Approximate Assertional Reasoning Over Expressive Ontologies

221 Pages·2010·2 MB·English

Approximate Assertional Reasoning
Over Expressive Ontologies
ZurErlangungdesakademischenGradeseines
DoktorsderWirtschaftswissenschaften
(Dr. rer. pol.)
vonderFakultätfür
Wirtschaftswissenschaften
desKarlsruherInstitutsfürTechnologie(KIT)
genehmigte
DISSERTATION
von
Dipl.-Inform. TuvshinturTserendorj
TagdermündlichenPrüfung: 27. Januar2010
Referent: Prof. Dr. RudiStuder
Korreferent: Prof. Dr. DetlefSeese
Prüfer: Prof. Dr. Karl-HeinzWaldmann
Karlsruhe2010
2
Abstract
In the Semantic Web, ontologies provide the required vocabulary for a meaningful
and machine-understandable interpretation of data. Nowadays, expressive ontolo-
giesareusuallywrittenintheW3CstandardlanguagecalledtheWebOntologyLan-
guage(OWL).InordertoleveragethefullpowerofOWLforemergingSemanticWeb
applications, ontology reasoning holds a key position by allowing access to implicit
knowledgein ontologies. Analyzing theapplication domain ofstate-of-the-artOWL
reasoning techniques, an important issue tobe consideredis theproblem ofscalable
assertionalreasoningoverexpressiveontologieswith large terminologicalas wellas
assertionalknowledge–acomputationallyintractableproblem.
In this thesis, we address this issue by means of logical approximation. Subse-
quently, we provide approximate reasoning methodsfor scalable assertionalreason-
ing whose computational properties can be established in a well-understood way,
namelyintermsofsoundnessandcompleteness,andwhosequalitycanbeanalyzed
in terms of statistical measurements, namely recall and precision. The basic idea of
these approximate reasoning methods is to speed up reasoning by trading off the
qualityofreasoningresultsagainstincreasedspeed.
Thevariousaspectsofthisthesisspanthefieldsofknowledgecompilation,query
answering, and resource-bounded reasoning. In the context of knowledge compila-
tion, exploiting the fact that data complexity is polynomial for non-disjunctive dat-
alog, a knowledge compilation technique with different useful approximations has
been created, which allows tractable assertional reasoning. The logical properties,
suchassoundnessandcompleteness,oftheseapproximationshavebeeninvestigated
and a comprehensive evaluation using well-known benchmark ontologies has been
conducted.
Regardingqueryanswering,afastapproximatereasoningsystemforinstancere-
trieval has been developed. A central aspect of this approach is the approximate
semantics for computing the approximate extensions of a complex concept expres-
sion. Basedonthissemantics,severalalgorithmshavebeendevelopedthatallowfor
scalable instance retrieval. In the context of resource-bounded reasoning, a combi-
nation of approximate reasoning algorithms has been examined by providing solid
formalfoundationsfortheassessmentandcomparisonofapproximatereasoningal-
gorithms.
Finally, an approximate ontology reasoning framework has been devised, which
enablesscalable assertionalreasoningoverexpressiveontologiesbylooselyintegrat-
ingtheapproximatereasoningsolutionsdevelopedinthiswork.
4
Acknowledgements
Foremost,I wouldlike to expressmy gratitudeto my advisor, Prof. Dr. RudiStuder
for giving me the opportunity to work in a very fruitful and stimulating working
atmosphereandtodothisresearch. Iamalsoextremelygratefulforhiscommitment
toreviewthisthesisdespitehisbusyschedule.
I would also like to thank Prof. Dr. Detlef Seese without hesitation, accepted
therequesttoserveontheexamination committeeassecondreviewerandprovided
detailedandvaluabletechnicalfeedback. ManythankstoProf. Dr. Karl-HeinzWald-
mann and Prof. Dr. Christian Hipp who served on the examination committee as
examinerandchairman,respectively.
