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Contents

Dedication v

Preface vii

Editors xi

Contributors xiii

Contents xv

I General Methods in Knowledge Representation and

Reasoning 1

1 Knowledge Representation and Classical Logic 3

Vladimir Lifschitz, Leora Morgenstern and David Plaisted

1.1 Knowledge Representation and Classical Logic . . . . . . . . . . . . 3

1.2 Syntax, Semantics and Natural Deduction . . . . . . . . . . . . . . . 4

1.2.1 Propositional Logic . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.2 First-OrderLogic ........................ 8

1.2.3 Second-Order Logic . . . . . . . . . . . . . . . . . . . . . . . 16

1.3 Automated Theorem Proving . . . . . . . . . . . . . . . . . . . . . . 18

1.3.1 Resolution in the Propositional Calculus . . . . . . . . . . . . 22

1.3.2 First-OrderProofSystems ................... 25

1.3.3 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1.3.4 Term Rewriting Systems . . . . . . . . . . . . . . . . . . . . 43

1.3.5 Confluence and Termination Properties . . . . . . . . . . . . 46

1.3.6 Equational Rewriting . . . . . . . . . . . . . . . . . . . . . . 50

1.3.7 OtherLogics........................... 55

1.4 Applications of Automated Theorem Provers . . . . . . . . . . . . . 58

1.4.1 Applications Involving Human Intervention . . . . . . . . . . 59

1.4.2 Non-Interactive KR Applications of Automated Theorem

Provers.............................. 61

1.4.3 Exploiting Structure . . . . . . . . . . . . . . . . . . . . . . . 64

1.4.4 Prolog .............................. 65

1.5 Suitability of Logic for Knowledge Representation . . . . . . . . . . 67

1.5.1 Anti-logicist Arguments and Responses . . . . . . . . . . . . 67

xvxvi Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Bibliography .................................. 74

2 Satisfiability Solvers 89

Carla P. Gomes, Henry Kautz, Ashish Sabharwal and Bart Selman

2.1 DefinitionsandNotation ........................ 91

2.2 SAT Solver Technology—Complete Methods . . . . . . . . . . . . . 92

2.2.1 The DPLL Procedure . . . . . . . . . . . . . . . . . . . . . . 92

2.2.2 Key Features of Modern DPLL-Based SAT Solvers . . . . . 93

2.2.3 Clause Learning and Iterative DPLL . . . . . . . . . . . . . . 95

2.2.4 A Proof Complexity Perspective . . . . . . . . . . . . . . . . 100

2.2.5 Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . 104

2.3 SAT Solver Technology—Incomplete Methods . . . . . . . . . . . . 107

2.3.1 The Phase Transition Phenomenon in Random k-SAT .... 109

2.3.2 A New Technique for Random k-SAT: Survey Propagation . 111

2.4 Runtime Variance and Problem Structure . . . . . . . . . . . . . . . 112

2.4.1 Fat and Heavy Tailed Behavior . . . . . . . . . . . . . . . . . 113

2.4.2 Backdoors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

2.4.3 Restarts.............................. 115

2.5 Beyond SAT: Quantified Boolean Formulas and Model Counting . . 117

2.5.1 QBFReasoning ......................... 117

2.5.2 Model Counting . . . . . . . . . . . . . . . . . . . . . . . . . 120

Bibliography .................................. 122

3 Description Logics 135

Franz Baader, Ian Horrocks and Ulrike Sattler

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

3.2 ABasicDLanditsExtensions ..................... 139

3.2.1 Syntax and Semantics of ALC ................. 140

3.2.2 Important Inference Problems . . . . . . . . . . . . . . . . . 141

3.2.3 Important Extensions to ALC ................. 142

3.3 Relationships with other Formalisms . . . . . . . . . . . . . . . . . . 144

3.3.1 DLs and Predicate Logic . . . . . . . . . . . . . . . . . . . . 144

3.3.2 DLs and Modal Logic . . . . . . . . . . . . . . . . . . . . . . 145

3.4 Tableau Based Reasoning Techniques . . . . . . . . . . . . . . . . . 146

3.4.1 A Tableau Algorithm for ALC ................. 146

3.4.2 Implementation and Optimization Techniques . . . . . . . . 150

3.5 Complexity................................ 151

3.5.1 ALC ABox Consistency is PSpace-complete . . . . . . . . . 151

3.5.2 Adding General TBoxes Results in ExpTime-Hardness . . . 154

3.5.3 The Effect of other Constructors . . . . . . . . . . . . . . . . 154

3.6 Other Reasoning Techniques . . . . . . . . . . . . . . . . . . . . . . 155

3.6.1 The Automata Based Approach . . . . . . . . . . . . . . . . 156

3.6.2 Structural Approaches . . . . . . . . . . . . . . . . . . . . . . 161

3.7 DLs in Ontology Language Applications . . . . . . . . . . . . . . . 166

3.7.1 The OWL Ontology Language . . . . . . . . . . . . . . . . . 166

3.7.2 OWL Tools and Applications . . . . . . . . . . . . . . . . . . 167Contents xvii

3.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Bibliography .................................. 169

4 Constraint Programming 181

Francesca Rossi, Peter van Beek and TobyWalsh

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

4.2 Constraint Propagation . . . . . . . . . . . . . . . . . . . . . . . . . 182

4.2.1 Local Consistency . . . . . . . . . . . . . . . . . . . . . . . . 183

4.2.2 Global Constraints . . . . . . . . . . . . . . . . . . . . . . . . 183

4.3 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

4.3.1 Backtracking Search . . . . . . . . . . . . . . . . . . . . . . 184

4.3.2 Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

4.3.3 Hybrid Methods . . . . . . . . . . . . . . . . . . . . . . . . . 188

4.4 Tractability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

4.4.1 Tractable Constraint Languages . . . . . . . . . . . . . . . . 189

4.4.2 Tractable Constraint Graphs . . . . . . . . . . . . . . . . . . 191

4.5 Modeling................................. 191

4.5.1 CP ∨¬ CP............................ 192

4.5.2 Viewpoints............................ 192

4.5.3 Symmetry ............................ 193

4.6 Soft Constraints and Optimization . . . . . . . . . . . . . . . . . . . 193

4.6.1 Modeling Soft Constraints . . . . . . . . . . . . . . . . . . . 194

4.6.2 Searching for the Best Solution . . . . . . . . . . . . . . . . . 195

4.6.3 Inference in Soft Constraints . . . . . . . . . . . . . . . . . . 195

4.7 ConstraintLogicProgramming..................... 197

4.7.1 LogicPrograms ......................... 197

4.7.2 Constraint Logic Programs . . . . . . . . . . . . . . . . . . . 198

4.7.3 LP and CLP Languages . . . . . . . . . . . . . . . . . . . . . 198

4.7.4 Other Programming Paradigms . . . . . . . . . . . . . . . . . 199

4.8 Beyond Finite Domains . . . . . . . . . . . . . . . . . . . . . . . . . 199

4.8.1 Intervals ............................. 199

4.8.2 TemporalProblems ....................... 200

4.8.3 Sets and other Datatypes . . . . . . . . . . . . . . . . . . . . 200

4.9 Distributed Constraint Programming . . . . . . . . . . . . . . . . . . 201

4.10ApplicationAreas ............................ 202

4.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Bibliography .................................. 203

5 Conceptual Graphs 213

John F. Sowa

5.1 From Existential Graphs to Conceptual Graphs . . . . . . . . . . . . 213

5.2 CommonLogic ............................. 217

5.3 Reasoning with Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 223

5.4 Propositions, Situations, and Metalanguage . . . . . . . . . . . . . . 230

5.5 ResearchExtensions........................... 233

Bibliography .................................. 235xviii Contents

6 Nonmonotonic Reasoning 239

Gerhard Brewka, Ilkka Niemelä and Mirosław Truszczy´ nski

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Rules with exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Theframeproblem ........................... 240

