arcoe-09

54 Pages·2009·0.83 MB·English

by  Ivan José Varzinczak

Workshop Notes
The IJCAI-09 Workshop on
Automated Reasoning about Context and Ontology Evolution
ARCOE-09
July 11-12, 2009
Pasadena, California, USA
held at the
International Joint Conference on Artificial Intelligence
Co-Chairs
Alan Bundy
Jos Lehmann
Guilin Qi
Ivan José Varzinczak
AAAI Press

IntroductiontotheNotesoftheIJCAI-09WorkshopARCOE-09
Automated Reasoning about Context and Ontology Evolution
AlanBundya,JosLehmanna,GuilinQib,IvanJose´ Varzinczakc
a SchoolofInformatics,UniversityofEdinburgh
b InstituteAIFB,UniversitaetKarlsruhe
c MerakaInstitute,Pretoria,SouthAfrica
MethodsofautomatedreasoninghavesolvedalargenumberofproblemsinComputerSciencebyusing
formalontologiesexpressedinlogic.Overtheyears,though,eachproblemorclassofproblemshasrequired
adifferentontology,andsometimesadifferentversionoflogic.Moreover,theprocessesofconceiving,con-
trollingandmaintaininganontologyanditsversionshaveturnedouttobeinherentlycomplex. Allthishas
motivatedmuchinvestigationinawiderangeofdisparatedisciplinesabouthowtorelateontologiestoone
another.
TheIJCAI-09WorkshopARCOE-09bringstogetherresearchersandpractitionersfromcoreareasofArtifi-
cialIntelligence(e.g. KnowledgeRepresentationandReasoning,Contexts,andOntologies)todiscussthese
kindsofproblemsandrelevantresults.
Historically, therehavebeenatleastthreedifferent, yetinterdependentmotivationsbehindthistypeofre-
search:providingsupporttoontologyengineers,especiallyinmodelingCommonSenseandNon-Monotonic
Reasoning; defining the relationship between an ontology and its context; enhancing problem solving and
communicationforsoftwareagents,oftenbyallowingfortheevolutionoftheverybasisoftheirontologies
orontologylanguages.
ARCOECallforAbstractshasbeenformulatedagainstsuchhistoricalbackground.SubmissionstoARCOE-
09havebeenreviewedbytwotothreeChairsorPCmembersandrankedonrelevanceandquality.Approx-
imately seventy-five percent of the submissions have been selected for presentation at the workshop and
for inclusion in these Workshop Notes. Accordingly, the abstracts are here grouped in three sections and
sequencedwithineachsectionbytheirorderofsubmission.
CommonSenseandNon-MonotonicReasoning Ontologyengineersarenotsupposedtosucceedright
fromthebeginningwhen(individuallyorcollaboratively)developinganontology.Despitetheirexpertiseand
anyassistancefromdomainexperts,revisioncyclesaretherule. Researchontheautomationoftheprocess
ofengineeringanontologyhasimprovedefficiencyandreducedtheintroductionofunintendedmeaningsby
meansofinteractiveontologyeditors. Moreover,ontologymatchinghasstudiedtheprocessofmanual,off-
linealignmentoftwoormoreknownontologies.Thefollowingworksfocusonthedevelopmentofrevision
techniquesforlogicswithlimitedexpressivity.
Ribeiro,Wasserman.AGMRevisioninDescriptionLogics.
Wang,Wang,Topor.ForgettingforKnowledgeBasesinDL-Litebool.
Moguillansky,WassermannInconsistent-TolerantDL-LiteReasoning:AnArgumentativeApproach.
Booth,Meyer,Varzinczak.FirstStepsinELContraction.
Context and Ontology Most application areas have recognized the need for representing and reasoning
aboutknowledgethatisdistributedovermanyresources. Suchknowledgedependsonitscontext, i.e., on
thesyntacticand/orsemanticstructureofsuchresources. Researchoninformationintegration, distributed
knowledgemanagement,thesemanticweb,multi-agentanddistributedreasoninghavepinneddowndifferent
aspectsofhowontologiesrelatetoand/ordevelopwithintheircontext. Thefollowingworksconcentrateon
therelationshipbetweencontextsandontologies.
Ptaszynski,Dybala,Shi,Rzepka,Araki.ShiftingValenceHelpsVerifyContextualAppropriatenessofEmo-
tions.
Kutz,Normann.ContextDiscoveryviaTheoryInterpretation.
Redavid,Palmisano,Iannone.ContextualizedOWL-DLKBforthemanagementofOWL-Seffects.
Sboui,Be´dard,Brodeur,BadardModelingtheExternalQualityofContexttoFine-tuneContextReasoning
inGeo-spatialInteroperability.
Qi,Ji,Haase.AConflict-basedOperatorforMappingRevision.
AutomatedOntologyEvolution Agentsthatcommunicatewithoneanotherwithouthavingfullaccessto
theirrespectiveontologiesorthatareprogrammedtofacenewnon-classifiablesituationsmustchangetheir
ownontologydynamicallyatrun-time–theycannotrelyonhumanintervention. Researchonthisproblem
haseitherconcentratedonnon-monotonicreasoningandbeliefrevisionoronchangesofsignature,i.e.,ofthe
grammaroftheontology’slanguage,withaminimaldisruptiontotheoriginaltheory. Thefollowingworks
concentrateonAutomatedOntologyEvolution,anareawhichinrecentyearshasbeendrawingtheattention
ofArtificialIntelligenceandKnowledgeRepresentationandReasoning.
Bundy.Unite:ANewPlanforAutomatedOntologyEvolutioninPhysics.
Chan,Bundy.AnArchitectureofGALILEO:ASystemforAutomatedOntologyEvolutioninPhysics.
Lehmann.ACaseStudyofOntologyEvolutioninAtomicPhysicsastheBasisoftheOpenStructureOntol-
ogyRepairPlan.
Jouis,Habib,Liu.AtypicalitiesinOntologies:InferringNewFactsfromTopologicalAxioms.
Thanks to the invaluable and much appreciated contributions of the Program Committee, the Invited
Speakers and the authors, ARCOE-09 provides participants with an opportunity to position various ap-
proaches with respect to one another. Hopefully, though the workshop and these Notes will also start a
process of cross-pollination and set out the constitution of a truly interdisciplinary research-community
dedicatedtoautomatedreasoningaboutcontextsandontologyevolution.
(Edinburgh,Karlsruhe,Pretoria–May2009)
ARCOE-09Co-Chairs
AlanBundy(UniversityofEdinburgh,UK)
JosLehmann(UniversityofEdinburgh,UK)
GuilinQi(Universita¨tKarlsruhe,Germany)
IvanJose´Varzinczak(MerakaInstitute,SouthAfrica)
ARCOE-09InvitedSpeakers
FranzBaader(TechnischeUniversita¨tDresden,Germany)
DeborahMcGuinness(RensselaerPolytechnicInstitute,USA)
ARCOE-09ProgramCommittee
RichardBooth(Ma´ha˘aW´ıtta´yaalaiMahasarakham,Thailand)
PaoloBouquet(Universita`diTrento,Italy)
Je´roˆmeEuzenat(INRIAGrenobleRhoˆne-Alpes,France)
ChiaraGhidini(FBKFondazioneBrunoKessler,Italy)
AlainLeger(FranceTelecomR&D,France)
DeborahMcGuinness(RensselaerPolytechnicInstitute,USA)
ThomasMeyer(MerakaInstitute,SouthAfrica)
MauricePagnucco(TheUniversityofNewSouthWales,Australia)
ValeriadePaiva(PaloAltoResearchCenter(PARC),USA)
LucianoSerafini(FBKFondazioneBrunoKessler,Italy)
PavelShvaiko(TasLab,InformaticaTrentinaS.p.A.,Italy)
JohnF.Sowa(VivoMindIntelligence,Inc.,RockvilleMD,USA)
HolgerWache(FachhochschuleNordwestschweiz,Switzerland)
RenataWassermann(UniversidadedeSa˜oPaulo,Brazil)
Table of Contents

