N onmonotoniRce asoning ( ) ArtificiIanlt elligesneclee catneddr ecetnitt les PatriHcekn rWyi nstofno,u ndgi enditor J.M ichael BDraandiye,Gl . B obrowa,n dR andalDla vis, curreendti tors ArtificIinatle lligAenn McIeT: P erspectViolvuem,e Is a ndII ,e ditebdyP atrick Henry Winstoann dR ichardH enryB rown1, 979 RoboMto tioPnl:a nnianngdC ontreodli,t beydM ichaBerla dJyo,h nM .H ollerbach, TimothJyo hnsoTno,m Lozanoraenzd,M attheTw. M ason,1 982 TheA cquisiotfiS oynn tacKtniocw ledRgoeb,e rCt. B erwic1k9,8 5 , TheC onnectMiaocnh inWe., D anieHlill is1985 Reasonianbgo uCth angeT:i mea ndC ausatifroonm theS tandpooifnA tr tificial IntelligYoeanvcS eho,h am,1 988 SoliSdh apJea,n J . oenKdeirnk,1 990 ObjeRcetc ognibtyiC oonm puteTrh:e R oloef G eometrCiocn strainWt.s E,r iLc . Grims1o9n9,0 RepresenatnidnR ge asoniwnigt Phr obabilKinsotwilce dgAe L:o gicAaplp roactho ProbabilFiahtieiemsB ,ac chu1s9, 90 Dot heR ighTth ingS:t udiienLs i mitReadt ionaSlituatryR,tu seslaln dE riWce fald, 1991 Three-DimensiCoonmaplu teVri sioAn :G eometrViice wpoiOnlitvi,er Faugeras, 1993 ContemplaMtiinndgs A: Forumf orA rtificIinatle lligeednicteeb,yd W ilaml iJ. , ClanceSyt,e pheWn. SmoliarandM arkJ .S tefik1,9 94 Ruleosf E ncounteDre:s igniCnogn ventifoonrAs u tomatNeedg otiataimoonn g ComputeJresff,r eSy. R osenschaenidnG ilaZdl ot.ki1n9,9 4 QualitaRteiavseo niMnogd:e lianngdS imulatwiiotnIh n complKentoew ledBgee,n ­ jamiKnui per1s9,9 4 ComputatiTohneaolr ioefIs n teractainodnA genceyd,i tbeydP hiliEp.A grea nd StanleJy. R osensche1i9n9,6 TheA rto fC ausaClo njectGulreen,nS hafe1r9, 96 NonmonotoRneiacs oniGnrgi,g oArntiosn io1u9,9 7 NonmonotoRneiacs oning GrigorAinst oniou witcho ntributbiyMo anrsy -AnWniel liams TheM IT Press CambridgMea,s sachusetts LondonE,n gland ©1997M assachusetItnss titouftT ee chnology Allr ighrtesse rved. Nop arto ft hibso okm ay ber eproducienad n yf orbmy a nye lectroonri c mechanicmaela ns( includpihnogt ocopyirnegc,o rdionrgi ,n formatsitoonr aagned r etrevial) withopuetrm issiionwn r itifnrgo mt hep ublisher. Thisb oowkas seti nIh- TEXb yt hea uthoarn dw as printaendd b oundi nt heU nietdS tateosf America. LibraroyfC ongreCsast aloging-in-PubDlaitcaa tion AntonioGu., ( Grigoris) Nonmonotroeasnoincin g /G rigorAinst oniou. p. cm.-(ArtifiIcnitaell ligence) Includbeisb liograprheifcearle nacnedsi ndex. ISBN0 -262-011(5h7b-:3a lkp.a per) 1.N onmonotroenasiocn inIg..T i tleI.IS .e riAerst:i ficIianlt elli(gCeamnbcrei dgMeas,s .) Q339.2.A581 996 51I. 3-dc20 96-15528 CIP ToP opain dG iogros,m y parenttosw, h oml owee verytgh in Contents SeriFeosr eword Xlll I PRELUDE 1 1 Introduction 3 1.1 Whatt hibso oki sa bout 3 1.2S tylaei,m asn di ntendaeudd ience 5 1.3 Booko verview 7 1.4 Howt ou set hibso ok 9 1.5 Acknowledgments 9 2 PredicaLtoeg ic* 11 2.1T he synotfpa rxe diclaotgei c 11 2.1T.h1el anguaogfpe r ediclaotgei c 11 2.1S.u2b stitutions 13 2.2T hes emantoifcp sr ediclaotgei c 14 2.2I.n1t erpretaantdiv oanlsi dity 14 2.2N.o2r maflo rms 15 2.2H.e3r braanldg ebras 16 2.3P rootfh eory 16 2.3S.e1q uent calculi 16 2.3R.e2s olution 17 II DEFAULT LOGIC 19 3 DefaulRte asoning 21 3.1 Then otioofna default 21 3.2T hes yntaoxfD efauLlotg ic 25 3.3 Informdails cusosfit ohnes emantics 26 4 OperationSaelm anticosfD efaulLto gic 31 4.1T hed efinitoifoe nx tensions 31 4.2S omee xamples 35 viii Contents 4.3 A prototyPpreo loigm plementation 38 4.4 An alternacthiavrea cteriozfae txitoenn sions 39 4.5S omper opertoifDe esaf ultL ogic 43 5 NormalD efaulTth eories 49 5.1 Normadle faults 49 5.2 Somet heoretpircoaple rties 50 5.3 A protohfoer y forn ormadle fault