About this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

6.2 DefaultLogic .............................. 242

6.2.1 Basic Definitions and Properties . . . . . . . . . . . . . . . . 242

6.2.2 Computational Properties . . . . . . . . . . . . . . . . . . . . 246

6.2.3 Normal Default Theories . . . . . . . . . . . . . . . . . . . . 249

6.2.4 Closed-World Assumption and Normal Defaults . . . . . . . 250

6.2.5 VariantsofDefaultLogic.................... 252

6.3 Autoepistemic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

6.3.1 Preliminaries, Intuitions and Basic Results . . . . . . . . . . 253

6.3.2 Computational Properties . . . . . . . . . . . . . . . . . . . . 258

6.4 Circumscription ............................. 260

6.4.1 Motivation............................ 260

6.4.2 Defining Circumscription . . . . . . . . . . . . . . . . . . . . 261

6.4.3 Semantics ............................ 263

6.4.4 Computational Properties . . . . . . . . . . . . . . . . . . . . 264

6.4.5 Variants.............................. 266

6.5 Nonmonotonic Inference Relations . . . . . . . . . . . . . . . . . . . 267

6.5.1 Semantic Specification of Inference Relations . . . . . . . . . 268

6.5.2 Default Conditionals . . . . . . . . . . . . . . . . . . . . . . 270

6.5.3 Discussion............................ 272

6.6 Further Issues and Conclusion . . . . . . . . . . . . . . . . . . . . . 272

6.6.1 Relating Default and Autoepistemic Logics . . . . . . . . . . 273

6.6.2 Relating Default Logic and Circumscription . . . . . . . . . 275

6.6.3 Further Approaches . . . . . . . . . . . . . . . . . . . . . . . 276

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

Bibliography .................................. 277

7 Answer Sets 285

Michael Gelfond

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

7.2 Syntax and Semantics of Answer Set Prolog . . . . . . . . . . . . . . 286

7.3 Properties of Logic Programs . . . . . . . . . . . . . . . . . . . . . . 292

7.3.1 Consistency of Logic Programs . . . . . . . . . . . . . . . . 292

7.3.2 Reasoning Methods for Answer Set Prolog . . . . . . . . . . 295

7.3.3 Properties of Entailment . . . . . . . . . . . . . . . . . . . . 297

7.3.4 Relations between Programs . . . . . . . . . . . . . . . . . . 298

7.4 A Simple Knowledge Base . . . . . . . . . . . . . . . . . . . . . . . 300

7.5 Reasoning in Dynamic Domains . . . . . . . . . . . . . . . . . . . . 302

7.6 Extensions of Answer Set Prolog . . . . . . . . . . . . . . . . . . . . 307

7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

Bibliography .................................. 310Contents xix

8 Belief Revision 317

Pavlos Peppas

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

8.2 Preliminaries............................... 318

8.3 TheAGMParadigm........................... 318

8.3.1 The AGM Postulates for Belief Revision . . . . . . . . . . . 319

8.3.2 The AGM Postulates for Belief Contraction . . . . . . . . . . 320

8.3.3 Selection Functions . . . . . . . . . . . . . . . . . . . . . . . 323

8.3.4 Epistemic Entrenchment . . . . . . . . . . . . . . . . . . . . 325

8.3.5 System of Spheres . . . . . . . . . . . . . . . . . . . . . . . . 327

8.4 Belief Base Change . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

8.4.1 Belief Base Change Operations . . . . . . . . . . . . . . . . . 331

8.4.2 Belief Base Change Schemes . . . . . . . . . . . . . . . . . . 332

8.5 Multiple Belief Change . . . . . . . . . . . . . . . . . . . . . . . . . 335

8.5.1 Multiple Revision . . . . . . . . . . . . . . . . . . . . . . . . 336

8.5.2 Multiple Contraction . . . . . . . . . . . . . . . . . . . . . . 338

8.6 IteratedRevision............................. 340

8.6.1 Iterated Revision with Enriched Epistemic Input . . . . . . . 340

8.6.2 Iterated Revision with Simple Epistemic Input . . . . . . . . 343

8.7 Non-PrioritizedRevision ........................ 346

8.8 Belief Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

8.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

Bibliography .................................. 353

9 Qualitative Modeling 361

Kenneth D. Forbus

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

9.1.1 KeyPrinciples.......................... 362

9.1.2 Overview of Basic Qualitative Reasoning . . . . . . . . . . . 363

9.2 Qualitative Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 365

9.2.1 Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

9.2.2 Functions and Relationships . . . . . . . . . . . . . . . . . . 369

9.3 Ontology................................. 371

9.3.1 Component Ontologies . . . . . . . . . . . . . . . . . . . . . 372

9.3.2 Process Ontologies . . . . . . . . . . . . . . . . . . . . . . . 373

9.3.3 FieldOntologies......................... 374

9.4 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

9.5 Compositional Modeling . . . . . . . . . . . . . . . . . . . . . . . . 376

9.5.1 Model Formulation Algorithms . . . . . . . . . . . . . . . . . 378

9.6 Qualitative States and Qualitative Simulation . . . . . . . . . . . . . 379

9.7 Qualitative Spatial Reasoning . . . . . . . . . . . . . . . . . . . . . . 381

9.7.1 Topological Representations . . . . . . . . . . . . . . . . . . 381

9.7.2 Shape, Location, and Orientation Representations . . . . . . 382

9.7.3 DiagrammaticReasoning.................... 382

9.8 Qualitative Modeling Applications . . . . . . . . . . . . . . . . . . . 383xx Contents

9.8.1 Automating or Assisting Professional Reasoning . . . . . . . 383

9.8.2 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

9.8.3 CognitiveModeling....................... 386

9.9 FrontiersandResources......................... 387

Bibliography .................................. 387

10 Model-based Problem Solving 395

Peter Struss

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

10.2 Tasks.................................. 398

10.2.1 Situation Assessment/Diagnosis . . . . . . . . . . . . . . 398

10.2.2 Test Generation, Measurement Proposal, Diagnosability

Analysis ........................... 399

10.2.3 Design and Failure-Modes-and-Effects Analysis . . . . . 401

10.2.4 Proposal of Remedial Actions (Repair, Reconfiguration,

Recovery,Therapy) ..................... 402

10.2.5 Ingredients of Model-based Problem Solving . . . . . . . 402

10.3 Requirements on Modeling . . . . . . . . . . . . . . . . . . . . . . 403

10.3.1 Behavior Prediction and Consistency Check . . . . . . . 404

10.3.2 Validity of Behavior Modeling . . . . . . . . . . . . . . . 405

10.3.3 Conceptual Modeling . . . . . . . . . . . . . . . . . . . . 405

10.3.4 (Automated) Model Composition . . . . . . . . . . . . . 406

10.3.5 Genericity . . . . . . . . . . . . . . . . . . . . . . . . . . 406

10.3.6 Appropriate Granularity . . . . . . . . . . . . . . . . . . 407

10.4 Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

10.4.1 Consistency-based Diagnosis with Component-oriented

Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

10.4.2 Computation of Diagnoses . . . . . . . . . . . . . . . . . 418

10.4.3 Solution Scope and Limitations of Component-Oriented

Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . 422

10.4.4 Diagnosis across Time . . . . . . . . . . . . . . . . . . . 423

10.4.5 Abductive Diagnosis . . . . . . . . . . . . . . . . . . . . 431

10.4.6 Process-Oriented Diagnosis . . . . . . . . . . . . . . . . 434

10.4.7 Model-based Diagnosis in Control Engineering . . . . . . 438

