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Mathserve – a Framework for Semantic Reasoning Services

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Mathserve – a Framework for Semantic Reasoning Services MathServe – A Framework for Semantic Reasoning Services Jurgen¨ Zimmer Dissertation zur Erlangung des Grades des Doktors der Ingenieurwissenschaften der Naturwissenschaftlich-Technischen Fakult¨aten der Universit¨at des Saarlandes Saarbrucken,¨ Juli 2008 Dekan Prof. Dr. Joachim Weickert Vorsitzender Prof. Dr. Christoph Weidenbach Gutachter Prof. Dr. (PhD) J¨org Siekmann, Universit¨at des Saarlandes Prof. Dr. Dr. h.c. mult. Wolfgang Wahlster, Universit¨at des Saarlandes Prof. Alan Bundy, University of Edinburgh, Edinburgh, UK Beisitzer Dr. Dominikus Heckmann Tag des Kolloquiums 11. Juli 2008 Contents Kurzzusammenfassung VII Abstract IX Acknowledgements XI I Preliminaries 1 1 Introduction 3 1.1 ContributionsofthisThesis . 9 1.1.1 Contributions to the Mathematical Semantic Web and Auto- matedReasoningResearch. 9 1.1.2 Contributions to Semantic Web Research . 9 1.2 WhatthisThesisisnotabout .. .. 9 1.3 OutlineofthisThesis............................ 10 2 Mechanised Reasoning in Artificial Intelligence 13 2.1 History of Mechanised Reasoning . 13 2.2 Mechanised Reasoning Systems . 14 2.2.1 First-Order Automated Theorem Proving Systems . ... 15 2.2.2 Propositional Satisfiability Solvers . .... 17 2.2.3 DecisionProcedures . 17 2.2.4 FiniteModelGenerators . 18 2.2.5 ProofTransformationSystems . 19 2.3 DistributedAutomatedReasoning. .. 20 2.3.1 Frameworks for Distributed Automated Reasoning . .... 20 2.3.2 Frameworks for the Integration of Reasoning Systems . ..... 20 2.3.3 TheMathWebSoftwareBus . 22 2.3.4 Computation Systems as Semantic Web Services . .. 23 2.4 ReasoningaboutActionsandChange . 23 2.4.1 TheSituationCalculus . 24 2.4.2 Golog – High-level programming in the Situation Calculus ... 29 2.4.3 ClassicalAIPlanning. 32 2.4.4 Stochastic Actions and Decision-Theoretic Planning ....... 33 2.4.5 DTGolog–GologandDecisionTheory . 38 2.5 Summary .................................. 42 II CONTENTS 3 Semantic Web Services 43 3.1 TheSemanticWeb ............................. 43 3.1.1 The Extensible Markup Language . 45 3.1.2 The Resource Description Framework . 45 3.1.3 Knowledge Representation and Description Logics . ..... 47 3.1.4 TheWebOntologyLanguage . 49 3.1.5 DescriptionLogicsandOWL-DL . 50 3.2 SemanticWebServices ........................... 53 3.2.1 WebServices ............................ 54 3.2.2 The OWL-S Upper Ontology for Web Services . 57 3.2.3 WSMO ............................... 60 3.3 Composition of Semantic Web Services . .. 61 3.3.1 AI Planning for Web Service Composition . 61 3.3.2 GologandtheSituationCalculus . 63 3.3.3 MarkovDecisionProcesses . 63 3.3.4 ProgramSynthesisinLinearLogic . 63 3.4 DefinitionsandNotation . .. .. 64 3.4.1 OWL Ontologies – Classes, Properties and Individuals ..... 64 3.4.2 TheSemanticWebRuleLanguage . 66 3.4.3 OWL-SServiceDescriptions . 69 3.5 Summary .................................. 74 II Brokering Semantic Reasoning Services 77 4 Semantic Reasoning Services 79 4.1 ADomainOntology ............................ 79 4.2 ATaxonomyofReasoningSystems . 81 4.3 ProblemTransformationServices . .. 82 4.3.1 ClauseNormalFormGenerators. 83 4.3.2 Higher-Order to First-Order Translation . ... 84 4.4 First-Order Automated Theorem Proving Services . ...... 86 4.4.1 First-order Theorem Proving Problems . 86 4.4.2 AnOntologyofATPStatuses . 87 4.4.3 Results of First-Order ATP Systems . 89 4.4.4 Specialist Problem Classes and System Performance . ..... 90 4.4.5 ATPServicesinOWL-S . 93 4.5 A Service for TPTP Problem Analysis . 97 4.6 Finite Model Generation Services . .. 98 4.7 Decision Procedure Services . 98 4.8 ProofTransformationServices . 101 4.8.1 The Otterfier Service – Transforming CNF Derivations . .... 102 4.8.2 The TRAMP Service – Generating Natural Deduction Proofs . 103 4.9 Summary .................................. 104 CONTENTS III 5 The MathServe Framework 105 5.1 Queries and Composite Services in MathServe . .... 105 5.1.1 OWL-SQueryProfiles . 105 5.1.2 Composite Services as Golog Procedures . 107 5.2 TheMathServeBroker . .. .. 108 5.2.1 TheServiceRegistry . 109 5.2.2 TheQueryManager . .. .. 109 5.2.3 TheServiceMatchmaker . 110 5.2.4 TheServiceComposer . 111 5.2.5 ThePelletOntologyReasoner . 112 5.2.6 TheGologInterpreter . 113 5.2.7 The Automated Theorem Proving Interface . 115 5.3 SystemImplementation. 116 5.4 Availability & Usability . 117 5.5 Summary .................................. 117 6 Composition of Reasoning Services 119 6.1 Requirements on Web Service Composition . 119 6.2 Analysis of Existing Approaches . 121 6.2.1 Planning for Web Service Composition . 121 6.2.2 GologandtheSituationCalculus . 121 6.2.3 Classical Markov Decision Processes . 122 6.2.4 ProgramSynthesis . 122 6.2.5 Summary .............................. 