Martin O. Moguillansky and Renata Wassermann
Inconsistent-Tolerant DL-Lite Reasoning: An Argumentative Approach…………………….…...…...7-9

Zhe Wang, Kewen Wang and Rodney Topor
Forgetting for Knowledge Bases in DL-Lite .……………………………………………….………10-12
bool

Márcio Ribeiro and Renata Wassermann
AGM Revision in Description Logics……………………………………………….…………………13-15

Richard Booth, Thomas Meyer and Ivan Varzinczak
First Steps in EL Contraction..………………………………………………………………...………16-18

Michal Ptaszynski, Pawel Dybala, Wenhan Shi
Rafal Rzepka and Kenji Araki
Shifting Valence Helps Verify Contextual Appropriateness of Emotions…………………………...…19-21

Oliver Kutz and Immanuel Normann
Context Discovery via Theory Interpretation…….……………………………………………..……...22-24

Domenico Redavid, Ignazio Palmisano and Luigi Iannone
Contextualized OWL-DL KB for the Management of OWL-S Effects………………………….………25-27

Tarek Sboui, Yvan Bédard, Jean Brodeur and Thierry Badard
Modeling the External Quality of Context to Fine-tune Context
Reasoning in Geo-spatial Interoperability…………………………………………….……………….28-30