10.5 Test and Measurement Proposal, Diagnosability Analysis . . . . . 438

10.5.1 Test Generation . . . . . . . . . . . . . . . . . . . . . . . 439

10.5.2 Entropy-based Test Selection . . . . . . . . . . . . . . . . 444

10.5.3 ProbeSelection ....................... 445

10.5.4 Diagnosability Analysis . . . . . . . . . . . . . . . . . . . 446

10.6 Remedy Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . 446

10.6.1 Integration of Diagnosis and Remedy Actions . . . . . . 448

10.6.2 Component-oriented Reconfiguration . . . . . . . . . . . 450

10.6.3 Process-oriented Therapy Proposal . . . . . . . . . . . . 453

10.7 OtherTasks .............................. 454

10.7.1 Configuration and Design . . . . . . . . . . . . . . . . . . 454

10.7.2 Failure-Modes-and-Effects Analysis . . . . . . . . . . . . 456

10.7.3 Debugging and Testing of Software . . . . . . . . . . . . 456Contents xxi

10.8 State and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . 458

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

Bibliography ................................. 460

11 Bayesian Networks 467

Adnan Darwiche

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

11.2 Syntax and Semantics of Bayesian Networks . . . . . . . . . . . . 468

11.2.1 Notational Conventions . . . . . . . . . . . . . . . . . . . 468

11.2.2 Probabilistic Beliefs . . . . . . . . . . . . . . . . . . . . . 469

11.2.3 Bayesian Networks . . . . . . . . . . . . . . . . . . . . . 470

11.2.4 Structured Representations of CPTs . . . . . . . . . . . . 471

11.2.5 Reasoning about Independence . . . . . . . . . . . . . . . 471

11.2.6 Dynamic Bayesian Networks . . . . . . . . . . . . . . . . 472

11.3 Exact Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

11.3.1 Structure-Based Algorithms . . . . . . . . . . . . . . . . 474

11.3.2 Inference with Local (Parametric) Structure . . . . . . . . 479

11.3.3 Solving MAP and MPE by Search . . . . . . . . . . . . . 480

11.3.4 Compiling Bayesian Networks . . . . . . . . . . . . . . . 481

11.3.5 Inference by Reduction to Logic . . . . . . . . . . . . . . 482

11.3.6 Additional Inference Techniques . . . . . . . . . . . . . . 484

11.4 Approximate Inference . . . . . . . . . . . . . . . . . . . . . . . . 485

11.4.1 Inference by Stochastic Sampling . . . . . . . . . . . . . 485

11.4.2 Inference as Optimization . . . . . . . . . . . . . . . . . 486

11.5 Constructing Bayesian Networks . . . . . . . . . . . . . . . . . . 489

11.5.1 Knowledge Engineering . . . . . . . . . . . . . . . . . . 489

11.5.2 High-Level Specifications . . . . . . . . . . . . . . . . . 490

11.5.3 Learning Bayesian Networks . . . . . . . . . . . . . . . . 493

11.6 Causality and Intervention . . . . . . . . . . . . . . . . . . . . . . 497

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

Bibliography ................................. 499

II Classes of Knowledge and Specialized Representations 511

12 Temporal Representation and Reasoning 513

Michael Fisher

12.1 TemporalStructures.......................... 514

12.1.1 InstantsandDurations ................... 514

12.1.2 From Discreteness to Density . . . . . . . . . . . . . . . 515

12.1.3 Granularity Hierarchies . . . . . . . . . . . . . . . . . . . 516

12.1.4 TemporalOrganisation ................... 517

12.1.5 MovinginRealTime .................... 517

12.1.6 Intervals ........................... 518

12.2 Temporal Language . . . . . . . . . . . . . . . . . . . . . . . . . . 520

12.2.1 Modal Temporal Logic . . . . . . . . . . . . . . . . . . . 520

12.2.2 BacktotheFuture...................... 521

12.2.3 Temporal Arguments and Reified Temporal Logics . . . . 521xxii Contents

12.2.4 Operators over Non-discrete Models . . . . . . . . . . . . 522

12.2.5 Intervals ........................... 523

12.2.6 Real-Time and Hybrid Temporal Languages . . . . . . . 524

12.2.7 Quantification........................ 525

12.2.8 Hybrid Temporal Logic and the Concept of “now” . . . . 528

12.3 TemporalReasoning ......................... 528

12.3.1 ProofSystems........................ 529

12.3.2 Automated Deduction . . . . . . . . . . . . . . . . . . . . 529

12.4 Applications.............................. 530

12.4.1 Natural Language . . . . . . . . . . . . . . . . . . . . . . 530

12.4.2 Reactive System Specification . . . . . . . . . . . . . . . 531

12.4.3 Theorem-Proving . . . . . . . . . . . . . . . . . . . . . . 532

12.4.4 Model Checking . . . . . . . . . . . . . . . . . . . . . . . 532

12.4.5 PSL/Sugar .......................... 534

12.4.6 Temporal Description Logics . . . . . . . . . . . . . . . . 534

12.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 535

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

Bibliography ................................. 535

13 Qualitative Spatial Representation and Reasoning 551

Anthony G. Cohn and Jochen Renz

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551

13.1.1 What is Qualitative Spatial Reasoning? . . . . . . . . . . 551

13.1.2 Applications of Qualitative Spatial Reasoning . . . . . . 553

13.2 Aspects of Qualitative Spatial Representation . . . . . . . . . . . . 554

13.2.1 Ontology........................... 554

13.2.2 SpatialRelations ...................... 556

13.2.3 Mereology.......................... 557

13.2.4 Mereotopology . . . . . . . . . . . . . . . . . . . . . . . 557

13.2.5 Between Mereotopology and Fully Metric Spatial Repre-

sentation........................... 566

13.2.6 Mereogeometry . . . . . . . . . . . . . . . . . . . . . . . 570

13.2.7 Spatial Vagueness . . . . . . . . . . . . . . . . . . . . . . 571

13.3 SpatialReasoning........................... 572

13.3.1 Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . 574

13.3.2 Composition . . . . . . . . . . . . . . . . . . . . . . . . . 575

13.3.3 Constraint-based Spatial Reasoning . . . . . . . . . . . . 576

13.3.4 Finding Efficient Reasoning Algorithms . . . . . . . . . . 578

13.3.5 Planar Realizability . . . . . . . . . . . . . . . . . . . . . 581

13.4 Reasoning about Spatial Change . . . . . . . . . . . . . . . . . . . 581

13.5 CognitiveValidity........................... 582

13.6 FinalRemarks............................. 583

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584

Bibliography ................................. 584Contents xxiii

14 Physical Reasoning 597

Ernest Davis

14.1 Architectures ............................. 600

14.1.1 Component Analysis . . . . . . . . . . . . . . . . . . . . 600

14.1.2 Process Model . . . . . . . . . . . . . . . . . . . . . . . . 601

14.2 Domain Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

14.2.1 Rigid Object Kinematics . . . . . . . . . . . . . . . . . . 603

14.2.2 Rigid Object Dynamics . . . . . . . . . . . . . . . . . . . 605

14.2.3 Liquids............................ 608

14.3 Abstraction and Multiple Models . . . . . . . . . . . . . . . . . . 611

14.4 Historical and Bibliographical . . . . . . . . . . . . . . . . . . . . 614

14.4.1 Logic-based Representations . . . . . . . . . . . . . . . . 614

14.4.2 Solid Objects: Kinematics . . . . . . . . . . . . . . . . . 615

14.4.3 Solid Object Dynamics . . . . . . . . . . . . . . . . . . . 616

14.4.4 Abstraction and Multiple Models . . . . . . . . . . . . . 616

14.4.5 Other............................. 616

14.4.6 Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Bibliography ................................. 618

