Knowledge Integration Methods for Probabilistic Knowledge-based Systems

Knowledge-based systems and solving knowledge integrating problems have seen a great surge of research activity in recent years. Knowledge Integration Methods provides a wide snapshot of building knowledge-based systems, inconsistency measures, methods for handling con-sistency, and methods for integrating knowledge bases. The book also provides the mathematical background to solving problems of restoring consistency and integrating probabilistic knowledge bases in the inte-grating process. The research results presented in the book can be ap-plied in decision support systems, semantic web systems, multimedia information retrieval systems, medical imaging systems, cooperative information systems, and more. This text will be useful for computer science graduates and PhD students, in addition to researchers and readers working on knowledge management and ontology interpreta-tion. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Contents 6 Preface 10 Authors 12 CHAPTER 1: Introduction 14 1.1. MOTIVATION 14 1.2. THE OBJECTIVES OF THIS BOOK 18 1.3. THE STRUCTURE OF THIS BOOK 19 CHAPTER 2: Probabilistic knowledge-based systems 21 2.1. KNOWLEDGE BASE REPRESENTATION 21 2.1.1. Knowledge Representation Methods 21 2.1.2. Probabilistic Knowledge Base Representation 23 2.2. TYPES OF KNOWLEDGE-BASED SYSTEMS 27 2.3. THE KNOWLEDGE-BASED SYSTEM DEVELOPMENT 29 2.4. COMPONENTS OF A PROBABILISTIC KNOWLEDGE-BASED SYSTEM 30 2.5. COMPARING PROBABILISTIC KNOWLEDGE-BASED SYSTEM WITH OTHER SYSTEMS 32 2.6. CONCLUDING REMARKS 35 CHAPTER 3: Inconsistency measures for probabilistic knowledge bases 36 3.1. OVERVIEW OF INCONSISTENCY MEASURES 36 3.1.1. Distance Functions 36 3.1.2. Development of Inconsistency Measures 37 3.2. REPRESENTING THE INCONSISTENCY OF THE PROBABILISTIC KNOWLEDGE BASE 40 3.2.1. Basic Notions 40 3.2.2. Characteristic Model 42 3.2.3. Desired Properties of Inconsistency Measures 44 3.3. INCONSISTENCY MEASURES FOR PROBABILISTIC KNOWLEDGE BASES 46 3.3.1. The Basic Inconsistency Measures 46 3.3.2. The Norm-based Inconsistency Measures 53 3.3.3. The Unnormalized Inconsistency Measure 58 3.4. ALGORITHMS FOR COMPUTING THE INCONSISTENCY MEASURES 62 3.4.1. The Computational Complexity 62 3.4.2. The General Methods 63 3.4.3. Algorithms 64 3.5. CONCLUDING REMARKS 70 CHAPTER 4: Methods for restoring consistency in probabilistic knowledge bases 71 4.1. OVERVIEW OF HANDLING INCONSISTENCIES 71 4.1.1. The Inconsistency Resolution Problem 71 4.1.2. Methods of Handling Inconsistencies 73 4.2. RESTORING CONSISTENCY IN PROBABILISTIC KNOWLEDGE BASES 76 4.2.1. Basic Notions 76 4.2.2. Desired Properties of Consistency-Restoring Operator 77 4.2.3. A General Model for Restoring Consistency 79 4.3. METHODS FOR RESTORING CONSISTENCY 80 4.3.1. The Norm-based Consistency-restoring Problem 80 4.3.2. The Unnormalized Consistency-Restoring Problem 90 4.4. ALGORITHMS FOR RESTORING CONSISTENCY 97 4.5. CONCLUDING REMARKS 103 CHAPTER 5: Distance-based methods for integrating probabilistic knowledge bases 104 5.1. OVERVIEW OF KNOWLEDGE INTEGRATION METHODS 104 5.1.1. The Knowledge Integration Problem 104 5.1.2. Methods for Integrating Knowledge Bases 107 5.2. PROBABILISTIC KNOWLEDGE INTEGRATION 111 5.2.1. Divergence Functions 111 5.2.2. Distance-based Model for Integrating Probabilistic Knowledge Bases 115 5.2.3. Desired Properties of Distance-based Probabilistic Integrating Operator 117 5.2.4. Finding the Satisfying Probability Vector 119 5.3. THE PROBLEMS WITH DISTANCE-BASED INTEGRATING PROBABILISTIC KNOWLEDGE BASES 123 5.4. DISTANCE-BASED INTEGRATING OPERATORS 125 5.4.1. The Class of Probabilistic Integrating Operators Γϑ 125 5.4.2. The Class of Probabilistic Integrating Operators ΓHU 128 5.5. INTEGRATION ALGORITHMS 140 5.5.1. Algorithm for Finding the Satisfying Probability Vector 140 5.5.2. The