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Front Cover |
1 |
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Readings in Qualitative Reasoning About Physical Systems |
4 |
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Copyright Page |
5 |
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Table of Contents |
8 |
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Preface |
6 |
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Qualitative Physics: A Personal View |
14 |
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1. The Confusion Seminar |
15 |
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2. Qualitative Reasoning for Solving Physics Problems |
15 |
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3. Qualitative and Causal Reasoning for Circuit Diagnosis |
17 |
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4. Qualitative and Causal Reasoning for Design |
18 |
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5. Causality, Structure, and Function |
19 |
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6. Are We Doing Physics or Psychology? |
20 |
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7· Whither Qualitative Physics? |
20 |
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Part 1: Overview and Motivation |
22 |
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Introduction |
22 |
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Chapter 1. Qualitative Physics: Past, Present, and Future |
24 |
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1 Introduction |
24 |
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2 Why Qualitative Physics |
24 |
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3 The Past |
27 |
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4 The State of the Art |
30 |
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5 The Frontier |
45 |
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Acknowledgments |
49 |
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References |
49 |
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Chapter 1.2 Multiple Representations of Knowledge in a Mechanics Problem-Solver |
53 |
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Abstract |
53 |
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Introduction |
53 |
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Theory |
53 |
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The Program NEWTON |
54 |
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Envisioning and Planning |
56 |
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Problem Formulation |
57 |
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Concluding Remarks |
57 |
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Acknowledgements |
58 |
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References |
58 |
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Chapter 1.3 The Second Naive Physics Manifesto |
59 |
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1. Preface |
59 |
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2. Introduction |
59 |
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3. What the Proposal Isn't |
59 |
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4. Theories, Tokens and Closure |
61 |
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5. Meanings, Theories and Model Theory |
63 |
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6. Discovering Intuitions and Building Theories |
65 |
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7. Clusters |
67 |
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8. Getting It Done |
73 |
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9. Why It Needs To Be Done |
75 |
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10. Is This Science? |
76 |
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Acknowledgments |
76 |
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Reference |
76 |
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Chapter 1.4 Modeling Simultaneous Actions and Continuous Processes |
77 |
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1. Introduction: World Modeling |
77 |
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2. Realizing the Philosophy of Processes |
77 |
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3. World Modeling in Conventional Robot Systems |
78 |
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4. A Qoser Look at the Nature of Processes |
79 |
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5. The Process Model: An Overview |
80 |
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6. A Sample World |
82 |
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7. Elementary Examples of Scenarios |
82 |
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8. More Complex Scenarios: The Filling of a Bucket |
84 |
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9. Scenarios with Effects Sandwiches |
86 |
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10. Scenarios for Conventional Robot Operati |
88 |
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11. Modeling the Execution of Plans |
91 |
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12. Implementation |
93 |
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13. Summary |
93 |
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ACKNOWLEDGMENTS |
94 |
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REFERENCES |
94 |
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Chapter 2. Qualitative Simulation |
96 |
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Introduction |
96 |
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2.1 A Qualitative Physics Based on Confluences |
101 |
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1. Introduction |
101 |
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2. Naive Physics |
104 |
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3. Modeling Structure |
107 |
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4. Prediction of Behavior |
114 |