15 Reasoning about Knowledge and Belief 621

Yoram Moses

15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621

15.2 The Possible Worlds Model . . . . . . . . . . . . . . . . . . . . . 622

15.2.1 A Language for Knowledge and Belief . . . . . . . . . . 622

15.3 Properties of Knowledge . . . . . . . . . . . . . . . . . . . . . . . 626

15.4 The Knowledge of Groups . . . . . . . . . . . . . . . . . . . . . . 628

15.4.1 Common Knowledge . . . . . . . . . . . . . . . . . . . . 629

15.4.2 Distributed Knowledge . . . . . . . . . . . . . . . . . . . 632

15.5 RunsandSystems........................... 633

15.6 AddingTime ............................. 635

15.6.1 Common Knowledge and Time . . . . . . . . . . . . . . 636

15.7 Knowledge-based Behaviors . . . . . . . . . . . . . . . . . . . . . 637

15.7.1 Contexts and Protocols . . . . . . . . . . . . . . . . . . . 637

15.7.2 Knowledge-based Programs . . . . . . . . . . . . . . . . 639

15.7.3 A Subtle kb Program . . . . . . . . . . . . . . . . . . . . 641

15.8 Beyond Square One . . . . . . . . . . . . . . . . . . . . . . . . . . 643

15.9 How to Reason about Knowledge and Belief . . . . . . . . . . . . 644

15.9.1 Concluding Remark . . . . . . . . . . . . . . . . . . . . . 645

Bibliography ................................. 645

Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647

16 Situation Calculus 649

Fangzhen Lin

16.1 Axiomatizations............................ 650

16.2 The Frame, the Ramification and the Qualification Problems . . . 652

16.2.1 The Frame Problem—Reiter’s Solution . . . . . . . . . . 654

16.2.2 The Ramification Problem and Lin’s Solution . . . . . . . 657xxiv Contents

16.2.3 The Qualification Problem . . . . . . . . . . . . . . . . . 660

16.3 Reiter’s Foundational Axioms and Basic Action Theories . . . . . 661

16.4 Applications.............................. 665

16.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 667

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

Bibliography ................................. 667

17 Event Calculus 671

Erik T. Mueller

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671

17.2 Versions of the Event Calculus . . . . . . . . . . . . . . . . . . . . 672

17.2.1 Original Event Calculus (OEC) . . . . . . . . . . . . . . 672

17.2.2 Simplified Event Calculus (SEC) . . . . . . . . . . . . . . 674

17.2.3 Basic Event Calculus (BEC) . . . . . . . . . . . . . . . . 676

17.2.4 EventCalculus(EC) .................... 679

17.2.5 Discrete Event Calculus (DEC) . . . . . . . . . . . . . . 681

17.2.6 Equivalence of DEC and EC . . . . . . . . . . . . . . . . 683

17.2.7 OtherVersions........................ 683

17.3 Relationship to other Formalisms . . . . . . . . . . . . . . . . . . 684

17.4 DefaultReasoning .......................... 684

17.4.1 Circumscription....................... 684

17.4.2 Computing Circumscription . . . . . . . . . . . . . . . . 685

17.4.3 HistoricalNote ....................... 686

17.4.4 NegationasFailure ..................... 687

17.5 Event Calculus Knowledge Representation . . . . . . . . . . . . . 687

17.5.1 Parameters.......................... 687

17.5.2 EventEffects ........................ 688

17.5.3 Preconditions . . . . . . . . . . . . . . . . . . . . . . . . 689

17.5.4 StateConstraints ...................... 689

17.5.5 Concurrent Events . . . . . . . . . . . . . . . . . . . . . . 690

17.5.6 Triggered Events . . . . . . . . . . . . . . . . . . . . . . 691

17.5.7 Continuous Change . . . . . . . . . . . . . . . . . . . . . 692

17.5.8 Nondeterministic Effects . . . . . . . . . . . . . . . . . . 693

17.5.9 IndirectEffects ....................... 694

17.5.10 Partially Ordered Events . . . . . . . . . . . . . . . . . . 696

17.6 Action Language E .......................... 697

17.7 Automated Event Calculus Reasoning . . . . . . . . . . . . . . . . 699

17.7.1 Prolog ............................ 699

17.7.2 Answer Set Programming . . . . . . . . . . . . . . . . . 700

17.7.3 Satisfiability (SAT) Solving . . . . . . . . . . . . . . . . 700

17.7.4 First-Order Logic Automated Theorem Proving . . . . . 700

17.8 Applications of the Event Calculus . . . . . . . . . . . . . . . . . 700

Bibliography ................................. 701

18 Temporal Action Logics 709

Patrick Doherty and Jonas Kvarnström

18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709Contents xxv

18.1.1 PMONandTAL...................... 710

18.1.2 PreviousWork ....................... 711

18.1.3 Chapter Structure . . . . . . . . . . . . . . . . . . . . . 713

18.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

18.3 TALNarratives ............................ 716

18.3.1 The Russian Airplane Hijack Scenario . . . . . . . . . . 717

18.3.2 Narrative Background Specification . . . . . . . . . . . 718

18.3.3 Narrative Specification . . . . . . . . . . . . . . . . . . 723

18.4 The Relation Between the TAL Languages L(ND) and L(FL) . . 724

18.5 The TAL Surface Language L(ND) ................. 725

18.5.1 Sorts, Terms and Variables . . . . . . . . . . . . . . . . 725

18.5.2 Formulas .......................... 726

18.5.3 Statements ......................... 727

18.6 The TAL Base Language L(FL) ................... 728

18.6.1 Translation from L(ND) to L(FL) ............ 728

18.7 CircumscriptionandTAL....................... 730

18.8 Representing Ramifications in TAL . . . . . . . . . . . . . . . . . 735

18.9 Representing Qualifications in TAL . . . . . . . . . . . . . . . . . 737

18.9.1 Enabling Fluents . . . . . . . . . . . . . . . . . . . . . . 738

18.9.2 StrongQualification.................... 740

18.9.3 WeakQualification..................... 740

18.9.4 Qualification: Not Only For Actions . . . . . . . . . . . 741

18.9.5 Ramifications as Qualifications . . . . . . . . . . . . . . 742

18.10ActionExpressivityinTAL ..................... 742

18.11 Concurrent Actions in TAL . . . . . . . . . . . . . . . . . . . . . . 744

18.11.1 Independent Concurrent Actions . . . . . . . . . . . . . 744

18.11.2 Interacting Concurrent Actions . . . . . . . . . . . . . . 745

18.11.3 LawsofInteraction .................... 745

18.12 An Application of TAL: TALplanner . . . . . . . . . . . . . . . . 747

18.13Summary ............................... 752

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752

Bibliography ................................. 753

19 Nonmonotonic Causal Logic 759

Hudson Turner

19.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762

19.1.1 Finite Domain Propositional Logic . . . . . . . . . . . . 762

19.1.2 Causal Theories . . . . . . . . . . . . . . . . . . . . . . 763

19.2 Strong Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . 765

19.3 Completion .............................. 766

19.4 Expressiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768

19.4.1 Nondeterminism: Coin Tossing . . . . . . . . . . . . . . 768

19.4.2 Implied Action Preconditions: Moving an Object . . . . 768

19.4.3 Things that Change by Themselves: Falling Dominos . 769

19.4.4 Things that Tend to Change by Themselves: Pendulum . 769

19.5 High-Level Action Language C+ .................. 770

19.6 Relationship to Default Logic . . . . . . . . . . . . . . . . . . . . 771xxvi Contents

19.7 Causal Theories in Higher-Order Classical Logic . . . . . . . . . . 772

19.8 ALogicofUniversalCausation ................... 773

Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774

Bibliography ................................. 774

III Knowledge Representation in Applications 777

20 Knowledge Representation and Question Answering 779

Marcello Balduccini, Chitta Baral and Yuliya Lierler

20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779

20.1.1 Role of Knowledge Representation and Reasoning in QA 780

20.1.2 Architectural Overview of QA Systems Using Knowl-

edge Representation and Reasoning . . . . . . . . . . . 782

20.2 From English to Logical Theories . . . . . . . . . . . . . . . . . . 783

20.3 The COGEX Logic Prover of the LCC QA System . . . . . . . . 790

