,valve2)true)).

specification(1,(connect(airLoadvalve2,

airLoad,pump)true)).

NotethattheconnectionsairSupplyvalve1,powerSupplycoilMagnetandairLoadvalve2aretheexternalconnectionsofthesystemregardingthepumpsystemwhoseinternalconnectionsarethefirstfivefromtheabove.Accordingtofigure5theexternalconnectionsconnecttheoutsideindividualswithanindi-vidualinsidepumpandthepumpitself.Theontologicalconstraintsofthistopologicallayerarethefollowing:

error(2,connection(C),connects(C,X,Y)).error(2,connects(C,X,Y),connects(C,Y,X)).error(2,connects(C,X,Y),(partof(Y,X))).error(2,connects(C,X1,Y1),(connects(C,X2,Y2)

((disjoint(X1,X2)disjoint(X1,Y2))(disjoint(Y1,X2)disjoint(Y1,Y2))))).

Thefirsttwoconditionsusedtotrapside-effectsofthesymmetricalpropertythatholdsfortheairpumpsystemconnectionsaswellasinvaliddefinitionsofconnections.Thethirdconditionprohibitsthatapartisconnectedtoit-selforitswhole.Thelasterrorconditionusedtodetecterrorswhenaconnectionconnectstwoentirelyseparatedpairofindividuals.Itusesthemereologicalrelationdis-jointthathasalreadybeendefinedinlayer2.Thesecondi-tionsareplacedinlayer2ofthearchitecturetomonitorthetopologicalstatementsoflayer1.5.3Systemstheory-Layer0

Atthelowestlayerofthearchitecture,layer0,weplacethesystemstheoryontology.Itdefinesstandardsystem-theoreticnotionssuchassystem,sub-system,systemboundary,environment,openness/closeness,etc.Anex-cerptofthisontologyisgivenbelowinthespecificationformatweadopt:

specification(0,(in

part

boundary(C,S)

connection(C)system(S)

connects(C,X,Y)in

system(Y,S))).

specification(0,(subsystem(SUB,SUP)system(SUB)

system(SUP)properof(SUB,SUP))).

specification(0,(open

boundary(C,S))).

specification(0,(closed

system(S))).

5-9

Thedeclarativereadingfortheabovesystemstheoryspecificationisasfollows:thein

predicatedefinesa

connectiontobeintheboundaryofasystemwhenitcon-nectsanindividualinthesystemtoanindividualoutsidethesystem;thesubsystem/2predicateholdsforindi-vidualsthatarepartofasystemandmustbesystemthem-selves;theopen

system/1predicate

statesthatasystemisaclosedsystemwhenitisnotanopensystem.Apartfromthesedefinitionswefoundalsodefinitionsofsysteminstanceswithrespecttothediagramoffigure5:pump,powerSupply,airSupplyandairLoadareallsystems.

Theontologicalconstraintsofsystemstheoryare:

error(1,in

error(1,inXsystem(S),insy(properThreeerrorshavebeendetected:twoatthemereologicallayerwithrespecttotheerroneousdefinitionofdisjoint,andoneatthetopologicallayerwheretheconditiondefinedovertheconnectsrelationwasprovedbytheinterpreter.Inparticularthedisjoint(reservoir,reservoir)anddisjoint(valve2,valve2)thatbelongintheconditionofconnectsrelationareerroneousandreportedatthelayerabove.

Themostinterestingcaseiswhenwecheckthemodelfromthesystemstheorypointofview.Wecanask,forexample,whetherthepumpisanopensystem.Wewillgeta,correct,positiveanswer.However,thehiddenerroristrappedandreported:

error

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