Guilin Qi, Qiu Ji and Peter Haase
A Conflict-based Operator for Mapping Revision…………………………………….……………….31-33

Alan Bundy
Unite: A New Plan for Automated Ontology Evolution in Physics……………………………….……34-36

Michael Chan and Alan Bundy
Architecture of GALILEO: A System for Automated Ontology
Evolution in Physics…………………………………………………………………….…….………..37-39

Jos Lehmann
A Case Study of Ontology Evolution in Atomic Physics as the Basis
of the Open Structure Ontology Repair Plan…….……………………………………………………40-42

Christophe Jouis, Bassel Habib and Jie Liu
Atypicalities in Ontologies: Inferring New Facts from Topological Axioms………………………….43-45

ARCOE-09 Workshop Notes
Inconsistent-TolerantDL-Lite Reasoning:
An ArgumentativeApproach
Mart´ınO.Moguillansky RenataWassermann
ScientificResearch’sNationalCouncil(CONICET) DepartmentofComputerScience(DCC)
AIResearchandDevelopmentLab(LIDIA) InstituteofMathematicsandStatistics(IME)
DepartmentofComputerScienceandEng.(DCIC)
UniversityofSa˜oPaulo(USP),BRAZIL.
UniversidadNacionaldelSur(UNS),ARGENTINA.
[email protected] [email protected]
R(cid:6)Eforroles;andafinitesetoffunctionalrestrictionsof
theform(functR). AssumingthesetsN ofvariablesand
V
1 Introduction NCofconstantnames,anABoxiscomposedbyafinitesetof
membershipassertionsonatomicconceptsandatomicroles,
Thisarticleisdevotedtotheproblemofreasoningoverin- oftheformA(a)andP(a,b),where{a,b}⊆N .
consistentontologiesexpressedthroughthedescriptionlogic C
AsusualinDLs,semanticsisgivenintermsofinterpreta-
DL-Lite[Calvaneseetal.,2007]. Aspecializedargumenta- tionsI =(ΔI,·I). Reasoningservices(RS)representlogi-
tion machinery is proposed through which DL-Lite knowl-
calimplicationsofKBassertionsverifying:
edge bases (KB) may be reinterpreted a` la argumentation.
SuchmachineryarisesfromthereificationtoDL-Liteofthe (subsumption) Σ|=C1(cid:6)C2orΣ|=E1(cid:6)E2;
argumentationframeworkintroducedin[Moguillanskyetal., (functionality) Σ|=(functR)orΣ|=¬(functR);and
2008a], which in turnwas formalizedontop of the widely (queryanswering) Σ|=q(x¯).
acceptedDung’sargumentationframework[Dung,1995]. A Aconjunctivequeryq(x¯),withatuplex¯ ∈ (N )n ofar-
pcorenlsimistiennatryonitnovleosgtyigeavtioolnuttioonhoafndAleLContthorloouggyhdaerbguugmgeinntgatainodn izt1y=nz2≥, o0r,z1is(cid:8)=azn2,onwheemreptCy saentdoEf aatoremrsesCp(ezc)ti,veEVly(za1,gze2n)-,
waspresentedin[Moguillanskyetal.,2008a]. Butthispro- eralconceptandageneralroleofΣ,andsomeofthenames
pctooonsraseilassatoeimnncisnygarteoshvtaeonrrdaotlniiontongl.oognAiteorsglouagmpypeeneavtraotaliuostniaotnpecrwohmnitihiqsusnoeosrynaefpuepdsliioeondf tx{¯hz.e,Wzfu1h,nezcn2ti}ox¯n⊆ivsatNhreC:e∪(mNNpVt)Vynt−aur→pele2c,NonVnostiodfreierdeeednvtaiirnfiyax¯bt.hleesWvaaerreiwacbiolllnessuisdine-
toworkincertaindomainsinwhichitismandatorytoavoid eredandthequeryisidentifiedasboolean. Intuitively,q(x¯)
loosinganykindofknowledgedisregardinginconsistencies. representsthe conjunctionof its elements. Let I bean in-
Therefore,weprovidethetheoryforaninconsistent-tolerant terpretation, and m : var(x¯)∪N −→ΔI a total function.
argumentationDL-Litereasoner,andfinallythematterofon- If z ∈ N then m(z) = zI otheCrwise m(z) = a ∈ ΔI.
tologydynamicsisreintroduced. We writeCI |=m C(z) if m(z) ∈ CI, I |=m E(z1,z2) if
(m(z1),m(z2)) ∈ EI, I |=m (z1=z2) if m(z1)=m(z2),
2 DL-LiteBriefOverview andI |=m (z1(cid:8)=z2) if m(z1)(cid:8)=m(z2). If I |=m φ forall
Next we describe in a very brief manner the language φ∈q(x¯),wewriteI |=mq(x¯)andcallmamatchforIand