20.4 Extracting Relevant Facts from Logical Theories and its Use in the

DD QA System about Dynamic Domains and Trips . . . . . . . . 792

20.4.1 The Overall Architecture of the DD System . . . . . . . 793

20.4.2 From Logic Forms to QSR Facts: An Illustration . . . . 794

20.4.3 OSR: From QSR Relations to Domain Relations . . . . 796

20.4.4 An Early Travel Module of the DD System . . . . . . . 798

20.4.5 Other Enhancements to the Travel Module . . . . . . . . 802

20.5 From Natural Language to Relevant Facts in the ASU QA System 803

20.6 Nutcracker—System for Recognizing Textual Entailment . . . . . 806

20.7 Mueller’s Story Understanding System . . . . . . . . . . . . . . . 810

20.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815

Bibliography ................................. 815

21 The SemanticWeb:Webizing Knowledge Representation 821

Jim Hendler and Frank van Harmelen

21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821

21.2 The Semantic Web Today . . . . . . . . . . . . . . . . . . . . . . 823

21.3 Semantic Web KR Language Design . . . . . . . . . . . . . . . . 826

21.3

Contents
Dedication v
Preface vii
Editors xi
Contributors xiii
Contents xv
I General Methods in Knowledge Representation and
Reasoning 1
1 Knowledge Representation and Classical Logic 3
Vladimir Lifschitz, Leora Morgenstern and David Plaisted
1.1 Knowledge Representation and Classical Logic . . . . . . . . . . . . 3
1.2 Syntax, Semantics and Natural Deduction . . . . . . . . . . . . . . . 4
1.2.1 Propositional Logic . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 First-OrderLogic ........................ 8
1.2.3 Second-Order Logic . . . . . . . . . . . . . . . . . . . . . . . 16
1.3 Automated Theorem Proving . . . . . . . . . . . . . . . . . . . . . . 18
1.3.1 Resolution in the Propositional Calculus . . . . . . . . . . . . 22
1.3.2 First-OrderProofSystems ................... 25
1.3.3 Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.3.4 Term Rewriting Systems . . . . . . . . . . . . . . . . . . . . 43
1.3.5 Confluence and Termination Properties . . . . . . . . . . . . 46
1.3.6 Equational Rewriting . . . . . . . . . . . . . . . . . . . . . . 50
1.3.7 OtherLogics........................... 55
1.4 Applications of Automated Theorem Provers . . . . . . . . . . . . . 58
1.4.1 Applications Involving Human Intervention . . . . . . . . . . 59
1.4.2 Non-Interactive KR Applications of Automated Theorem
Provers.............................. 61
1.4.3 Exploiting Structure . . . . . . . . . . . . . . . . . . . . . . . 64
1.4.4 Prolog .............................. 65
1.5 Suitability of Logic for Knowledge Representation . . . . . . . . . . 67
1.5.1 Anti-logicist Arguments and Responses . . . . . . . . . . . . 67
xvxvi Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Bibliography .................................. 74
2 Satisfiability Solvers 89
Carla P. Gomes, Henry Kautz, Ashish Sabharwal and Bart Selman
2.1 DefinitionsandNotation ........................ 91
2.2 SAT Solver Technology—Complete Methods . . . . . . . . . . . . . 92
2.2.1 The DPLL Procedure . . . . . . . . . . . . . . . . . . . . . . 92
2.2.2 Key Features of Modern DPLL-Based SAT Solvers . . . . . 93
2.2.3 Clause Learning and Iterative DPLL . . . . . . . . . . . . . . 95
2.2.4 A Proof Complexity Perspective . . . . . . . . . . . . . . . . 100
2.2.5 Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . 104
2.3 SAT Solver Technology—Incomplete Methods . . . . . . . . . . . . 107
2.3.1 The Phase Transition Phenomenon in Random k-SAT .... 109
2.3.2 A New Technique for Random k-SAT: Survey Propagation . 111
2.4 Runtime Variance and Problem Structure . . . . . . . . . . . . . . . 112
2.4.1 Fat and Heavy Tailed Behavior . . . . . . . . . . . . . . . . . 113
2.4.2 Backdoors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
2.4.3 Restarts.............................. 115
2.5 Beyond SAT: Quantified Boolean Formulas and Model Counting . . 117
2.5.1 QBFReasoning ......................... 117
2.5.2 Model Counting . . . . . . . . . . . . . . . . . . . . . . . . . 120
Bibliography .................................. 122
3 Description Logics 135
Franz Baader, Ian Horrocks and Ulrike Sattler
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.2 ABasicDLanditsExtensions ..................... 139
3.2.1 Syntax and Semantics of ALC ................. 140
3.2.2 Important Inference Problems . . . . . . . . . . . . . . . . . 141
3.2.3 Important Extensions to ALC ................. 142
3.3 Relationships with other Formalisms . . . . . . . . . . . . . . . . . . 144
3.3.1 DLs and Predicate Logic . . . . . . . . . . . . . . . . . . . . 144
3.3.2 DLs and Modal Logic . . . . . . . . . . . . . . . . . . . . . . 145
3.4 Tableau Based Reasoning Techniques . . . . . . . . . . . . . . . . . 146
3.4.1 A Tableau Algorithm for ALC ................. 146
3.4.2 Implementation and Optimization Techniques . . . . . . . . 150
3.5 Complexity................................ 151
3.5.1 ALC ABox Consistency is PSpace-complete . . . . . . . . . 151
3.5.2 Adding General TBoxes Results in ExpTime-Hardness . . . 154
3.5.3 The Effect of other Constructors . . . . . . . . . . . . . . . . 154
3.6 Other Reasoning Techniques . . . . . . . . . . . . . . . . . . . . . . 155
3.6.1 The Automata Based Approach . . . . . . . . . . . . . . . . 156
3.6.2 Structural Approaches . . . . . . . . . . . . . . . . . . . . . . 161
3.7 DLs in Ontology Language Applications . . . . . . . . . . . . . . . 166
3.7.1 The OWL Ontology Language . . . . . . . . . . . . . . . . . 166
3.7.2 OWL Tools and Applications . . . . . . . . . . . . . . . . . . 167Contents xvii
3.8 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Bibliography .................................. 169
4 Constraint Programming 181
Francesca Rossi, Peter van Beek and TobyWalsh
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
4.2 Constraint Propagation . . . . . . . . . . . . . . . . . . . . . . . . . 182
4.2.1 Local Consistency . . . . . . . . . . . . . . . . . . . . . . . . 183
4.2.2 Global Constraints . . . . . . . . . . . . . . . . . . . . . . . . 183
4.3 Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
4.3.1 Backtracking Search . . . . . . . . . . . . . . . . . . . . . . 184
4.3.2 Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
4.3.3 Hybrid Methods . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.4 Tractability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
4.4.1 Tractable Constraint Languages . . . . . . . . . . . . . . . . 189
4.4.2 Tractable Constraint Graphs . . . . . . . . . . . . . . . . . . 191
4.5 Modeling................................. 191
4.5.1 CP ∨¬ CP............................ 192
4.5.2 Viewpoints............................ 192
4.5.3 Symmetry ............................ 193
4.6 Soft Constraints and Optimization . . . . . . . . . . . . . . . . . . . 193
4.6.1 Modeling Soft Constraints . . . . . . . . . . . . . . . . . . . 194
4.6.2 Searching for the Best Solution . . . . . . . . . . . . . . . . . 195
4.6.3 Inference in Soft Constraints . . . . . . . . . . . . . . . . . . 195
4.7 ConstraintLogicProgramming..................... 197
4.7.1 LogicPrograms ......................... 197
4.7.2 Constraint Logic Programs . . . . . . . . . . . . . . . . . . . 198
4.7.3 LP and CLP Languages . . . . . . . . . . . . . . . . . . . . . 198
4.7.4 Other Programming Paradigms . . . . . . . . . . . . . . . . . 199
4.8 Beyond Finite Domains . . . . . . . . . . . . . . . . . . . . . . . . . 199
4.8.1 Intervals ............................. 199
4.8.2 TemporalProblems ....................... 200
4.8.3 Sets and other Datatypes . . . . . . . . . . . . . . . . . . . . 200
4.9 Distributed Constraint Programming . . . . . . . . . . . . . . . . . . 201
4.10ApplicationAreas ............................ 202
4.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Bibliography .................................. 203
5 Conceptual Graphs 213
John F. Sowa
5.1 From Existential Graphs to Conceptual Graphs . . . . . . . . . . . . 213
5.2 CommonLogic ............................. 217
5.3 Reasoning with Graphs . . . . . . . . . . . . . . . . . . . . . . . . . 223