The research reportedherein would not have been possible without my supervi-
sors Prof. Dr. Pascal Hitzler and Dr. Stephan Grimm. I warmly thank Pascal for
continuous support over the past years, and Stephan for extensive discussions, in-
sightfulcomments, and ideas. Hitzler’s tolerancecombined with brilliance has been
amajoryardstickforme.
Thanks to the “Semantic Karlsruhe Team” that consists of all my colleagues at
the Institute AIFB, the FZI research center and at Ontoprise GmbH, for providing a
very fruitful and stimulating working atmosphere – even after work. In particular
I thankfully mention Andreas Abecker, Sebastian Rudolph, Joachim Kleb, Markus
Krötzsch, Jürgen Bock, Andreas Walter, Jens Wissmann, Mark Hefke and Hans-Jörg
Happelforvaluable commentsandideas.
MyparentslivinginMongoliareceivemydeepestgratitudeandloveforthemany
yearsofsupportandespeciallyforalwaysbelievinginme. Last,butnotleast,Ithank
my wife Tumee who gave me love and support for realizing this work. I also thank
herforacceptingthelosttimeonalltheweekendsthatwecouldhavespenttogether
while I was working on this thesis. And my little son who always reminds me that
thereissomethingelsetolivefor...
Karlsruhe,January2010
TuvshinturTserendorj
6
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ResearchQuestionsandGoals . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 OverallApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 KnowledgeCompilationMethod . . . . . . . . . . . . . . . . . . 5
1.3.2 QueryApproximation . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.3 AnytimeReasoningandCombination . . . . . . . . . . . . . . . 6
1.3.4 MethodologyonBenchmarkingApproximateReasoning . . . . 6
1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Thesisoutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
I Foundations 11
2 TheSemanticWebandOntologies 13
2.1 TheSemanticWebVision. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 OntologyLanguagesfortheSemanticWeb . . . . . . . . . . . . . . . . 17
2.2.1 ResourceDescriptionFramework(RDF). . . . . . . . . . . . . . 17
2.2.2 WebOntologyLanguage(OWL) . . . . . . . . . . . . . . . . . . 18
2.3 OtherOntologyFormalismsandTools . . . . . . . . . . . . . . . . . . . 21
3 DescriptionLogics 25
3.1 BasicNotions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 ExpressiveDescriptionLogicSHOIN . . . . . . . . . . . . . . . . . . 28
3.3 DLReasoningProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 DLReasoningComplexities . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 LogicProgramming,RelationalandDeductivedatabases 33
4.1 LogicProgramming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 RelationalDatabases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 DeductiveDatabases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
ii CONTENTS
II ApproximateReasoning For the SemanticWeb 39
5 AFoundationofApproximateReasoningResearch 41
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 AMathematicalFrameworkfortheStudyofApproximateReasoning. 43
5.2.1 ComparingAlgorithmsAfterTermination . . . . . . . . . . . . 46
5.2.2 AnytimeBehaviour . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3 State-of-theartofBenchmarking . . . . . . . . . . . . . . . . . . . . . . 48
5.4 BenchmarkingofApproximateInstanceRetrievalAlgorithms . . . . . 49
5.5 RequirementsForanAutomatedBenchmarkingFramework . . . . . . 50
5.5.1 RequirementsForMeasuringPerformance . . . . . . . . . . . . 51
5.5.2 RequirementsForMeasuringSoundnessandCompleteness . . 52
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6 KnowledgeCompilation 55
6.1 PrincipleIdeaofKnowledgeCompilation . . . . . . . . . . . . . . . . . 55
6.2 AClassificationofKnowledgeCompilationMethods . . . . . . . . . . 57
6.2.1 ExactKnowledgeCompilation . . . . . . . . . . . . . . . . . . . 57
6.2.2 ApproximateKnowledgeCompilation . . . . . . . . . . . . . . 58
6.3 ApproximateReasoningwith SCREECH . . . . . . . . . . . . . . . . . . 60
6.3.1 TheKAON2-Transformation . . . . . . . . . . . . . . . . . . . . 60
6.3.2 FromDisjunctiveDatalogtoHornClauses . . . . . . . . . . . . 61