DL-LiteA used to representDL-Lite knowledge. In the se- q(x¯).WesaythatIsatisfiesq(x¯)andwriteI|=q(x¯)ifthere
quelwewillwriteφ∈DL-LiteA,orΣ⊆DL-LiteA,toiden- isamatchmforI andq(x¯). IfI |= q(x¯)forallmodelsI
tifyaDL-Liteassertionφ,andaDL-LiteknowledgebaseΣ, ofaKBΣ,wewriteΣ |= q(x¯)andsaythatΣentailsq(x¯).
respectively. For full details about DL-Lite please refer to NotethatthewellknowninstancecheckingRS(Σ |= C(a)
[Calvaneseetal.,2007].ConsidertheDL-Litegrammar: orΣ|=E(a,b))isgeneralizedbyqueryanswering. Finally,
B−→A|∃R C−→B|¬B R−→P|P− E−→R|¬R theknowledgebasesatisfiabilityRS(whethertheKBadmits
atleastonemodel)willbediscussedinSect.4.
whereAdenotesanatomicconcept,P anatomicrole, P−
theinverseoftheatomicroleP,andBabasicconceptthatis 3 TheArgumentationDL-LiteReasoner
eitheratomicorconformingto∃R,whereRdenotesabasic
rolethatiseitheratomicoritsinverse. Finally,C denotesa Weareparticularlyinterestedinhandlingthereasoningser-
(general)concept,whereasEdenotesa(general)role. vices presented before. This will be achieved through the
AKBΣdetailstherepresentedknowledgeintermsofthe claimofanargument. Intuitively,anargumentmaybeseen
intensionalinformationdescribedintheTBoxT,andtheex- as a set of interrelated pieces of knowledgeprovidingsup-
tensional,intheABoxA. ATBoxisformedbyafiniteset port to a claim. Hence, the claim should take the form of
ofinclusionassertionsoftheformB (cid:6)Cforconcepts,and anypossibleRS,andtheknowledgeinsideanargumentwill
berepresentedthroughDL-LiteA assertions. Thenotionof
Writtenduringthefirstauthor’svisittoUSP,financedbyLACCIR. argumentwillrelyonthelanguageforclaims:
7
ARCOE-09 Workshop Notes
Lcl−→C1(cid:6)C2|E1(cid:6)E2|(functR)|¬(functR)|q(x¯) P(cid:2)(cid:6)P},¬(functP)(cid:11). Finally,coherency-negationoffunc-
Anargumentisdefinedasastructureimplyingtheclaim tionalassertionsisnotallowed,whereasnegationofqueries
fromaminimalconsistentsubsetofΣ,namelythebody. isonlyallowedforsingletons,i.e.,|q(x¯)|=1.
DguemfineinttioBni1s(aAsrtgruumctuernet)(cid:10)ΔG,ivβe(cid:11)n,awKheBreΣΔ⊆⊆DLΣ-LiistetAhe,abnoadry-, leaCdosmtopathriengnotthioenaorgfuamtteanctkswinhvioclhveudsuianllyarceolineflsicotnivaenpaari-r
βand∈(L3)cl(cid:2)Xthe⊂claΔim:,Xan|d=itβh.oWldess(a1y)thΔat|=Bsβu,p(p2o)rtΔsβ(cid:8)|=. T⊥he, gdeucmideendtcifomthpeacroisuonntecrrairtgeurimone.ntTphrervoauiglshfsruocmhacrciotenrflioicnt,,iatnids
domainofargumentsfromΣisidentifiedthroughthesetAΣ. hapepreeianrsthteoasttpaecckifeyndsuscuhpcidrietenrtiiofine.d.IAnvgaernieetryalo,fthaelteqrunaantitvietys
Consider a KB Σ and an RS α ∈ Lcl, the argumenta- and/orqualityofknowledgeissomehowweightedtoobtain
tive DL reasoner verifies Σ |= α if there exists (cid:10)Δ,β(cid:11) ∈ a confidencerate of an argument. The exhaustive analysis
AΣ such that β unifies with α and (cid:10)Δ,β(cid:11) is warranted. goesbeyondthescopeofthisarticle,henceanabstractargu-
An argument is warranted if it ends up accepted (or un- mentcomparisoncriterion“(cid:16)”willbeassumed. Thenotion
defeated) from the argumentation interplay. This notion ofattackisbasedonthecriterion“(cid:16)”overconflictivepairs.
will be made clear in the sequel. Primitive arguments are
Definition3(Attack) Givenaconflictivepairofarguments
fat(cid:10)hu{onApscr(etiaimow)ni}tha,iovl{seaAes(sabaerorg)t}duio(cid:11)ym.necΣsno(tn|=fsu(cid:10)ins{(tcf(sutfuRnoncf)tctRcthRae)n)ic}sbl,eas(iifmpmuapnriltctystoeRvflef)a,r(cid:11)ni.ffioaerrdgBiutnhemsrstoieadunnegtcs’hes, Baorf1gBu∈1mA(eoΣnrtaBann1ddisBBd22e(cid:16)∈feBaAt1Σedh,oBblyd2sBd.e2Af)e,ragntuosmtBeed1natisBffB2B2is(cid:5)→2siaBsit1dh.aecdoeufenateterr-