5.4 Propositions, Situations, and Metalanguage . . . . . . . . . . . . . . 230
5.5 ResearchExtensions........................... 233
Bibliography .................................. 235xviii Contents
6 Nonmonotonic Reasoning 239
Gerhard Brewka, Ilkka Niemelä and Mirosław Truszczy´ nski
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Rules with exceptions . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Theframeproblem ........................... 240
About this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
6.2 DefaultLogic .............................. 242
6.2.1 Basic Definitions and Properties . . . . . . . . . . . . . . . . 242
6.2.2 Computational Properties . . . . . . . . . . . . . . . . . . . . 246
6.2.3 Normal Default Theories . . . . . . . . . . . . . . . . . . . . 249
6.2.4 Closed-World Assumption and Normal Defaults . . . . . . . 250
6.2.5 VariantsofDefaultLogic.................... 252
6.3 Autoepistemic Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
6.3.1 Preliminaries, Intuitions and Basic Results . . . . . . . . . . 253
6.3.2 Computational Properties . . . . . . . . . . . . . . . . . . . . 258
6.4 Circumscription ............................. 260
6.4.1 Motivation............................ 260
6.4.2 Defining Circumscription . . . . . . . . . . . . . . . . . . . . 261
6.4.3 Semantics ............................ 263
6.4.4 Computational Properties . . . . . . . . . . . . . . . . . . . . 264
6.4.5 Variants.............................. 266
6.5 Nonmonotonic Inference Relations . . . . . . . . . . . . . . . . . . . 267
6.5.1 Semantic Specification of Inference Relations . . . . . . . . . 268
6.5.2 Default Conditionals . . . . . . . . . . . . . . . . . . . . . . 270
6.5.3 Discussion............................ 272
6.6 Further Issues and Conclusion . . . . . . . . . . . . . . . . . . . . . 272
6.6.1 Relating Default and Autoepistemic Logics . . . . . . . . . . 273
6.6.2 Relating Default Logic and Circumscription . . . . . . . . . 275
6.6.3 Further Approaches . . . . . . . . . . . . . . . . . . . . . . . 276
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
Bibliography .................................. 277
7 Answer Sets 285
Michael Gelfond
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
7.2 Syntax and Semantics of Answer Set Prolog . . . . . . . . . . . . . . 286
7.3 Properties of Logic Programs . . . . . . . . . . . . . . . . . . . . . . 292
7.3.1 Consistency of Logic Programs . . . . . . . . . . . . . . . . 292
7.3.2 Reasoning Methods for Answer Set Prolog . . . . . . . . . . 295
7.3.3 Properties of Entailment . . . . . . . . . . . . . . . . . . . . 297
7.3.4 Relations between Programs . . . . . . . . . . . . . . . . . . 298
7.4 A Simple Knowledge Base . . . . . . . . . . . . . . . . . . . . . . . 300
7.5 Reasoning in Dynamic Domains . . . . . . . . . . . . . . . . . . . . 302
7.6 Extensions of Answer Set Prolog . . . . . . . . . . . . . . . . . . . . 307
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
Bibliography .................................. 310Contents xix
8 Belief Revision 317
Pavlos Peppas
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
8.2 Preliminaries............................... 318
8.3 TheAGMParadigm........................... 318
8.3.1 The AGM Postulates for Belief Revision . . . . . . . . . . . 319
8.3.2 The AGM Postulates for Belief Contraction . . . . . . . . . . 320
8.3.3 Selection Functions . . . . . . . . . . . . . . . . . . . . . . . 323
8.3.4 Epistemic Entrenchment . . . . . . . . . . . . . . . . . . . . 325
8.3.5 System of Spheres . . . . . . . . . . . . . . . . . . . . . . . . 327
8.4 Belief Base Change . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
8.4.1 Belief Base Change Operations . . . . . . . . . . . . . . . . . 331
8.4.2 Belief Base Change Schemes . . . . . . . . . . . . . . . . . . 332
8.5 Multiple Belief Change . . . . . . . . . . . . . . . . . . . . . . . . . 335
8.5.1 Multiple Revision . . . . . . . . . . . . . . . . . . . . . . . . 336
8.5.2 Multiple Contraction . . . . . . . . . . . . . . . . . . . . . . 338
8.6 IteratedRevision............................. 340
8.6.1 Iterated Revision with Enriched Epistemic Input . . . . . . . 340
8.6.2 Iterated Revision with Simple Epistemic Input . . . . . . . . 343
8.7 Non-PrioritizedRevision ........................ 346
8.8 Belief Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
8.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Bibliography .................................. 353
9 Qualitative Modeling 361
Kenneth D. Forbus
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
9.1.1 KeyPrinciples.......................... 362
9.1.2 Overview of Basic Qualitative Reasoning . . . . . . . . . . . 363
9.2 Qualitative Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . 365
9.2.1 Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
9.2.2 Functions and Relationships . . . . . . . . . . . . . . . . . . 369
9.3 Ontology................................. 371
9.3.1 Component Ontologies . . . . . . . . . . . . . . . . . . . . . 372
9.3.2 Process Ontologies . . . . . . . . . . . . . . . . . . . . . . . 373
9.3.3 FieldOntologies......................... 374
9.4 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
9.5 Compositional Modeling . . . . . . . . . . . . . . . . . . . . . . . . 376
9.5.1 Model Formulation Algorithms . . . . . . . . . . . . . . . . . 378
9.6 Qualitative States and Qualitative Simulation . . . . . . . . . . . . . 379
9.7 Qualitative Spatial Reasoning . . . . . . . . . . . . . . . . . . . . . . 381
9.7.1 Topological Representations . . . . . . . . . . . . . . . . . . 381
9.7.2 Shape, Location, and Orientation Representations . . . . . . 382
9.7.3 DiagrammaticReasoning.................... 382
9.8 Qualitative Modeling Applications . . . . . . . . . . . . . . . . . . . 383xx Contents
9.8.1 Automating or Assisting Professional Reasoning . . . . . . . 383
9.8.2 Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
9.8.3 CognitiveModeling....................... 386
9.9 FrontiersandResources......................... 387
Bibliography .................................. 387
10 Model-based Problem Solving 395
Peter Struss
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
10.2 Tasks.................................. 398
10.2.1 Situation Assessment/Diagnosis . . . . . . . . . . . . . . 398
10.2.2 Test Generation, Measurement Proposal, Diagnosability
Analysis ........................... 399
10.2.3 Design and Failure-Modes-and-Effects Analysis . . . . . 401
10.2.4 Proposal of Remedial Actions (Repair, Reconfiguration,
Recovery,Therapy) ..................... 402
10.2.5 Ingredients of Model-based Problem Solving . . . . . . . 402
10.3 Requirements on Modeling . . . . . . . . . . . . . . . . . . . . . . 403
10.3.1 Behavior Prediction and Consistency Check . . . . . . . 404
10.3.2 Validity of Behavior Modeling . . . . . . . . . . . . . . . 405
10.3.3 Conceptual Modeling . . . . . . . . . . . . . . . . . . . . 405
10.3.4 (Automated) Model Composition . . . . . . . . . . . . . 406
10.3.5 Genericity . . . . . . . . . . . . . . . . . . . . . . . . . . 406
10.3.6 Appropriate Granularity . . . . . . . . . . . . . . . . . . 407
10.4 Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
10.4.1 Consistency-based Diagnosis with Component-oriented
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
10.4.2 Computation of Diagnoses . . . . . . . . . . . . . . . . . 418
10.4.3 Solution Scope and Limitations of Component-Oriented
Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . 422
10.4.4 Diagnosis across Time . . . . . . . . . . . . . . . . . . . 423
10.4.5 Abductive Diagnosis . . . . . . . . . . . . . . . . . . . . 431
10.4.6 Process-Oriented Diagnosis . . . . . . . . . . . . . . . . 434
10.4.7 Model-based Diagnosis in Control Engineering . . . . . . 438
10.5 Test and Measurement Proposal, Diagnosability Analysis . . . . . 438
10.5.1 Test Generation . . . . . . . . . . . . . . . . . . . . . . . 439
10.5.2 Entropy-based Test Selection . . . . . . . . . . . . . . . . 444