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5. Explanation of Behavior |
122 |
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6. Causality and Digital Physics |
126 |
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7. Summary |
135 |
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Appendix A. Interpretations |
136 |
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Appendix B. A Procedure for Constructing the Expanded Episode Diagram |
138 |
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ACKNOWLEDGMENT |
138 |
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REFERENCES |
138 |
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Chapter 2.2 Qualitative Reasoning with Higher-Order Derivatives |
140 |
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ABSTRACT |
140 |
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INTRODUCTION |
140 |
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QUALITATIVE MODELING |
140 |
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SIMULATION |
141 |
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RULE(O) : VALUE CONTINUITY |
141 |
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RULE(1): CONTRADICTION AVOIDANCE |
142 |
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QUALITATIVE AMBIGUITY |
142 |
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RULE(2): INSTANT CHANGK RULE |
143 |
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RULE(3): DERIVATIVE CONTINUITY |
143 |
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RULE(4) : DERIVA UVE INSTANT CHANGE RULE |
143 |
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INSTANTS |
143 |
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RULE (5): HIGHER-ORDER DERIVATIVES |
144 |
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RULE(6): NO CHANGE TO ALL ZERO DERIVATIVES |
144 |
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QUALITATIVE vs. QUANTITATIVE |
144 |
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OPEN PROBLEMS |
145 |
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ACKNOWLEDGMENTS |
145 |
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REFERENCES |
145 |
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Chapter 2.3 Temporal Qualitative Analysis: Explaining How Physical Systems Work |
146 |
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Abstract |
146 |
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1. Introduction |
146 |
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2. Qualitative Values |
150 |
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3. Causal Propagation |
152 |
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4. Transition Analysis |
157 |
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5. Feedback Analysis |
164 |
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6. Complex Qualitative Values and Operating Regions |
177 |
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7. Discussion |
184 |
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8. Appendix: Transition Ordering Rules |
188 |
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References |
189 |
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Chapter 2.4 Qualitative Process Theory |
191 |
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1. Introduction |
191 |
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2. Objects and Quantities |
195 |
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3. Processes |
200 |
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4. Examples |
209 |
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5. Further Consequences |
223 |
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6. Discussion |
229 |
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ACKNOWLEDGMENT |
231 |
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REFERENCES |
231 |
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Chapter 2.5 The Qualitative Process Engine |
233 |
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1. Introduction |
233 |
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2. Using an ATMS |
234 |
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3. The Qualitative Process Engine |
238 |
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4. Conclusions |
246 |
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5. Acknowledgements |
247 |
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References |
247 |
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Chapter 2.6 Qualitative Simulation |
249 |
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1. Introduction |
249 |
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2. Qualitative Behavior |
253 |
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3. Qualitative Structure |
255 |
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4. Qualitative Simulation |
257 |
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5. Questions and Answers |
261 |
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Appendix A. The Qualitative State Transitions |
265 |
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Appendix B. Constraint Consistency |
268 |
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Appendix C. The QSIM Program and its Output |
272 |
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ACKNOWLEDGMENT |
272 |
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REFERENCES |
273 |
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Chapter 2.7 Taming Intractable Branching in Qualitative Simulation |
274 |
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Abstract |
274 |
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1. Introduction |
274 |
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2. Ignoring Irrelevant Distinctions |
276 |
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3. Applying Higher-Order Derivatives |
277 |
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4. Conclusions |
279 |
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5. References |
280 |
