an anytime algorithm for hindsight knowledge-base optimization

328 Pages·2006·1.31 MB·English

D -D R :
EPENDENCY IRECTED ECONSIDERATION
A A A
N NYTIME LGORITHM
FOR
H K -B O
INDSIGHT NOWLEDGE ASE PTIMIZATION
by
Frances Laird Johnson
January 11, 2006
A dissertation submitted to the
Faculty of the Graduate School of
the State University of New York at Buffalo
in partial fulfillment of the requirements for
the degree of
Doctor of Philosophy
Department of Computer Science and Engineering
Copyrightby
FrancesLairdJohnson
2006
ii
Acknowledgements
AsIthinkofthosewhohavesupportedandinspiredmeovertheyears,Iamoverwhelmedbytheirnumber.
Space limitations and a somewhat legendary scatterbrain memory assure that I will be revising this list for
yearstocome,soIapologizeinadvancetothosewhoarenotmentionedbelow.
Withoutquestion,thisresearchisatestimonytotheguidance,patienceandperseveranceofmyadvisor,
Stuart Shapiro. He is a very rare and unique researcher—a versatile and ever publishing scholar who also
loves working with implementations and is an excellent programmer. This made Stu the perfect advisor
for my dissertation. I am especially grateful to him for holding the reins tight enough to guide me to this
destination yet loose enough to choose my own path. Stu’s ethics and professionalism meet the highest
standards,andIonlyhopethatIcanfollowhisexample.
WilliamRapaportandCarlAlphoncejoinedStutoformmycommittee. Billhasalwaysbeenareliable
source of knowledge, grammar, vocabulary, support, and humor. There were many times when Stu and I
wouldsettlesomepointofconfusionwith“askBill,he’llknow.”Carl’sinputwasanexcellentcomplement
to Bill and Stu’s, and this combination improved the readability of my work. My thanks also go to Erwin
Segal whose feedback from a background outside that of computer science was very helpful; relocation
forcedhimtostepdownfrommycommittee.
There is no way that I can sufficiently thank Sven Ove Hansson—who agreed to receive a 300-page
dissertation duringthe winter holidays(having never metme or, as far asI know, read my work), andwho
returnedafavorablereportwithrevisionsuggestionswithintwoweeks! Hisreportwillbeapermanentpart
iii
ofmycollectionoftreasuredcorrespondence.
IamgratefulforthefriendshipandcodingskillsofMichaelKandefer,whoseassistancenotonlyhelped
metorefinemyimplementation,butitfreedmetocompletethisdissertationwithinthetimeframerequired.
Ken Regan, Helene Kershner and Jodi Reiner provided a measure of support that was essential to my
successful survival and the completion of this work. Together, they gave me (and the graduate school)
confidence that I would finish. I am especially grateful to Helene for her consistent support and advice
throughoutmyentiretimeatUB.
Ihadanespeciallybadtimein2005-2006,physically,andtraditionalmedicinefailedme. SteveGrande,
Joe Cerceo, and John Zilliox kept me out of a wheelchair and, possibly, a hospice bed. This dissertation
wouldhaveneverbeencompletedwithouttheirhealingknowledge.
TheinterestandfeedbackofthemembersoftheSNePSResearchGroupwasinvaluableinthedevelop-
mentofmythesis. ThosenotalreadymentionedincludeJosephineAnstey,DebraBurhans,BharatBushan,
Alistair Campbell, Albert Goldfain, Haythem Ismail, Jean-Pierre Koenig, Joa˜o Martins, David Pierce, and
JohnSantore. IespeciallycommendJoa˜oforhisinitialcontributiontothedevelopmentoftheSNePSbelief
revisionsystem. And,IwillforeverbegratefulthatIhadHaythemandJohnasmylong-termoffice-mates.
Theywerealwaysthereforme,andtheyaretrulyexemplarypeople.
Other UB professors and staff and fellow students (past and present) who have helped, encouraged
and advised me during this journey are: Eloise Benzel, Jan Chomicki, Chris Egert, Sally Elder, Margaret
Evans,JoannGlinski,ElleHeffner,BharatJayaraman,KathyPohlman,BinaRamamurthy,KennethSmith,
MatthewStock,JayneeStraw,MarianneSullivan,LenTalmy,PallaviTambay,LynneTerrana,andDeborah
Walters. Thank you all. Special thanks go to James Llinas who jump-started my belief revision research
through funding from a group headed by Joseph Karakowski, who later supported this work (both profes-
sionallyandfinancially)forseveralyears.
iv
InadditiontothoseatUB,manyresearchersoutsidetheUBcommunityhaveprovidedvaluablefeedback
and insight. I am especially grateful to Samir Chopra, Doug Lenat, Thomas Meyer, Leora Morgenstern,
RenataWassermann,andMary-AnneWilliams.
To the teachers from my past, without the foundation you laid, I would not be the person I am, today.
From my earlier years, I especially thank Bill ”Doc” Chase, Debbie Coates, Mary Louise Kelley, Bob-
bette Mason, and Betty Richardson. And to Linda Brinkerhoff, Jeannette Neal, and Alison Girod, of Erie
CommunityCollege,yourexcellenceasteachersinspiredmetocontinueonatthePh.D.level.