10.5.3 ProbeSelection ....................... 445
10.5.4 Diagnosability Analysis . . . . . . . . . . . . . . . . . . . 446
10.6 Remedy Proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
10.6.1 Integration of Diagnosis and Remedy Actions . . . . . . 448
10.6.2 Component-oriented Reconfiguration . . . . . . . . . . . 450
10.6.3 Process-oriented Therapy Proposal . . . . . . . . . . . . 453
10.7 OtherTasks .............................. 454
10.7.1 Configuration and Design . . . . . . . . . . . . . . . . . . 454
10.7.2 Failure-Modes-and-Effects Analysis . . . . . . . . . . . . 456
10.7.3 Debugging and Testing of Software . . . . . . . . . . . . 456Contents xxi
10.8 State and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . 458
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
Bibliography ................................. 460
11 Bayesian Networks 467
Adnan Darwiche
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
11.2 Syntax and Semantics of Bayesian Networks . . . . . . . . . . . . 468
11.2.1 Notational Conventions . . . . . . . . . . . . . . . . . . . 468
11.2.2 Probabilistic Beliefs . . . . . . . . . . . . . . . . . . . . . 469
11.2.3 Bayesian Networks . . . . . . . . . . . . . . . . . . . . . 470
11.2.4 Structured Representations of CPTs . . . . . . . . . . . . 471
11.2.5 Reasoning about Independence . . . . . . . . . . . . . . . 471
11.2.6 Dynamic Bayesian Networks . . . . . . . . . . . . . . . . 472
11.3 Exact Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
11.3.1 Structure-Based Algorithms . . . . . . . . . . . . . . . . 474
11.3.2 Inference with Local (Parametric) Structure . . . . . . . . 479
11.3.3 Solving MAP and MPE by Search . . . . . . . . . . . . . 480
11.3.4 Compiling Bayesian Networks . . . . . . . . . . . . . . . 481
11.3.5 Inference by Reduction to Logic . . . . . . . . . . . . . . 482
11.3.6 Additional Inference Techniques . . . . . . . . . . . . . . 484
11.4 Approximate Inference . . . . . . . . . . . . . . . . . . . . . . . . 485
11.4.1 Inference by Stochastic Sampling . . . . . . . . . . . . . 485
11.4.2 Inference as Optimization . . . . . . . . . . . . . . . . . 486
11.5 Constructing Bayesian Networks . . . . . . . . . . . . . . . . . . 489
11.5.1 Knowledge Engineering . . . . . . . . . . . . . . . . . . 489
11.5.2 High-Level Specifications . . . . . . . . . . . . . . . . . 490
11.5.3 Learning Bayesian Networks . . . . . . . . . . . . . . . . 493
11.6 Causality and Intervention . . . . . . . . . . . . . . . . . . . . . . 497
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Bibliography ................................. 499
II Classes of Knowledge and Specialized Representations 511
12 Temporal Representation and Reasoning 513
Michael Fisher
12.1 TemporalStructures.......................... 514
12.1.1 InstantsandDurations ................... 514
12.1.2 From Discreteness to Density . . . . . . . . . . . . . . . 515
12.1.3 Granularity Hierarchies . . . . . . . . . . . . . . . . . . . 516
12.1.4 TemporalOrganisation ................... 517
12.1.5 MovinginRealTime .................... 517
12.1.6 Intervals ........................... 518
12.2 Temporal Language . . . . . . . . . . . . . . . . . . . . . . . . . . 520
12.2.1 Modal Temporal Logic . . . . . . . . . . . . . . . . . . . 520
12.2.2 BacktotheFuture...................... 521
12.2.3 Temporal Arguments and Reified Temporal Logics . . . . 521xxii Contents
12.2.4 Operators over Non-discrete Models . . . . . . . . . . . . 522
12.2.5 Intervals ........................... 523
12.2.6 Real-Time and Hybrid Temporal Languages . . . . . . . 524
12.2.7 Quantification........................ 525
12.2.8 Hybrid Temporal Logic and the Concept of “now” . . . . 528
12.3 TemporalReasoning ......................... 528
12.3.1 ProofSystems........................ 529
12.3.2 Automated Deduction . . . . . . . . . . . . . . . . . . . . 529
12.4 Applications.............................. 530
12.4.1 Natural Language . . . . . . . . . . . . . . . . . . . . . . 530
12.4.2 Reactive System Specification . . . . . . . . . . . . . . . 531
12.4.3 Theorem-Proving . . . . . . . . . . . . . . . . . . . . . . 532
12.4.4 Model Checking . . . . . . . . . . . . . . . . . . . . . . . 532
12.4.5 PSL/Sugar .......................... 534
12.4.6 Temporal Description Logics . . . . . . . . . . . . . . . . 534
12.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 535
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
Bibliography ................................. 535
13 Qualitative Spatial Representation and Reasoning 551
Anthony G. Cohn and Jochen Renz
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551
13.1.1 What is Qualitative Spatial Reasoning? . . . . . . . . . . 551
13.1.2 Applications of Qualitative Spatial Reasoning . . . . . . 553
13.2 Aspects of Qualitative Spatial Representation . . . . . . . . . . . . 554
13.2.1 Ontology........................... 554
13.2.2 SpatialRelations ...................... 556
13.2.3 Mereology.......................... 557
13.2.4 Mereotopology . . . . . . . . . . . . . . . . . . . . . . . 557
13.2.5 Between Mereotopology and Fully Metric Spatial Repre-
sentation........................... 566
13.2.6 Mereogeometry . . . . . . . . . . . . . . . . . . . . . . . 570
13.2.7 Spatial Vagueness . . . . . . . . . . . . . . . . . . . . . . 571
13.3 SpatialReasoning........................... 572
13.3.1 Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . 574
13.3.2 Composition . . . . . . . . . . . . . . . . . . . . . . . . . 575
13.3.3 Constraint-based Spatial Reasoning . . . . . . . . . . . . 576
13.3.4 Finding Efficient Reasoning Algorithms . . . . . . . . . . 578
13.3.5 Planar Realizability . . . . . . . . . . . . . . . . . . . . . 581
13.4 Reasoning about Spatial Change . . . . . . . . . . . . . . . . . . . 581
13.5 CognitiveValidity........................... 582
13.6 FinalRemarks............................. 583
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584
Bibliography ................................. 584Contents xxiii
14 Physical Reasoning 597
Ernest Davis
14.1 Architectures ............................. 600
14.1.1 Component Analysis . . . . . . . . . . . . . . . . . . . . 600
14.1.2 Process Model . . . . . . . . . . . . . . . . . . . . . . . . 601
14.2 Domain Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
14.2.1 Rigid Object Kinematics . . . . . . . . . . . . . . . . . . 603
14.2.2 Rigid Object Dynamics . . . . . . . . . . . . . . . . . . . 605
14.2.3 Liquids............................ 608
14.3 Abstraction and Multiple Models . . . . . . . . . . . . . . . . . . 611
14.4 Historical and Bibliographical . . . . . . . . . . . . . . . . . . . . 614
14.4.1 Logic-based Representations . . . . . . . . . . . . . . . . 614
14.4.2 Solid Objects: Kinematics . . . . . . . . . . . . . . . . . 615
14.4.3 Solid Object Dynamics . . . . . . . . . . . . . . . . . . . 616
14.4.4 Abstraction and Multiple Models . . . . . . . . . . . . . 616
14.4.5 Other............................. 616
14.4.6 Books . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617
Bibliography ................................. 618
15 Reasoning about Knowledge and Belief 621
Yoram Moses
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621
15.2 The Possible Worlds Model . . . . . . . . . . . . . . . . . . . . . 622
15.2.1 A Language for Knowledge and Belief . . . . . . . . . . 622
15.3 Properties of Knowledge . . . . . . . . . . . . . . . . . . . . . . . 626
15.4 The Knowledge of Groups . . . . . . . . . . . . . . . . . . . . . . 628
15.4.1 Common Knowledge . . . . . . . . . . . . . . . . . . . . 629
15.4.2 Distributed Knowledge . . . . . . . . . . . . . . . . . . . 632
15.5 RunsandSystems........................... 633
15.6 AddingTime ............................. 635
15.6.1 Common Knowledge and Time . . . . . . . . . . . . . . 636
15.7 Knowledge-based Behaviors . . . . . . . . . . . . . . . . . . . . . 637
15.7.1 Contexts and Protocols . . . . . . . . . . . . . . . . . . . 637
15.7.2 Knowledge-based Programs . . . . . . . . . . . . . . . . 639
15.7.3 A Subtle kb Program . . . . . . . . . . . . . . . . . . . . 641
