Non-axiomatic logic a model of intelligent reasoning

✍ Scribed by World Scientific (Firme); Wang, Pei

• Publisher: World Scientific Publishing Company
• Year: 2013
• Tongue: English
• Leaves: 275
• Category: Library

✦ Synopsis

This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author's research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the laws of thought followed by the human mind. Different from mathematical logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thinking. To achieve this goal, the logic is designed under the assumption that the system has insufficient knowledge and resources with respect to the problems to be solved, so that the logical conclusions are only valid with respect to the available knowledge and resources. Reasoning processes according to this logic covers cognitive functions like learning, planning, decision making, problem solving, etc.

This book is written for researchers and students in Artificial Intelligence and Cognitive Science, and can be used as a textbook for courses at graduate level, or upper-level undergraduate, on Non-Axiomatic Logic.

✦ Table of Contents

CONTENTS......Page 8
Preface......Page 12
Acknowledgments......Page 14
List of Tables......Page 16
1.1 Intelligence......Page 18
1.2 Reasoning System......Page 21
1.3 NAL Overview......Page 26
2. IL-1: Idealized Situation......Page 30
2.1 Categorical Language......Page 31
2.2 Experience-Grounded Semantics......Page 33
2.3 Syllogistic Inference Rules......Page 38
3.1 Evidence and its Measurement......Page 42
3.2 Two-Dimensional Truth-Value......Page 45
3.3 Representations of Uncertainty......Page 48
3.4 Experience and Belief......Page 52
Revision......Page 58
Choice......Page 62
4.2 Forward Inference Rules......Page 66
Deduction......Page 69
Induction......Page 70
Abduction......Page 73
Conversion......Page 74
Exemplification......Page 76
4.3 Backward Inference Rules......Page 79
5.1 Inference Tasks......Page 82
5.2 Bag-Based Storage......Page 84
5.3 Concept as a Unit......Page 86
5.4 Inference Cycle......Page 88
5.5 Properties of NARS......Page 91
6.1 Similarity Copula......Page 94
Analogy......Page 97
Resemblance......Page 99
6.2 Instance Copula......Page 100
6.3 Property Copula......Page 102
7.1 Compound Term......Page 106
7.2 Intersections......Page 109
7.3 Differences......Page 113
7.4 Multi-Component Sets......Page 116
7.5 Inference on Compound Terms......Page 118
Choice......Page 119
Composition......Page 120
8.1 Product and Acquired Relation......Page 124
8.2 Types of Conceptual Relation......Page 127
8.3 Image and Structural Transformation......Page 129
9.1 Higher-Order Statement......Page 134
9.2 Implication and Inheritance......Page 136
9.3 Implication as Conditional......Page 141
9.4 Negation......Page 146
9.5 Analytic Truth in Inference......Page 149
10.1 Variable Terms Defined......Page 154
10.2 Variable Elimination and Introduction......Page 160
10.3 Symbolic Reasoning......Page 165
11.1 Time and Events......Page 172
11.2 Temporal Connectors and Copulas......Page 176
11.3 Temporal Inference......Page 180
12.1 Operations as Executable Events......Page 186
12.2 Goals as Desired Events......Page 190
12.3 Practical Reasoning......Page 192
12.4 Sensorimotor Interface......Page 197
13.1 Mental Operations......Page 202
13.2 Feeling and Emotion......Page 207
13.3 Consciousness......Page 210
14.1 The Nature of NAL......Page 214
14.2 Comparison with other Logics......Page 218
Classical logics......Page 219
Non-classical logics......Page 220
Probabilistic models......Page 223
Logic-based AGI......Page 226
Memory and control......Page 227
Physical experience......Page 229
Social experience......Page 231
Appendix A. Narsese Grammar......Page 234
Appendix B. NAL Inference Rules......Page 238
Appendix C. NAL Truth-Value Functions......Page 246
Appendix D. Proofs of Theorems......Page 248
Bibliography......Page 258
Index......Page 268