body. For instance, Σ |= ¬P(a,c) is verified through ei- Assaidbefore,thereasoningmethodologyweproposeis
theranargument(cid:10){P(a,b),(functP)},{¬P(a,z),z (cid:8)= b}(cid:11), basedontheanalysisofthewarrantstatusofthearguments
or(cid:10){P(b,c),(functP−)},{¬P(z,c),z(cid:8)=a}(cid:11),withz∈N . givingsupporttotherequiredRS.Thisisthebasisofdialec-
V
Observethatz(cid:8)=bandz(cid:8)=aarededucedfrom(2)inDef.1. tical argumentation[Chesn˜evar and Simari, 2007]. An ar-
Once an argument supporting the required RS is identi- gumentationlinemaybeseenastherepeatedinterchangeof
fied,theargumentationgamebegins: arepeatedinterchange argumentsandcounterargumentsresemblingadialoguebe-
of arguments and counterarguments (i.e.,arguments whose tweentwoparties,formally:
claimposesajustificationtodisbelieveinanotherargument). Definition4(ArgumentationLine) Given the arguments
Fromthestandpointoflogics,thisisinterpretedasacontra- B1,...,BnfromAΣ,anargumentationlineλisanon-empty
dictionbetweenanargumentB1andacounterargumentB2. sequenceofarguments[B1,...,Bn]suchthatBi(cid:5)→Bi−1,for
Suchcontradictioncouldappearwhileconsideringtheclaim 1<i≤n.WewillsaythatλisrootedinB1,andthatBnis
of B2 along with some piece of informationdeduced from theleafofλ.Argumentsplacedonevenpositionsarereferred
B1.Thereafter,B1andB2arereferredasaconflictivepair. ascon,whereasthoseonoddpositionswillbepro. Thedo-
Definition2(Conflict) Two arguments (cid:10)Δ,β(cid:11) ∈ AΣ and mainofeveryargumentationlineformedthrougharguments
(cid:10)Δ(cid:2),β(cid:2)(cid:11) ∈ AΣ are conflictive iff Δ |= ¬β(cid:2). Argument fromAΣisnotedasLΣ.
(cid:10)Δ(cid:2),β(cid:2)(cid:11)isidentifiedasthecounterargument. We will considerLΣ to containonly argumentationlines
Letusanalyzethe formationofcounterarguments. Con- that are exhaustive (lines only end when the leaf argument
sidertheargument(cid:10){A (cid:6) B,B (cid:6) C,C (cid:6) D},A (cid:6) D(cid:11), hasnoidentifiabledefeaterfromAΣ),andacceptable(lines
sinceA (cid:6) C isinferredfromitsbodyapossiblecounterar- whose configuration is compliant with the dialectical con-
gumentcouldsupportan axiomlike ¬(A (cid:6) C). But how straints). Indialecticalargumentation,thenotionofdialec-
couldnegatedaxiomsbeinterpretedinDLs? In[Flouriset ticalconstraints(DC)isintroducedtostateanacceptability
al., 2006], negation of general inclusion axioms was stud- conditionamongtheargumentationlines. TheDCsassumed
ied. Ingeneral,foranaxiomlikeB (cid:6) C,theconsistency- inthisworkwillincludenon-circularity(noargumentisrein-
negationis ¬(B (cid:6) C) = ∃(B (cid:14)¬C) and the coherency- troducedinasameline),andconcordance(thesetofbodies
negation∼(B (cid:6) C) = B (cid:6) ¬C. Fortheformer,although ofpro(resp.,con)argumentsinthesamelineisconsistent).
theexistenceassertion∃(B(cid:14)¬C)(x)fallsoutofDL-LiteA, Adialecticaltreeappearswhenseveraldialoguesabouta
it couldbe rewrittenas a queryq((cid:10)x(cid:11)) = {B(x),¬C(x)}. commonissue(i.e.,therootofthetree)aresettogether.Thus,
Forinstance,thecounterargument(cid:10){B(a),A(a),A(cid:6)¬C}, fromaparticularsetofargumentationlines(namelybundle
{B(a),¬C(a)}(cid:11)supportsq((cid:10)x(cid:11))withx = a. Ontheother set) the dialectical tree is formalized. A bundleset for B1
hand,coherency-negationissolvedbysimplylookingforan is the maximalset S(B1) ⊆ LΣ (wrt. set inclusion)of ex-