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Chapter 2.8 Non-intersection of Trajectories in Qualitative Phase Space: A Global Constraint for Qualitative Simulation |
281 |
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Abstract |
281 |
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1. Introduction |
281 |
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2. The Phase Space View |
281 |
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3. The Non-IntersectionConstraint |
282 |
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4. Implementation |
283 |
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5. An Example |
283 |
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6. Discussion |
284 |
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7. Related Work |
284 |
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8. Conclusions |
285 |
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Acknowledgments |
285 |
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References |
285 |
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Chapter 2.9 Global Filters for Qualitative Behaviors |
286 |
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Abstract |
286 |
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1. Introduction |
286 |
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2. Outline of the Paper |
286 |
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3. Some Questions |
286 |
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4. Infering Qualitative Behavior |
286 |
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5. Filtering Behaviors |
287 |
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6. Exploiting the Phase Portrait |
288 |
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7. Summary |
290 |
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Acknowledgements |
290 |
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References |
290 |
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Chapter 2.10 Reasoning about Discontinuous Change |
291 |
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ABSTRACT |
291 |
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I. Introduction |
291 |
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II. Properties of Discontinuous Change |
291 |
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?II. Previous Work |
292 |
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IV. The Approximation Method |
293 |
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V. The Direct Method |
294 |
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VI. Comparison and Concluding Remarks |
296 |
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References |
296 |
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Chapter 3. Mathematical Aspects of Qualitative Reasoning |
298 |
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Introduction |
298 |
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3.1 Problems of Interval-Based Qualitative Reasoning |
301 |
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Abstract |
301 |
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1. Introduction |
301 |
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2. A Framework for Analyzing Qualitative Reasoning Methods |
302 |
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3. Qualitative Reasoning Methods for Equations |
305 |
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4. Interval Arithmetic 1 |
306 |
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5. A Modified Concept of Solution -Interval Arithmetic 2 |
309 |
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6. Arithmetic on a Finite Number ofIntervals - Interval Arithmetic 3 |
315 |
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7. Summary |
317 |
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Acknowledgements |
317 |
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References |
318 |
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Chapter 3.2 Assembling a Device |
319 |
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Abstract |
319 |
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1. Introduction |
319 |
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2. Assembling some devices |
319 |
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3. Scanning the qualitative resolution rule |
321 |
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4. Completeness of qualitative resolution |
323 |
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5. Task-oriented confluences |
324 |
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6. Conclusion |
324 |
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References |
324 |
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Chapter 3.3 MINIMA A Symbolic Approach to Qualitative Algebraic Reasoning |
325 |
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Abstract |
325 |
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1. Introduction |
325 |
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2. Example: Culinary Design |
325 |
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3. The Qualitative Algebra Q1 |
326 |
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4. Properties of Q1 |
327 |
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5. Using a Qualitative Algebra for Design |
328 |
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6. MINIMA |
329 |
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7. Example Revisited |
330 |
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8. Discussion |
330 |
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References |
330 |
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Chapter 3.4 Order of Magnitude Reasoning |
331 |
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ABSTRACT |
331 |
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INTRODUCTION |
331 |
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I. A SIMPLE EXAMPLE |
331 |
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II. FOG |
332 |
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III. BACK TO THE EXAMPLE |