My full support structure of friends and family is too large to include here, but I must mention a select
few. ToHoward,Bud,Rose,Letty,Margie,Ted,and,especially,Dad—Iloveyouandmissyouall. Mirjana,
you have been such a help and inspiration to me. Wick and Donna, your advice and encouragement and
constant support for both me and Tom has been invaluable. Carol, your unconditional faith in me is an
ever-present source of strength. You are my bestest friend in the whole wide world. Clint and Tillie, you
havelightenedmyloadinsomanyways;thankyouforyoursupport. Mom,youweremyfirstteacherandI
stillhavesomuchtolearnfromyou;IhopeIwillcontinuetobecomemorelikeyoueveryday. Tomygirls,
ElizabethandKatherine: youaremyfavoriteteachers,andIloveyoumorethantonguecantell. And,Tom,
youaremyeverything;themagnitudeofyourfaithinmeandloveformeamazesmeeveryday. You’rethe
best.
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Formyfamily
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Contents
Acknowledgements iii
Abstract xix
1 Introduction 1
1.1 BeliefChange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 NotationandTerminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 ImplementingKR&RRequiresaDeparturefromtheIdeal . . . . . . . . . . . . . . 8
1.3.2 SpecificObservationsMotivatingthisResearch . . . . . . . . . . . . . . . . . . . . 9
1.4 ResearchContributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 DissertationOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 BackgroundandRelatedWork 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 PurposeofThisChapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 BeliefChangevs. BeliefRevision . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.3 MergingFactionsofBeliefChange . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 Agents: Idealvs. Resource-Bounded . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 AGM/BaseResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 FoundationsandCoherenceApproaches . . . . . . . . . . . . . . . . . . . . . . . . 19
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2.2.2 IntegrityConstraintsforBeliefChangeOperationsonaKnowledgeSpace . . . . . . 20
2.2.3 AGMOperations: Expansion,Contraction,andRevision . . . . . . . . . . . . . . . 21
2.2.4 Hansson’sPostulatesforExpansion,Contraction,andRevision,ofaBeliefBase . . 25
2.2.5 Hansson’sBeliefBasePostulatesforBeliefChangeOperationsUsingKernels . . . 28
2.2.6 Wassermann’sResource-BoundedTheories . . . . . . . . . . . . . . . . . . . . . . 32
2.2.7 BeliefLiberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3 Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 TMSResearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4.3 JTMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.4 ATMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.5 LTMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.6 ITMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.7 GeneralProsandCons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.4.8 WhatdocurrentTMSsystemsdo? . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.4.9 TMSConclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.5 DifferentWaystoOrdertheBaseBeliefs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.6 SomeKR&RImplementedSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.6.1 SATEN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.6.2 Cyc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.6.3 SNePS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.7 TheNeedforaDOBSFormalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
viii
2.7.1 SomeLimitationsoftheAboveSystems . . . . . . . . . . . . . . . . . . . . . . . . 59
2.7.2 NeedsofaDOBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3 Reconsideration 63
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.1 MotivationsandAssumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 ABriefExampleShowingOperationOrderSide-Effects . . . . . . . . . . . . . . . 67
3.1.3 Jury-roomReasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.1.4 AnticipatingReconsideration—OtherBeliefChangeOperationsthatAppearSimilar 69
3.2 Reconsideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.1 TheKnowledgeStateforReconsideration . . . . . . . . . . . . . . . . . . . . . . . 70
3.2.2 DefininganOptimalBaseandanOptimalKnowledgeState . . . . . . . . . . . . . 73
3.2.3 OperationsonaKnowledgeState . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2.4 ComparingReconsiderationToBeliefLiberation . . . . . . . . . . . . . . . . . . . 86
3.3 ImprovingRecoveryforBeliefBases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.1 ReconsiderationProvidesanImprovedRecoveryAspecttoBaseBeliefChange . . . 88
3.3.2 ComparingRecovery-likeFormulations . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 BeliefChangeIssuesforNon-linearOrders . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.4.2 ASingleNogoodWithaNon-SingletonSetofMinimalBeliefs . . . . . . . . . . . 98
3.4.3 MultipleNogoodsHavingNon-SingletonSetsofMinimalBeliefs . . . . . . . . . . 100
3.4.4 Dealingwithnon-linearissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5 BeliefChangeinaTotalPre-order: SixStrategiesUsedbySATEN . . . . . . . . . . . . . . 101
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3.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5.2 StandardAdjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
3.5.3 Maxi-Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.5.4 HybridAdjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.5 GlobalAdjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.5.6 LinearAdjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.5.7 QuickAdjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.5.8 PreparingtoTestReconsideration . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.6 ReconsiderationonaTotalPre-orderUsingSATENStrategies . . . . . . . . . . . . . . . . 111
3.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.6.2 PerformingaSecondRevision: (((B+¬a)!+a)!) . . . . . . . . . . . . . . . . . . 111
3.6.3 Reconsideration: (((B+¬a)+a)!) . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4 Dependency-DirectedReconsideration 119
4.1 Introduction,MotivationandAssumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2 Dependency-DirectedReconsideration(DDR) . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2.1 TheDDRProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.2.2 DefiningaKnowledgeState . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.2.3 DefiningaNAND-set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2.4 DefiningComplete-I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.2.5 DefiningCulprits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.2.6 DefinitionsRelevanttoKnowledgeStateConsistencyandOptimality . . . . . . . . 125
4.2.7 DDRBeliefCredibilityandBaseCredibility,Ordering,andOptimality . . . . . . . 127
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