Neural-Symbolic Learning Systems

1. Introduction and Overview.- 1.1 Why Integrate Neurons and Symbols?.- 1.2 Strategies of Neural-Symbolic Integration.- 1.3 Neural-Symbolic Learning Systems.- 1.4 A Simple Example.- 1.5 How to Read this Book.- 1.6 Summary.- 2. Background.- 2.1 General Preliminaries.- 2.2 Inductive Learning.- 2.3 Neural Networks.- 2.3.1 Architectures.- 2.3.2 Learning Strategy.- 2.3.3 Recurrent Networks.- 2.4 Logic Programming.- 2.4.1 What is Logic Programming?.- 2.4.2 Fixpoints and Definite Programs.- 2.5 Nonmonotonic Reasoning.- 2.5.1 Stable Models and Acceptable Programs.- 2.6 Belief Revision.- 2.6.1 Truth Maintenance Systems.- 2.6.2 Compromise Revision.- I. Knowledge Refinement in Neural Networks.- 3. Theory Refinement in Neural Networks.- 3.1 Inserting Background Knowledge.- 3.2 Massively Parallel Deduction.- 3.3 Performing Inductive Learning.- 3.4 Adding Classical Negation.- 3.5 Adding Metalevel Priorities.- 3.6 Summary and Further Reading.- 4. Experiments on Theory Refinement.- 4.1 DNA Sequence Analysis.- 4.2 Power Systems Fault Diagnosis.- 4.3.Discussion.- 4.4.Appendix.- II. Knowledge Extraction from Neural Networks.- 5. Knowledge Extraction from Trained Networks.- 5.1 The Extraction Problem.- 5.2 The Case of Regular Networks.- 5.2.1 Positive Networks.- 5.2.2 Regular Networks.- 5.3 The General Case Extraction.- 5.3.1 Regular Subnetworks.- 5.3.2 Knowledge Extraction from Subnetworks.- 5.3.3 Assembling the Final Rule Set.- 5.4 Knowledge Representation Issues.- 5.5 Summary and Further Reading.- 6. Experiments on Knowledge Extraction.- 6.1 Implementation.- 6.2 The Monk’s Problems.- 6.3 DNA Sequence Analysis.- 6.4 Power Systems Fault Diagnosis.- 6.5 Discussion.- III. Knowledge Revision in Neural Networks.- 7. Handling Inconsistencies in Neural Networks.- 7.1 Theory Revision in Neural Networks.- 7.1.1The Equivalence with Truth Maintenance Systems.- 7.1.2Minimal Learning.- 7.2 Solving Inconsistencies in Neural Networks.- 7.2.1 Compromise Revision.- 7.2.2 Foundational Revision.- 7.2.3 Nonmonotonic Theory Revision.- 7.3 Summary of the Chapter.- 8. Experiments on Handling Inconsistencies.- 8.1 Requirements Specifications Evolution as Theory Refinement.- 8.1.1Analysing Specifications.- 8.1.2Revising Specifications.- 8.2 The Automobile Cruise Control System.- 8.2.1Knowledge Insertion.- 8.2.2Knowledge Revision: Handling Inconsistencies.- 8.2.3Knowledge Extraction.- 8.3 Discussion.- 8.4 Appendix.- 9. Neural-Symbolic Integration: The Road Ahead.- 9.1 Knowledge Extraction.- 9.2 Adding Disjunctive Information.- 9.3 Extension to the First-Order Case.- 9.4 Adding Modalities.- 9.5 New Preference Relations.- 9.6 A Proof Theoretical Approach.- 9.7 The “Forbidden Zone” [Amax, Amin].- 9.8 Acceptable Programs and Neural Networks.- 9.9 Epilogue.