333 |
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IV. VALIDITY OF FOG IN NON-STANDARD ANALYSIS |
334 |
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V. HOW TO USE FOG |
334 |
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VI. FOG AND THE QUANTITY SPACE |
335 |
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CONCLUSION |
335 |
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ACKNOWLEDGMENTS |
335 |
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REFERENCES |
335 |
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Chapter 3.5 Formal Order-of-Magnitude Reasoning in Process Engineering |
336 |
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1. INTRODUCTION |
336 |
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2. PREVIOUS WORK |
337 |
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3. THE SCOPE OF ORDER-OF-MAGNITUDE REASONING IN PROCESS ENGINEERING |
338 |
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4. THE O(M) FORMALISM |
339 |
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5. IMPLEMENTATION |
344 |
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6. DETAILED REASONING EXAMPLES |
345 |
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7. DISCUSSION |
348 |
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8. CONCLUSIONS |
348 |
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REFERENCES |
348 |
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Chapter 3.6 "Commonsense" Arithmetic Reasoning |
350 |
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Abstract |
350 |
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1. Introduction |
350 |
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2. The Quantity Lattice |
350 |
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3. Results |
354 |
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4. Relation to Other Work |
355 |
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5. Conclusions |
356 |
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References |
356 |
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Chapter 3.7 Hierarchical Reasoning about Inequalities |
357 |
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Abstract |
357 |
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I. Introduction |
357 |
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II. The Context Manager |
358 |
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III· Bounding Algorithms |
358 |
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IV. Related Work |
360 |
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V. Conclusions |
361 |
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References |
362 |
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Chapter 4. History-Based Simulation and Temporal Reasoning |
364 |
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Introduction |
364 |
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4.1 Doing Time: Putting Qualitative Reasoning on Firmer Ground |
366 |
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Abstract |
366 |
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1. Introduction |
366 |
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2. Qualitative Reasoning In A Nutshell |
366 |
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3. Limitations of the Existing Approach |
367 |
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4. Representing Behavior Over Time |
367 |
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5. Propagation of Constraints |
368 |
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6. The Basic Constraint Propagator |
368 |
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7. Temporal Constraint Propagatior |
368 |
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8. Histories |
368 |
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9. Making Histories Concise |
369 |
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10. The Time Box |
370 |
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11. Modeling Time for Feedback Systems |
371 |
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12. Qualitative Reasoning Revisited |
372 |
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13. Summary and Research Status |
373 |
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14. Acknowledgements |
373 |
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References |
373 |
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Chapter 4.2 Maintaining Knowledge about Temporal Intervals |
374 |
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1. INTRODUCTION |
374 |
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2. BACKGROUND |
375 |
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3. TIME POINTS VS. TIME INTERVALS |
376 |
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4. MAINTAINING TEMPORAL RELATIONS |
376 |
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5. CONTROLLING PROPAGATION: REFERENCE INTERVALS |
380 |
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6. DISCUSSION |
383 |
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7. FUTURE RESEARCH AND EXTENSIONS |
383 |
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8. SUMMARY |
385 |
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REFERENCES |
385 |
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Chapter 4.3 Constraint Propagation Algorithms for Temporal Reasoning: A Revised Report |
386 |
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The Interval Algebra |
386 |
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Determining Closure in the Interval Algebra |
387 |
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Intractability of the Interval Algebra |
389 |
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Consequences of Intractability |
390 |
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Restricting the Interval Algebra |
390 |
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Time Point Algebras |
391 |
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Continuous Endpoint Uncertainty |