Distance-based Integration Algorithm 141 5.5.3. The HULL Algorithm 143 5.6. CONCLUDING REMARKS 144 CHAPTER 6: Value-based method for integrating probabilistic knowledge bases 145 6.1. VALUE-BASED PROBABILISTIC KNOWLEDGE INTEGRATION 145 6.1.1. Basic Notions 145 6.1.2. Value-based Model for Integrating Probabilistic Knowledge Bases 149 6.1.3. Desired Properties of Value-based Probabilistic Integrating Operator 150 6.2. THE PROBABILITY VALUE-BASED INTEGRATING OPERATORS 151 6.3. THE PROBABILITY VALUE-BASED INTEGRATION ALGORITHMS 154 6.3.1. Algorithm for Deducting Probabilistic Constraints 154 6.3.2. Probability Value-based Integration Algorithms 156 6.4. CONCLUDING REMARKS 159 CHAPTER 7: Experiments and Applications 160 7.1. EXPERIMENT 160 7.1.1. Experimental Purpose and Assumptions 160 7.1.2. Experiment Settings 162 7.1.3. Experimental Implementation 164 7.1.4. Results and Analysis 165 7.2. APPLICATIONS 175 7.2.1. Artificial Intelligence and Machine Learning 175 7.2.1.1. Machine Learning 175 7.2.1.2. Recommendation Systems 177 7.2.1.3. Group Decision-making 178 7.2.2. Knowledge Systems 178 7.2.3. Software Engineering 179 7.2.4. Other Applications 180 CHAPTER 8: Conclusions and open problems 181 8.1. CONCLUSIONS 181 8.2. OPEN PROBLEMS 183 Bibliography 184 Index 199 Inconsistency,measures;,Knowledge,and,integration,methods;,Knowledge,management;,Knowledge-based,systems;,Probabilistic,knowledge Inconsistency measures,Knowledge and integration methods,Knowledge management,Knowledge-based systems,Probabilistic knowledge Knowledge-based systems and solving knowledge integrating problems have seen a great surge of research activity in recent years. Knowledge Integration Methods provides a wide snapshot of building knowledge-based systems, inconsistency measures, methods for handling con-sistency, and methods for integrating knowledge bases. The book also provides the mathematical background to solving problems of restoring consistency and integrating probabilistic knowledge bases in the inte-grating process. The research results presented in the book can be ap-plied in decision support systems, semantic web systems, multimedia information retrieval systems, medical imaging systems, cooperative information systems, and more. This text will be useful for computer science graduates and PhD students, in addition to researchers and readers working on knowledge management and ontology interpreta-tion. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Contents 6 Preface 10 Authors 12 CHAPTER 1: Introduction 14 1.1. MOTIVATION 14 1.2. THE OBJECTIVES OF THIS BOOK 18 1.3. THE STRUCTURE OF THIS BOOK 19 CHAPTER 2: Probabilistic knowledge-based systems 21 2.1. KNOWLEDGE BASE REPRESENTATION 21 2.1.1. Knowledge Representation Methods 21 2.1.2. Probabilistic Knowledge Base Representation 23 2.2. TYPES OF KNOWLEDGE-BASED SYSTEMS 27 2.3. THE KNOWLEDGE-BASED SYSTEM DEVELOPMENT 29 2.4. COMPONENTS OF A PROBABILISTIC KNOWLEDGE-BASED SYSTEM 30 2.5. COMPARING PROBABILISTIC KNOWLEDGE-BASED SYSTEM WITH OTHER SYSTEMS 32 2.6. CONCLUDING REMARKS 35 CHAPTER 3: Inconsistency measures for probabilistic knowledge bases 36 3.1. OVERVIEW OF INCONSISTENCY MEASURES 36 3.1.1. Distance Functions 36 3.1.2. Development of Inconsistency Measures 37 3.2. REPRESENTING THE INCONSISTENCY OF THE PROBABILISTIC KNOWLEDGE BASE 40 3.2.1. Basic Notions 40 3.2.2. Characteristic Model 42 3.2.3. Desired Properties of Inconsistency Measures 44 3.3. INCONSISTENCY MEASURES FOR PROBABILISTIC KNOWLEDGE BASES 46 3.3.1. The Basic Inconsistency Measures 46 3.3.2. The Norm-based Inconsistency Measures 53 3.3.3. The Unnormalized Inconsistency Measure 58 3.4. ALGORITHMS FOR COMPUTING THE INCONSISTENCY MEASURES 62 3.4.1. The Computational Complexity 62 3.4.2. The General Methods 63 3.4.3. Algorithms 64 3.5. CONCLUDING REMARKS 70 CHAPTER 4: Methods for restoring consistency in probabilistic knowledge bases 71 