argumentsupportingB (cid:6) ¬C. Recallthataninconsistent haustiveandacceptableargumentationlinessuchthatevery
ontologyisthatwhichhasnopossibleinterpretation,whereas λ∈S(B1)isrootedinB1.Finally,adialecticaltreeis:
anincoherentontology[Flourisetal.,2006]isthatcontaining Definition5(DialecticalTree) GivenaKBΣ⊆ DL-LiteA,
atleastoneemptynamedconcept.Observethatincoherence a dialectical tree T(R) rooted in an argument R ∈ AΣ
doesnotinhibittheontologyfrombeingsatisfiable. is determined by a bundle set S(R) ⊆ LΣ such that B is
Weextendnegationofaxiomstofunctionalassertions,in- an inner node in a branch [R,...,B] of T(R) (resp., the
terpreting¬(functR)asaroleRthatdoesnotconformtothe root argument) iff each child of B is an argument D ∈
definitionofafunction.Theonlyoptiontoformanargument [R,...,B,D,...] ∈ S(R)(resp.,D ∈ [R,D,...] ∈ S(R)).
supporting such negation is through extensional informa- Leavesin T(R)andeachline inS(R), coincide. Thedo-
tion(ABox). Forinstance,theargument(cid:10){P(a,b),P(cid:2)(a,c), mainofalldialecticaltreesfromΣwillbenotedasTΣ.
8
ARCOE-09 Workshop Notes
Withalittleabuseofnotation,wewilloverloadthemem- wouldbesatisfiablefromourtheory.Ontheotherhand,what
bershipsymbolwritingB ∈ λtoidentifyB fromtheargu- isexactlyasatisfiableKBfortheproposedreasoner?Ifthere
mentationlineλ,andλ∈T(R)whenthelineλbelongsto isawarrantedargumentsupportinganRSαandthereisan-
thebundlesetassociatedtothetreeT(R). Dialecticaltrees otherwarrantedargumentsupporting¬α,thentheKBwould
allowtodeterminewhethertherootnodeofthetreeistobe beunsatisfiable.Anargumentationsystemfreeofsuchdraw-
accepted(ultimatelyundefeated)orrejected(ultimatelyde- backswoulddependontheappropriatedefinitionofthecom-
feated)asarationallyjustifiedbelief. Therefore,givenaKB parisonandwarrantingcriteria. Therequiredanalysisispart
Σ⊆DL-LiteAandadialecticaltreeT(R),theargumentR∈ ofthefutureworkinthisdirection.
AΣ is warranted from T(R) iff warrant(T(R)) = true. Argumentationwasstudiedin[WilliamsandHunter,2007]
The warranting function warrant : TΣ−→{true,false} toharnessontologiesfordecisionmaking. Throughsuchar-
willdeterminethestatusofthetreefromthemarkoftheroot gumentationsystemtheybasicallyallowtheaggregationof
argument. Thisevaluationwillbeobtainedbyweightingall defeasiblerulestoenrichtheontologyreasoningtasks.Inour
theinformationpresentinthetreethroughthemarkingfunc- approachanargumentativemethodologyisdefinedontopof
tionmark:AΣ×LΣ×TΣ−→M. Suchfunctiondefinesthe theDL-reasoneraimingatreasoningaboutinconsistenton-
acceptancecriterionappliedtoeachindividualargumentby tologies. Howeverourmainobjectivegoesfurtherbeyond:
assigningto eachargumentin T(R)a markingvaluefrom to manage ontology evolution disregarding inconsistencies.
thedomainM = [D,U]. Thisismorelikelytobedoneby Tosuchpurpose,atheoryofchangeisrequiredtobeapplied
obtainingthemarkofaninnernodeofthetreefromitschil- overargumentationsystems.In[Moguillanskyetal.,2008b],
dren(i.e.,itsdefeaters). Onceeachargumentinthetreehas atheorycapableofhandlingdynamicsofargumentsapplied
beenmarked(includingtheroot)thewarrantingfunctionwill overdefeasiblelogicprograms(DeLP)[Garc´ıa andSimari,
determinetheroot’sacceptancestatusfromitsmark.Hence, 2004] was presented under the name of Argument Theory
warrant(T(R))=true iff mark(R,λ,T(R))=U. Change(ATC).Basically,dialecticaltreesareanalyzedtobe
alteredinaformsuchthatthesamerootargumentendsup
DELP (Defeasible Logic Programming) [Garc´ıa and warranted from the resulting program. Ongoing work also