391 |
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Additional Results |
393 |
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Applying Temporal Representations |
394 |
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Acknowledgements |
394 |
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References |
394 |
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Chapter 4.4 Reasoning about Partially Ordered Events |
395 |
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1. Introduction |
395 |
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2. Temporal Projection |
395 |
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3. Incomplete Decision Procedures |
397 |
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4. Probabilistic Decision Procedures |
404 |
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5. Conclusions |
404 |
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Appendix A |
405 |
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Chapter 5. Other Styles of Reasoning |
408 |
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Introduction |
408 |
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Chapter 5.1 Comparative Analysis |
410 |
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1. Introduction |
410 |
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2. Preliminaries |
413 |
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3. Differential Qualitative Analysis |
416 |
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4. Changes in Behavioral Topology |
423 |
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5. Related Work |
427 |
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6. Future Directions |
428 |
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Appendix A. A Useful Example |
428 |
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ACKNOWLEDGMENT |
429 |
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REFERENCES |
429 |
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Chapter 5.2 Exaggeration |
430 |
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Abstract |
430 |
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1. Introduction |
430 |
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2. Transform Phase |
431 |
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3. Simulate Phase |
431 |
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4. Scale Phase |
433 |
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5. Related Work |
433 |
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References |
434 |
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Chapter 5.3 Order of Magnitude Reasoning in Qualitative Differential Equations |
435 |
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1. Introduction |
435 |
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2. Theory |
436 |
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3. Sample Inferences |
440 |
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4. Algorithm |
442 |
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5. The CHEPACHET Program |
445 |
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6. Further Work |
446 |
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7. References |
446 |
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Chapter 5.4 Troubleshooting: When Modeling Is the Trouble |
448 |
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I. Introduction |
448 |
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II. Complexity of Troubleshooting in Analog Circuits |
448 |
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III. Exploiting Significant Changes in Behavior |
449 |
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IV. Qualitative Modeling in DEDALE |
449 |
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V. Example of Diagnosis |
451 |
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VI. Strategy |
452 |
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VII. Conclusion |
453 |
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Acknowledgments |
453 |
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Appendix |
453 |
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References |
453 |
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Chapter 5.5 Interpreting Observations of Physical Systems |
454 |
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I. INTRODUCTION |
454 |
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II. INPUT DATA AND SEGMENTATION |
455 |
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III. INTERPRETING SEGMENTS |
458 |
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IV. CONSTRUCTING GLOBAL INTERPRETATIONS |
461 |
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ACKNOWLEDGMENT |
463 |
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REFERENCES |
463 |
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Chapter 6. Automating Quantitative Analysis |
464 |
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Introduction |
464 |
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Chapter 6.1 Intelligence in Scientific Computing |
466 |
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NUMERICAL MODELING CAN BE AUTOMATED |
467 |
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INTELLIGENT NUMERICAL COMPUTING RESTS ON AI TECHNOLOGY |
474 |
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INTELLIGENT TOOLS ARE FEASIBLE |
479 |
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REFERENCES |
481 |
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Chapter 6.2 Generating Global Behaviors Using Deep Knowledge of Local Dynamics |
483 |
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Abstract |
483 |
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1. Introduction |
483 |
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2. Ontology |
484 |
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3. The Task |
485 |
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4. Characteristics of Task Domain |
485 |