15.8 Beyond Square One . . . . . . . . . . . . . . . . . . . . . . . . . . 643
15.9 How to Reason about Knowledge and Belief . . . . . . . . . . . . 644
15.9.1 Concluding Remark . . . . . . . . . . . . . . . . . . . . . 645
Bibliography ................................. 645
Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647
16 Situation Calculus 649
Fangzhen Lin
16.1 Axiomatizations............................ 650
16.2 The Frame, the Ramification and the Qualification Problems . . . 652
16.2.1 The Frame Problem—Reiter’s Solution . . . . . . . . . . 654
16.2.2 The Ramification Problem and Lin’s Solution . . . . . . . 657xxiv Contents
16.2.3 The Qualification Problem . . . . . . . . . . . . . . . . . 660
16.3 Reiter’s Foundational Axioms and Basic Action Theories . . . . . 661
16.4 Applications.............................. 665
16.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . 667
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Bibliography ................................. 667
17 Event Calculus 671
Erik T. Mueller
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
17.2 Versions of the Event Calculus . . . . . . . . . . . . . . . . . . . . 672
17.2.1 Original Event Calculus (OEC) . . . . . . . . . . . . . . 672
17.2.2 Simplified Event Calculus (SEC) . . . . . . . . . . . . . . 674
17.2.3 Basic Event Calculus (BEC) . . . . . . . . . . . . . . . . 676
17.2.4 EventCalculus(EC) .................... 679
17.2.5 Discrete Event Calculus (DEC) . . . . . . . . . . . . . . 681
17.2.6 Equivalence of DEC and EC . . . . . . . . . . . . . . . . 683
17.2.7 OtherVersions........................ 683
17.3 Relationship to other Formalisms . . . . . . . . . . . . . . . . . . 684
17.4 DefaultReasoning .......................... 684
17.4.1 Circumscription....................... 684
17.4.2 Computing Circumscription . . . . . . . . . . . . . . . . 685
17.4.3 HistoricalNote ....................... 686
17.4.4 NegationasFailure ..................... 687
17.5 Event Calculus Knowledge Representation . . . . . . . . . . . . . 687
17.5.1 Parameters.......................... 687
17.5.2 EventEffects ........................ 688
17.5.3 Preconditions . . . . . . . . . . . . . . . . . . . . . . . . 689
17.5.4 StateConstraints ...................... 689
17.5.5 Concurrent Events . . . . . . . . . . . . . . . . . . . . . . 690
17.5.6 Triggered Events . . . . . . . . . . . . . . . . . . . . . . 691
17.5.7 Continuous Change . . . . . . . . . . . . . . . . . . . . . 692
17.5.8 Nondeterministic Effects . . . . . . . . . . . . . . . . . . 693
17.5.9 IndirectEffects ....................... 694
17.5.10 Partially Ordered Events . . . . . . . . . . . . . . . . . . 696
17.6 Action Language E .......................... 697
17.7 Automated Event Calculus Reasoning . . . . . . . . . . . . . . . . 699
17.7.1 Prolog ............................ 699
17.7.2 Answer Set Programming . . . . . . . . . . . . . . . . . 700
17.7.3 Satisfiability (SAT) Solving . . . . . . . . . . . . . . . . 700
17.7.4 First-Order Logic Automated Theorem Proving . . . . . 700
17.8 Applications of the Event Calculus . . . . . . . . . . . . . . . . . 700
Bibliography ................................. 701
18 Temporal Action Logics 709
Patrick Doherty and Jonas Kvarnström
18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709Contents xxv
18.1.1 PMONandTAL...................... 710
18.1.2 PreviousWork ....................... 711
18.1.3 Chapter Structure . . . . . . . . . . . . . . . . . . . . . 713
18.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713
18.3 TALNarratives ............................ 716
18.3.1 The Russian Airplane Hijack Scenario . . . . . . . . . . 717
18.3.2 Narrative Background Specification . . . . . . . . . . . 718
18.3.3 Narrative Specification . . . . . . . . . . . . . . . . . . 723
18.4 The Relation Between the TAL Languages L(ND) and L(FL) . . 724
18.5 The TAL Surface Language L(ND) ................. 725
18.5.1 Sorts, Terms and Variables . . . . . . . . . . . . . . . . 725
18.5.2 Formulas .......................... 726
18.5.3 Statements ......................... 727
18.6 The TAL Base Language L(FL) ................... 728
18.6.1 Translation from L(ND) to L(FL) ............ 728
18.7 CircumscriptionandTAL....................... 730
18.8 Representing Ramifications in TAL . . . . . . . . . . . . . . . . . 735
18.9 Representing Qualifications in TAL . . . . . . . . . . . . . . . . . 737
18.9.1 Enabling Fluents . . . . . . . . . . . . . . . . . . . . . . 738
18.9.2 StrongQualification.................... 740
18.9.3 WeakQualification..................... 740
18.9.4 Qualification: Not Only For Actions . . . . . . . . . . . 741
18.9.5 Ramifications as Qualifications . . . . . . . . . . . . . . 742
18.10ActionExpressivityinTAL ..................... 742
18.11 Concurrent Actions in TAL . . . . . . . . . . . . . . . . . . . . . . 744
18.11.1 Independent Concurrent Actions . . . . . . . . . . . . . 744
18.11.2 Interacting Concurrent Actions . . . . . . . . . . . . . . 745
18.11.3 LawsofInteraction .................... 745
18.12 An Application of TAL: TALplanner . . . . . . . . . . . . . . . . 747
18.13Summary ............................... 752
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752
Bibliography ................................. 753
19 Nonmonotonic Causal Logic 759
Hudson Turner
19.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
19.1.1 Finite Domain Propositional Logic . . . . . . . . . . . . 762
19.1.2 Causal Theories . . . . . . . . . . . . . . . . . . . . . . 763
19.2 Strong Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . 765
19.3 Completion .............................. 766
19.4 Expressiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768
19.4.1 Nondeterminism: Coin Tossing . . . . . . . . . . . . . . 768
19.4.2 Implied Action Preconditions: Moving an Object . . . . 768
19.4.3 Things that Change by Themselves: Falling Dominos . 769
19.4.4 Things that Tend to Change by Themselves: Pendulum . 769
19.5 High-Level Action Language C+ .................. 770
19.6 Relationship to Default Logic . . . . . . . . . . . . . . . . . . . . 771xxvi Contents
19.7 Causal Theories in Higher-Order Classical Logic . . . . . . . . . . 772
19.8 ALogicofUniversalCausation ................... 773
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774
Bibliography ................................. 774
III Knowledge Representation in Applications 777
20 Knowledge Representation and Question Answering 779
Marcello Balduccini, Chitta Baral and Yuliya Lierler
20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 779
20.1.1 Role of Knowledge Representation and Reasoning in QA 780
20.1.2 Architectural Overview of QA Systems Using Knowl-
edge Representation and Reasoning . . . . . . . . . . . 782
20.2 From English to Logical Theories . . . . . . . . . . . . . . . . . . 783
20.3 The COGEX Logic Prover of the LCC QA System . . . . . . . . 790
20.4 Extracting Relevant Facts from Logical Theories and its Use in the
DD QA System about Dynamic Domains and Trips . . . . . . . . 792
20.4.1 The Overall Architecture of the DD System . . . . . . . 793
20.4.2 From Logic Forms to QSR Facts: An Illustration . . . . 794
20.4.3 OSR: From QSR Relations to Domain Relations . . . . 796
20.4.4 An Early Travel Module of the DD System . . . . . . . 798
20.4.5 Other Enhancements to the Travel Module . . . . . . . . 802
20.5 From Natural Language to Relevant Facts in the ASU QA System 803
20.6 Nutcracker—System for Recognizing Textual Entailment . . . . . 806
20.7 Mueller’s Story Understanding System . . . . . . . . . . . . . . . 810
20.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815
Bibliography ................................. 815
21 The SemanticWeb:Webizing Knowledge Representation 821
Jim Hendler and Frank van Harmelen
21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821
21.2 The Semantic Web Today . . . . . . . . . . . . . . . . . . . . . . 823
21.3 Semantic Web KR Language Design . . . . . . . . . . . . . . . . 826
21.3
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