123 6.3 Automated Service Composition in MathServe . .... 124 6.4 Planning with Deterministic Agent Actions . ..... 125 6.4.1 ThePRODIGYSystem . 125 6.4.2 PRODIGY for Web Service Composition . 127 6.5 Service Profiles and Plans as DTGolog Domains . 133 6.5.1 GeneratingDTGologActionDomains. 134 6.5.2 GeneratingaGologProcedure . 138 6.6 ComputinganOptimalPolicy . 139 6.7 Summary .................................. 141 III Applications and Evaluation 143 7 MathServe at CADE System Competitions 145 7.1 TheCADESystemCompetition. 146 7.2 TrainingtheMathServeBroker . 147 7.3 MathServeatCASC-20. .. .. 150 7.3.1 ComparisonwiththeESystem. 151 7.3.2 Comparison with the Vampire System. 152 7.4 ImprovingMathServe. .. .. 153 7.5 MathServeatCASC-J3. .. .. 154 7.6 MathServeonSATProblems . 156 IV CONTENTS 7.7 Summary .................................. 156 8 MathServe on Higher-Order Problems 159 8.1 ASetofHigher-OrderProblems . 160 8.2 LeoandFirst-OrderATPSystems. 161 8.3 TheLEOServices.............................. 162 8.4 A Definition and Extensionality Expansion Service . ...... 164 8.5 TwoCompositeServices . 165 8.6 EvaluationofCompositeServices . 166 8.7 Summary .................................. 168 IV Conclusion 171 9 Conclusions and Related Work 173 9.1 Semantic Computation Services. 174 9.2 Online Access to ATP Systems. 175 9.3 Optimal Choice of Reasoning Systems. 175 10 Limitations and Future Work 177 10.1 LimitationsofMathServe . 177 10.1.1 ManagementofTimeResources . 178 10.1.2 Concurrent Service Invocations . 178 10.1.3 Reasoning Services with States . 179 10.1.4 Limitations of First-order Theorem Provers . .... 180 10.2FutureWork................................. 180 10.2.1 ManagementofTimeResources . 180 10.2.2 Concurrency. .. .. 182 10.2.3 StatefulReasoningServices . 183 10.2.4 Extending the Range of Reasoning Services . 184 10.2.5 NetworksofMathServeBrokers . 185 10.2.6 Online Update of System Performance . 185 10.3Summary .................................. 186 Bibliography 187 V Appendices 213 A The MathServe Domain Ontology 215 B Statuses of ATP Problems 219 C First-Order ATP Systems and their Performance 223 C.1 ATPSystemsinMathServe . 223 C.2 PerformanceoftheATPSystems . 225 D An OWL-S Service Description 227 CONTENTS V E Translation Functions for Web Service Composition 235 E.1 Translation to Planning Domains and Problems . .... 235 E.2 Translation to the Situation Calculus . .... 239 F Planning and Situation Calculus Domains 247 F.1 The PRODIGY Planning Domain for ResultQuery . 247 F.2 A Stochastic situation calculus Domain . .... 252 List of Figures 260 List of Tables 263 List of Acronyms and Symbols 265 Index 269 Kurzzusammenfassung Die vorliegende Arbeit beschreibt das Design und die Implementierung des MathSer- ve Systems. MathServe basiert auf einer dienstorientierten Architektur und bietet die Funktionalit¨at automatischer Deduktionssysteme und verwandter Systeme als seman- tische Web Dienste an. Die Semantik dieser Web Dienste wird mit Hilfe der OWL-S Ontologie beschrieben. Information uber¨ die Leistungsf¨ahigkeit von Diensten auf ver- schiedenen Problemklassen wird durch bedingte probabilistische Effekte in OWL-S Dienstprofilen beschrieben. Diese Information wird verwendet, um fur¨ ein anstehendes Beweisproblem den am besten geeigneten Dienst zu finden. Der MathServe broker ist ein spezialisierter Software Agent, der Dienst Matchmaking- und Kompositionsdiens- te anbietet. Unser Ansatz zur Komposition von Diensten kombiniert klassisches Pla- nen mit entscheidungstheoretischem Schließen im Situationenkalkul.¨ Zusammengestzte Dienste werden durch Golog Prozeduren beschrieben und k¨onnen sehr einfach von menschlichen Nutzern gelesen und bearbeitet werden. MathServe wurde erfolgreich so- wohl auf einer Menge von Beweisproblemen in Logik h¨oherer Ordnung als auch in den Demonstrations-Ligen von zwei CADE Wettbewerben fur¨ Theorembeweiser (CASC) evaluiert. Diese Arbeit stellt einen maßgeblichen Beitrag zur Entwicklung eines Mathe- matischen Semantischen Netzes dar. Sie pr¨asentiert aber auch neue Beitr¨age auf den Gebieten des automatischen Beweisens und der automatischen Komposition von Web Diensten. Abstract In this thesis we describe the design and implementation of the MathServe framework for semantic reasoning services. MathServe is based on a service-oriented architecture and integrates automated reasoning systems and related systems as Semantic Web Services. The semantics of MathServe’s reasoning Web Services is described using the OWL-S upper ontology. Data about the performance of reasoning services is provided in OWL-S service profiles as conditional probabilistic effects. This data can be used to select suitable services for specialised reasoning tasks. The MathServe broker is a middle agent which provides service matchmaking and composition facilities. Service
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