Simari,2004], isanargumentativemachineryforreasoning
involvesthestudyofATContopofthemodelpresentedhere.
overdefeasiblelogicprograms.Inthisarticlewewillassume
theDELPmarkingcriterion.Thatis,(1)allleavesaremarked References
U and(2)everyinnernodeBismarkedU iff everychildof
BismarkedD,otherwise,BismarkedD. [Calvaneseetal.,2007] D. Calvanese, G. De Giacomo,
Example1 ConsidertheKBΣandargumentsleadingtothe D.Lembo,M.Lenzerini,andR.Rosati.TractableReason-
dialecticaltreedepictedbelowtoanswerΣ|=B(a). ingandEfficientQueryAnsweringinDescriptionLogics:
Σ={A(cid:6)B,A(cid:6)C,C (cid:6)¬B,D(cid:6)A,A(a),C(b),D(b)} TheDL-Litefamily. JAR,39(3):385–429,2007.
R=(cid:10){A(cid:6)B,A(a)},{B(a)}(cid:11) [Chesn˜evarandSimari,2007] C. Chesn˜evar and G. Simari.
B =(cid:10){C(cid:6)¬B,A(cid:6)C,A(a)},{¬B(a)}(cid:11) ALattice-basedApproachtoComputingWarrantedBelief
1
B =(cid:10){D(cid:6)A,A(cid:6)B,C(b),D(b)},{C(b),B(b)}(cid:11) inSkepticalArgumentationFrameworks. InIJCAI,pages
2
B =(cid:10){A(cid:6)C,C (cid:6)¬B},A(cid:6)¬B(cid:11) 280–285,2007.
3
[Dung,1995] P.Dung. OntheAcceptabilityofArguments
Assume λ1 = [R,B1,B2] and λ2 = [R,B3,B2]. Ob- and its Fundamental Role in Nonmonotonic Reasoning
wseerlvleatshaBt,2Bo3fisBa3)cobuunttesrinacrgeuBm2e(cid:16)ntBo3fBis2d(aes- R atenldl.,L7o7g:3ic21P–r3og5r7a,m19m9i5n.gandn-personGames. Artif.In-
Rduecgeadrdfirnogmλλ2,2,aBno3thcearnnjuosttiafitctaactikonB2to∈avλoi1d. B B [Flourisetal.,2006] G.Flouris, Z.Huang,J.Pan,D.Plex-
B3attackingB2isthatnon-circularitywould 1 3 ousakis, and H. Wache. Inconsistencies, Negations and
ChangesinOntologies.InAAAI,pages1295–1300,2006.
beviolated. Followingthemarkingfunction,
rsoinocteRB1is∈mλa1rkaendduBnd3e∈feaλt2eda.reTdheufse,attheed,trtheee B2 B2 [Gasribc´ılaeaLnodgSicimParorig,r2a0m0m4]inAg:.GAanrcA´ıargaunmdeGn.taStiivmeaAri.ppDroeafecah-.
endsupwarrantingtheargumentRwhichsupportstheRS TPLP,4(1-2):95–138,2004.
andthereforeΣ|=B(a)holds. [Moguillanskyetal.,2008a] M. Moguillansky,N.Rotstein,
andM.Falappa.ATheoreticalModeltoHandleOntology
4 ConcludingRemarksandFutureWork Debugging&ChangeThroughArgumentation.InIWOD,
AnovelDL-Litereasonerbasedonargumentationtechniques 2008.
was proposed. The machinerypresented here is definedto [Moguillanskyetal.,2008b] M.Moguillansky,N.Rotstein,
support the usual DL-Lite reasoning services, including an M. Falappa, A. Garc´ıa, and G. Simari. ArgumentThe-
extensionoftheconjunctivequeriespresentedin[Calvanese oryChangeAppliedtoDefeasibleLogicProgramming.In
et al., 2007]. In particular, the notion of satisfiability de- AAAI,pages132–137,2008.
servesspecialattentionsinceitsmeaningrequirestoberein-
[WilliamsandHunter,2007] M. Williams and A. Hunter.
terpreted. Given that the argumentation machinery would
Harnessing Ontologies for Argument-Based Decision-
answerconsistentlydisregardingthepotentiallyinconsistent
MakinginBreastCancer. ICTAI,2:254–261,2007.
KB, a KB that is unsatisfiable for standard DL reasoners
9
ARCOE-09 Workshop Notes
Forgetting for Knowledge Bases in DL-Lite
bool
ZheWang,KewenWangandRodneyTopor
GriffithUniversity,Australia
Abstract Inthispaper,weinvestigatetheissueofsemanticforget-
tingforDL-LiteKBs. Themaincontributionsofthispaper
WeaddresstheproblemoftermeliminationinDL-
canbesummarizedasfollows:
Liteontologiesbyadoptingtechniquesfromclas-
sicalforgettingtheory. Specifically,wegeneralize • Weintroduceamodel-baseddefinitionofforgettingfor