theories 53 5.4 Limitatoifon nosr madle fautlhte ories 56 6 Semi-normDaelf aulTth eories 59 6.1 Orderesde,m i-nordmeafla utlhte ories* 59 6.2 Prooofft hee xistoefen xctee ns*i ons 62 6.3 Translatiinotnso e mi-norfmoarlm 68 7 Alternative Approaches 71 7.1 PropertoifDe esf auLlotg ic 72 7.1E.x1i steonfce ex tensions 72 7.1.J2o incto nsistoefnj cusyt ifitcioans 73 7.1.C3u mulatiavnidtL ye mmas 74 7.2J ustifiDeedf auLlot gic 75 7.3 ConsratineDde fauLlotg ic 78 7.4I nterconneacntdei xoanmsp les 83 7.5 Computabialnidtc yo mplexciotnys iderations 87 8 PrioritAimeosn g Defaults 91 8.1 PDL:P rioritDiezfeadu Llotg ic 92 8.2 PRDL:R easoninagb ouptr iorities 94 8.3 Ane xamplfer oml egarleas oning 98 8.4 An alternacthiavre acterofie zxtaetnisoino ns* 99 8.5 PropertoifPe RsD L* 100 Contents ix Referencfeosr P artI I 105 IIIC LASSICALA PPROACHES TO NONMONOTONIC REASONING 107 9 AutoepistemLiogci c 109 9.1 Thel anguaogfae u toepistleomgiicc 110 9.2 Thes emantoifca su toepistfeomrimcu lae 112 9.3 Expansioofna su toepisttehmeiocr ies 114 9.4 Stabsleet asn dt heiprr operties 115 10 Computign ExpansionosfA E-Theories 121 10.1M otivatainodnd escripotfit ohnem ethod 121 10.2S omee xamples 124 10.C3o rrectness proofs* 126 104. A prototiymppel ementaitnPi roonl og 129 11 Embeddign DefaulLto gici ntoA E-Logic 131 11.1E xpressdienfga ult tash eAoEr-itehse ories 132 11.2M inimaelx pansions 133 11.3M oderatgerloyu ndeexdp ansions* 134 11.4S trongglryo undeexdp ans*i ons 136 11.5P roofs* 137 12 Circumscription 143 12.1P rediccaitrec umscription 144 12.M2 inimamlo dels 149 12.3C onsisteanncdey x presspiovwee r 152 12.4V ariabclier cumscription 154 12.5P rioritciizrecdu mpstciroin 157 Referencfeosr P art III 161 x Contents IV ABSTRACT AND DYNAMIC APPROACHES TO NONMONOTONIC REASONING 163 13 NonmonotoniIcn ferenRceel ations 165 13.T1h en otioonfa ni nfererneclea tion 165 13.B2as icp ropertpiuersec: o nditions 166 13.B3as icp ropertiinetse:r acwtiitolhno giccaoln nectives 168 13.4I nfererneclea tiiondn esf aullotg ic 172 135 Preferenmtoidaell s 175 . 13.6F urthperro pertoifie nsf ererneclea tions 178 14 BelieRfe vision 183 14.1I ntroduction 184 14.2E xpansion 186 14.C3o ntraction 187 14.4R evision 189 14.5I nterrelationships 190 14.E6p sitemiecn trenchmoerdnetr ings 191 14.7O ddsa nde nds* 195 15 ImplementiBnegl ieRfe vision 197 15.1F iniptaer tienatlre nchment rankings 198 15.2 A computatiomnoadle l 201 15.A3 p roceduarlaglo riftohram d justment* 204 15.4C onnectiwointsth h eorcyh ange 208 16 Interconnect* ions 213 16.Tr1a nslatiboentsw eerne visainodn nonm onotoniincf erence 214 16.N2o nmonotonrieasco ningu sinegn trenchment. 216 16.C3ha ngnig nonm onotoniincf ererneclea t.ions 219 16.E4x ample 221 Contents xi Referencfeosr P artI V 226 V NONMONOTONIC REASONING AND LOGIC PROG RAMM ING 227 17 The SystemT heorist 229 17.B1as icc oncepts 229 172 RelationtsohD iepf auLlotg ic 231 . 17.N3a mesa ndc onstraints 232 17.T4h ep rogrammlianngg uaogfTe heorist 237 17.E5x planatvieorns purse diction 239 18 StablMeo delS emanticosfL ogicP rograms 243 18.B1as icc oncepotfls o giprco gramming 243 18.S2t abmloed elosfl ogpirco grams 245 18.A3n alternacthiavrea cterization 248 18.L4o gipcr ograwmist chl assinceagla tion 250 19 Well-FoundSeedm antics 255 19.M1o tivation 255 19.P2a rtimaold els 256 19.D3e finitoifot nh ew ell-foumnoddeedl 258 19.S4o mep ragmatic guidelines 261 Referencfeosr P art V 267 VI FINALE 269 20 FutureD irectioonfNs onmonotoniRce asonign Re- 271 search 20.T1h eory veprrsaucst ice 271 20.D2y namiocfsn onmonotorneiasco ning 273 20.P3r agmatoifcn so nm onotonriecas oning 273