6.3.3 ASimpleExample . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.4 VariantsofScreech . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.5 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7 QueryApproximation 81
7.1 ApproximationofInstanceRetrieval . . . . . . . . . . . . . . . . . . . . 81
7.2 NotionOfApproximateExtension . . . . . . . . . . . . . . . . . . . . . 82
7.3 ComputingApproximateExtensions . . . . . . . . . . . . . . . . . . . . 85
7.3.1 SystemArchitecture . . . . . . . . . . . . . . . . . . . . . . . . . 85
7.3.2 DelegationofComputationtoDatabase . . . . . . . . . . . . . . 87
7.3.3 In-memoryComputation . . . . . . . . . . . . . . . . . . . . . . 89
7.3.4 ExampleofComputingtheApproximateInstanceExtension . . 91
7.4 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.4.1 TestData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.5 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.5.1 CombinationwithKnowledgeApproximation . . . . . . . . . . 98
7.5.2 ParallelComputationofAtomicExtensions . . . . . . . . . . . . 98
7.5.3 IncrementalMaintanceofMaterialisedKnowledgeBases . . . . 100
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
CONTENTS iii
8 ComposedAnytimeAlgorithms 105
8.1 Resource-boundedReasoningandAnytimeAlgorithms . . . . . . . . . 105
8.2 ConceptofComposedAlgorithms . . . . . . . . . . . . . . . . . . . . . 107
8.3 AnExampleoftheComposedAlgorithms . . . . . . . . . . . . . . . . . 109
8.4 ComposedAnytimeReasoners . . . . . . . . . . . . . . . . . . . . . . . 112
8.4.1 SCREECH-Anytime . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.4.2 AQA-Anytime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
III Implementationand Applications 117
9 Implementation 119
9.1 GeneralArchitecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.2 ImplementationoftheSCREECH Approach . . . . . . . . . . . . . . . . 121
9.3 ImplementationoftheAQAApproach . . . . . . . . . . . . . . . . . . . 123
9.3.1 ComputationOfApproximateExtensions. . . . . . . . . . . . . 123
9.3.2 EmbeddingDLReasonersandDatabases . . . . . . . . . . . . . 125
9.3.3 ApplyingKnowledgeCompilation . . . . . . . . . . . . . . . . . 125
9.4 AnytimeReasoningComponent . . . . . . . . . . . . . . . . . . . . . . 127
9.5 AutomatedBenchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.5.1 QueryGeneration . . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.5.2 OntologyPopulation . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.5.3 HistogramGeneration . . . . . . . . . . . . . . . . . . . . . . . . 133
9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
10 Applications 137
10.1 TheTHESEUSProject. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.2 ReasoningBrokerage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
10.3 ImplementationOfReasoningBrokerage . . . . . . . . . . . . . . . . . 141
10.3.1 BrokerStrategies . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.3.2 Userinterface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
10.3.3 IntegrationofAnytimeReasoners . . . . . . . . . . . . . . . . . 147
10.4 FurtherPotentialApplications . . . . . . . . . . . . . . . . . . . . . . . 149
10.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
IV Finale 153
11 RelatedWork 155
11.1 ApproximateReasoningintheSemanticWeb . . . . . . . . . . . . . . . 155
11.2 EvaluationofReasoningSystems . . . . . . . . . . . . . . . . . . . . . . 161
iv CONTENTS
12 ConclusionandOutlook 165
12.1 SummaryoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
12.1.1 StateoftheArtofExpressiveReasoningTechniques . . . . . . . 165
12.1.2 KnowledgeCompilation . . . . . . . . . . . . . . . . . . . . . . . 166
12.1.3 ApproximateQueryAnswering . . . . . . . . . . . . . . . . . . 167
12.1.4 EvaluatingApproximateReasoningSystems . . . . . . . . . . . 168
12.1.5 DevelopmentofComposedAnytimeAlgorithms . . . . . . . . 168
12.2 FurtherWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
V Appendix 173
13 AppendixA 175
13.1 UsedDataStructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
14 AppendixB 177
14.1 DetailedEvaluationResults . . . . . . . . . . . . . . . . . . . . . . . . . 177