our previous results on forgetting in DL-Litecore DLKBs. Weinvestigatesomereasoningandexpress-
TBox to forgetting in DL-Litebool KBs. We also ibilitypropertiesofforgetting,whichareimportantfor
introduce query-based forgetting, a parameterized DL-Liteontologyreuseandmerging.
definition of forgetting, which provides a unify- • We provide a resolution-like algorithm for forgetting
ingframeworkfordefiningandcomparingdifferent aboutconceptsinDL-Litebool KBs. Thealgorithmcan
definitionsofforgettinginDL-Liteontologies. alsobeappliedtoKBforgettinginDL-Litehorn,andto
anyspecificquery-basedforgetting.Itisprovedthatthe
1 Introduction algorithmiscomplete.
• Asageneralframeworkfordefiningandcomparingvar-
Anontologyisaformaldescriptionoftheterminologicalin-
iousnotionsofforgetting,weintroduceaparameterized
formationofanapplicationdomain. Anontologyisusually
forgettingbasedonquery-answering,bywhichagiven
representedasaDLknowledgebase(KB),whichconsistsof
collectionofqueriesdeterminestheresultofforgetting.
aTBoxandanABox. AsontologiesinSemanticWebappli-
Thus,ourapproachactuallyprovidesahierarchyoffor-
cationsarebecominglargerandmorecomplex,achallenge
gettingforDL-Lite.
ishowtoconstructandmaintainlargeontologiesefficiently.
Recently, ontology reuse and merging have received inten-
2 ForgettinginDL-Lite KnowledgeBases
sive interest, and different approaches have been proposed. bool
Amongseveralapproaches,theforgettingoperatorispartic- Inthissection,wedefinetheoperationofforgettingasigna-
ularlyimportant,whichconcernstheeliminationoftermsin turefromaDL-LiteboolKB.Weassumethereaders’familiar-
ontologies. Informally,forgettingisaparticularformofrea- itywithDL-Litebool. Forthesyntaxandsemanticsdetailsof
soningthatallowsasetofattributesF (suchaspropositional DL-Litebool,thereadersshouldreferto[Artaleetal.,2007].
variables,predicates,conceptsandroles)inaKBtobedis- Let L and Lh, respectively, denote the languages DL-
cardedorhiddeninsuchawaythatfuturereasoningonin- Litebool and DL-Litehorn. Without special mentioning, we
formationirrelevanttoF willnotbeaffected.Forgettinghas use K to denote a KB in L and S a signature (a finite set
beenwellinvestigatedinclassicallogic[LinandReiter,1994; of concept names and role names) in L. Our model-based
Langetal.,2003]andlogicprogramming[EiterandWang, definition of forgetting in DL-Lite is analogous to the defi-
2008;Wangetal.,2005]. nitionforforgettinginclassicallogic[LinandReiter,1994;
Efforts have also been made to define forgetting in DL- Langetal.,2003].
Lite[Kontchakovetal., 2008;Wangetal., 2008], afamily LetI1,I2betwointerpretationsofL.DefineI1∼S I2iff
oflightweightontologylanguages. However,adrawbackin 1. ΔI1 =ΔI2,andaI1 =aI2foreachindividualnamea.
theseapproachesisthatforgettingisdefinedonlyforTBoxes.
Althoughasyntacticnotionofforgettinginontologiesisdis- 2. ForeachconceptnameAnotinS,AI1 =AI2.
cussedin[Wangetal.,2008],nosemanticjustificationispro- 3. ForeachrolenameP notinS,PI1 =PI2.
vided.Inmostapplications,anontologyisexpressedasaKB,
whichisapairofaTBoxandanABox. Webelievethatfor- Clearly,∼Sisanequivalencerelation.
gettingshouldbedefinedforDL-LiteKBsratherthanonly Definition1 WecallKBK(cid:2) aresultofmodel-basedforget-
forTBoxes. Althoughitisnothardtoextendthedefinitions tingaboutSinKif:
offorgettingtoKBs,oureffortsshowthatitisnon-trivialto • Sig(K(cid:2))⊆Sig(K)−S,
extendresultsofforgettinginTBoxestoforgettinginKBs,
duetotheinvolvementofABoxes. • Mod(K(cid:2))={I(cid:2)|∃I ∈Mod(K)s.t.I ∼S I(cid:2)}.
10