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5. Implementation |
486 |
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6. Experiments |
487 |
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7. Evaluating the performance |
487 |
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8. Conclusion |
488 |
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References |
488 |
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Chapter 6.3 Piecewise Linear Reasoning |
489 |
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Abstract |
489 |
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I. Introduction |
489 |
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II. The PLR Methodology |
489 |
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III. The Lienard Equation |
490 |
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IV. The Van der Pol Equation |
491 |
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V. Previous Work |
492 |
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VI. Implementation Status |
493 |
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VII. Conclusions |
493 |
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References |
493 |
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Chapter 7. Multiple Ontologies and Automated Modeling |
494 |
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Introduction |
494 |
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Chapter 7.1 Naive Physics I: Ontology for Liquids |
497 |
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1. Introduction |
497 |
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2. Individuals and Individuation |
497 |
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3. The Problem With Liquids |
498 |
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4. Doing Without Liquid Individuals: Containment |
499 |
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5. Space: Places, Enclosures and Portals |
500 |
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6. The Fifteen States of Liquids |
504 |
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7. Change and Movement: Histories |
506 |
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8. Histories of Lazy Bulk Liquid |
508 |
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9. Some Examples |
511 |
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10. Liquid Individuals Revisited |
513 |
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11. Further Works |
514 |
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Acknowledgments |
515 |
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References |
515 |
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Chapter 7.2 Reasoning about Fluids via Molecular Collections |
516 |
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Abstract |
516 |
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I. Introduction |
516 |
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II. The theory of molecular collections |
516 |
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III. Examples |
518 |
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IV. Discussion |
519 |
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V. Acknowledgements |
520 |
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References |
520 |
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Chapter 7.3 Multiple Models of Evaporation Processes |
521 |
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Aggregate ?odels |
523 |
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A Molecular Model |
524 |
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Conclusion |
525 |
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References |
525 |
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Chapter 7.4 The Use of Aggregation in Causal Simulation |
526 |
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1. Introduction |
526 |
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2. Demonstration |
528 |
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3. Representing State and Change |
530 |
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4. Aggregation |
532 |
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5. Applicability |
539 |
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6. Related Work |
541 |
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7. Conclusion |
542 |
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ACKNOWLEDGMENT |
542 |
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REFERENCES |
542 |
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Chapter 7.5 Abstraction by Time-Scale in Qualitative Simulation |
543 |
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1. The Problem of Scale |
543 |
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2. Time-Scale Abstraction |
543 |
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3. Communicating Across Time-Scales |
545 |
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4. Conclusions |
547 |
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5. References |
547 |
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Chapter 7.6 Diagnosis via Causal Reasoning: Paths of Interaction and the Locality Principle |
548 |
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Abstract |
548 |
|
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1. INTRODUCTION |
548 |
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2. CENTRAL CONCERNS |
548 |
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3. BACKGROUND |
548 |
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4. LAYERS OF INTERACTION EXAMPLE: DIAGNOSING A BRIDGE FAULT |
550 |
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5. PATHS OF INTERACTION |
553 |
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6. SUMMARY |
554 |
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REFERENCES |
554 |
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Chapter 7.7 Granularity |
555 |
|
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Abstract |
555 |