4.1. OVERVIEW OF HANDLING INCONSISTENCIES 71 4.1.1. The Inconsistency Resolution Problem 71 4.1.2. Methods of Handling Inconsistencies 73 4.2. RESTORING CONSISTENCY IN PROBABILISTIC KNOWLEDGE BASES 76 4.2.1. Basic Notions 76 4.2.2. Desired Properties of Consistency-Restoring Operator 77 4.2.3. A General Model for Restoring Consistency 79 4.3. METHODS FOR RESTORING CONSISTENCY 80 4.3.1. The Norm-based Consistency-restoring Problem 80 4.3.2. The Unnormalized Consistency-Restoring Problem 90 4.4. ALGORITHMS FOR RESTORING CONSISTENCY 97 4.5. CONCLUDING REMARKS 103 CHAPTER 5: Distance-based methods for integrating probabilistic knowledge bases 104 5.1. OVERVIEW OF KNOWLEDGE INTEGRATION METHODS 104 5.1.1. The Knowledge Integration Problem 104 5.1.2. Methods for Integrating Knowledge Bases 107 5.2. PROBABILISTIC KNOWLEDGE INTEGRATION 111 5.2.1. Divergence Functions 111 5.2.2. Distance-based Model for Integrating Probabilistic Knowledge Bases 115 5.2.3. Desired Properties of Distance-based Probabilistic Integrating Operator 117 5.2.4. Finding the Satisfying Probability Vector 119 5.3. THE PROBLEMS WITH DISTANCE-BASED INTEGRATING PROBABILISTIC KNOWLEDGE BASES 123 5.4. DISTANCE-BASED INTEGRATING OPERATORS 125 5.4.1. The Class of Probabilistic Integrating Operators Γθ 125 5.4.2. The Class of Probabilistic Integrating Operators ΓHU 128 5.5. INTEGRATION ALGORITHMS 140 5.5.1. Algorithm for Finding the Satisfying Probability Vector 140 5.5.2. The Distance-based Integration Algorithm 141 5.5.3. The HULL Algorithm 143 5.6. CONCLUDING REMARKS 144 CHAPTER 6: Value-based method for integrating probabilistic knowledge bases 145 6.1. VALUE-BASED PROBABILISTIC KNOWLEDGE INTEGRATION 145 6.1.1. Basic Notions 145 6.1.2. Value-based Model for Integrating Probabilistic Knowledge Bases 149 6.1.3. Desired Properties of Value-based Probabilistic Integrating Operator 150 6.2. THE PROBABILITY VALUE-BASED INTEGRATING OPERATORS 151 6.3. THE PROBABILITY VALUE-BASED INTEGRATION ALGORITHMS 154 6.3.1. Algorithm for Deducting Probabilistic Constraints 154 6.3.2. Probability Value-based Integration Algorithms 156 6.4. CONCLUDING REMARKS 159 CHAPTER 7: Experiments and Applications 160 7.1. EXPERIMENT 160 7.1.1. Experimental Purpose and Assumptions 160 7.1.2. Experiment Settings 162 7.1.3. Experimental Implementation 164 7.1.4. Results and Analysis 165 7.2. APPLICATIONS 175 7.2.1. Artificial Intelligence and Machine Learning 175 7.2.1.1. Machine Learning 175 7.2.1.2. Recommendation Systems 177 7.2.1.3. Group Decision-making 178 7.2.2. Knowledge Systems 178 7.2.3. Software Engineering 179 7.2.4. Other Applications 180 CHAPTER 8: Conclusions and open problems 181 8.1. CONCLUSIONS 181 8.2. OPEN PROBLEMS 183 Bibliography 184 Index 199 Inconsistency,measures;,Knowledge,and,integration,methods;,Knowledge,management;,Knowledge-based,systems;,Probabilistic,knowledge Inconsistency measures,Knowledge and integration methods,Knowledge management,Knowledge-based systems,Probabilistic knowledge "Knowledge-based systems and solving knowledge integrating problems have seen a great surge of research activity in recent years. This book provides a wide snapshot of building knowledge-based systems, inconsistency measures, methods for handling consistency, and methods for integrating knowledge bases. It also provides the mathematical background to solve problems of restoring consistency and problems of integrating probabilistic knowledge bases in the integrating process. The research results presented in the book can be applied in decision support systems, semantic web systems, multimedia information retrieval systems, medical imaging systems, cooperative information systems, and more. Knowledge Integration Methods will be useful for Computer Science graduates and Ph.D students, in addition to researchers and readers working on knowledge management and ontology interpretation"-- Provided by publisher