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Abstraction |
555 |
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Simplification |
555 |
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Idealization |
556 |
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Articulation |
557 |
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Intelligence |
558 |
|
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Acknowledgments |
558 |
|
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References |
558 |
|
|
Chapter 7.8 Reasoning About Assumptions in Graphs of Models |
559 |
|
|
Abstract |
559 |
|
|
1. Introduction |
559 |
|
|
2. Graphs of Models |
560 |
|
|
3. Conflicts |
561 |
|
|
4. Delta-Vectors |
561 |
|
|
5. Assumption Knowledge |
562 |
|
|
6. Selecting a Better Model |
563 |
|
|
7. Conclusions and Future Work |
564 |
|
|
References |
565 |
|
|
Chapter 7.9 Setting Up Large-Scale Qualitative Models |
566 |
|
|
Abstract |
566 |
|
|
1. Introduction |
566 |
|
|
2. The Modeling Process |
566 |
|
|
3. A steam plant model |
567 |
|
|
4. Modeling Assumptions |
567 |
|
|
5. Organization of the model |
569 |
|
|
6. Model selection for question-answering |
570 |
|
|
7. Discussion |
571 |
|
|
8. Acknowledgements |
571 |
|
|
References |
571 |
|
|
Chapter 8. Reasoning About Shape and Space |
572 |
|
|
Introduction |
572 |
|
|
Chapter 8.1 Qualitative Kinematics: A Framework |
575 |
|
|
Abstract |
575 |
|
|
I. Introduction |
575 |
|
|
II. A Framework for Qualitative Kinematics |
576 |
|
|
III. Example: FROB |
578 |
|
|
IV. The Clock system |
579 |
|
|
V. Other QK systems |
579 |
|
|
VI. Discussion |
580 |
|
|
VII. Acknowledgements |
580 |
|
|
References |
580 |
|
|
Chapter 8.2 Qualitative Kinematics in Mechanisms |
581 |
|
|
Abstract |
581 |
|
|
1. Introduction |
581 |
|
|
2. Place Vocabularies |
582 |
|
|
3. Descriptive Power of the Place Vocab-ulary |
584 |
|
|
4. Computation of Place Vocabular |
584 |
|
|
5. Conclusions |
586 |
|
|
References |
586 |
|
|
Chapter 8.3 Shape and Function in Mechanical Devices |
588 |
|
|
Abstract |
588 |
|
|
I. Introduction |
588 |
|
|
II. An algorithm for the analysis of mechanisms |
589 |
|
|
III. Local Interactions Analysis |
589 |
|
|
IV. Global Interactions Analysis |
591 |
|
|
V. Conclusions and future work |
592 |
|
|
Acknowledgments |
592 |
|
|
References |
592 |
|
|
Chapter 8.4 Automated Reasoning about Machine Geometry and Kinematics |
593 |
|
|
Abstract |
593 |
|
|
Bibliography |
604 |
|
|
Chapter 8.5 A Qualitative Approach to Mechanical Constraint |
605 |
|
|
Abstract |
605 |
|
|
1. Introduction |
605 |
|
|
2. Representations |
605 |
|
|
3. Mechanical Motion |
606 |
|
|
4. Sample Mechanism |
609 |
|
|
5. Discussion |
609 |
|
|
6. Acknowledgements |
609 |
|
|
References |
609 |
|
|
Chapter 8.6 Simplification and Abstraction of Kinematic Behaviors |
610 |
|
|
Abstract |
610 |
|
|
1. Introduction |
610 |
|
|
2. Describing Kinematic Behavior |
611 |
|
|
3. Simplification and Abstraction Operators |
612 |
|
|
4. Comparing Two Mechanisms |
614 |
|
|
5. Conclusion |
615 |
|
|
References |
615 |
|
|
Chapter 8.7 A Framework for Qualitative Reasoning about Solid Objects |
616 |
|
|
1. Abstract |
616 |
|
|
2. Introduction |
616 |
|
|
3. Background |
616 |
|
|
4. Examples and Analysis |
618 |
|
|
5. The Block on the Table |
619 |
|
|
6. The Underlying Knowledge |
619 |
|
|
7. Ontology |
620 |
|
|
8. Axioms for Physical Reasoning |
620 |
|
|
9. Conclusions |
621 |
|
|
10. Acknowledgements |
622 |
|
|
11. References |
622 |
|
|
Chapter 9. Causal Explanations of Behavior |
624 |
|
|
Introduction |
624 |
|
|
Chapter 9.1 The Declarative Representation and Procedural Simulation of Causality in Physical Mechanisms |
630 |
|
|
Abstract: |
630 |
|
|
1. Introduction |
630 |
|
|
2. Motivation |
630 |
|
|
3. Background and Related Work |
630 |
|
|
4. Theoretical Framework |
630 |
|
|
5. Simulation Strategy |
632 |
|
|
6. The Mechanisms Simulator |
633 |
|
|
7. Simulation Philosophy |
634 |
|
|
8. Conclusions |
635 |
|
|
Acknowledgments |
635 |
|
|
References |
635 |
|
|
Chapter 9.2 The Origin and Resolution of Ambiguities in Causal Arguments |
637 |
|
|
Abstract |
637 |
|
|
Introduction |
637 |
|
|
Theory |
638 |
|
|
Generating Causal Arguments |
639 |
|
|
Device Models for Electronics |
639 |
|
|
Ambiguities and Assumptions |
641 |
|
|
The Role of Teleology |
642 |
|
|
Conclusions |
642 |
|
|
Acknowledgements |
643 |
|
|
References |
643 |
|
|
Chapter 9.3 Causality in Device Behavior |
644 |
|
|
1. Introduction |
644 |
|
|
2. Causal Ordering |
647 |
|
|
3. Mythical Causality |
649 |
|
|
4. Comparison of the Two Concepts of Causality |
651 |
|
|
5. Systems with Feedback |
654 |
|
|
6. Conclusion |
657 |
|
|
Appendix A. Derived Structures of Higher Orders, for the Evaporator Model |
658 |
|
|
A.2. Derived structure of the second order |
658 |
|
|
A.3. Derived structure of the third order |
658 |
|
|
ACKNOWLEDGMENT |
658 |
|
|
REFERENCES |
658 |
|
|
Chapter 9.4 Theories of Causal Ordering |
659 |
|
|
1. Introduction |
659 |
|
|
2. Propagation of Constraints |
661 |
|
|
3. Comparison of the Differing Approaches to Causality |
664 |
|
|
4. Feedback in the Conduit |
665 |
|
|
5. Comparative Statics |
667 |
|
|
6. Ambiguity and Feedback |
670 |
|
|
7. Conclusion |
671 |
|
|
ACKNOWLEDGMENT |
672 |
|
|
REFERENCES |
673 |
|
|
Chapter 9.5 Theories of Causal Ordering: Reply to de Kleer and Brown |
674 |
|
|
1. Introduction |
674 |
|
|
2. Propagation of Constraints |
675 |
|
|
3. Comparison of the Differing Approaches to Causality |
676 |
|
|
4. Feedback in the Conduit |
676 |
|
|
5. Comparative Statics |
677 |
|
|
6. Ambiguity and Feedback |
677 |
|
|
7. Conclusion |
678 |
|
|
REFERENCES |
678 |
|
|
Chapter 9.6 Causal Reasoning about Quantities |
679 |
|
|
Abstract |
679 |
|
|
1· Introduction |
679 |
|
|
2. Models of causality in changing quantities |
679 |
|
|
3. Psychological Implications |
684 |
|
|
4· Conclusions |
689 |
|
|
5. Acknowledgements |
689 |
|
|
6. Bibliography |
689 |
|
|
Bibliography |
692 |
|
|
Author Index |
706 |
|
|
Subject Index |
710 |
|
|
Credits |
732 |
|