Abduction and Induction

From the very beginning of their investigation of human reasoning, philosophers have identified two other forms of reasoning, besides deduction, which we now call abduction and induction. Deduction is now fairly well understood, but abduction and induction have eluded a similar level of understanding. The papers collected here address the relationship between abduction and induction and their possible integration. The approach is sometimes philosophical, sometimes that of pure logic, and some papers adopt the more task-oriented approach of AI. The book will command the attention of philosophers, logicians, AI researchers and computer scientists in general.

Foreword

ix

Preface

xiii

Contributing Authors

xv

Abductive and inductive reasoning: background and issues

1

(30)

Peter A. Flach

Antonis C. Kakas

Introduction

1

(1)

Abduction and induction in philosophy and logic

2

(9)

Abduction and induction in logic programming and artificial intelligence

11

(13)

Integration of abduction and induction

24

(3)

Conclusions

27

(4)

Part I The philosophy of abduction and induction

Smart inductive generalizations are abductions

31

(14)

John R. Josephson

A distinctive pattern of inference

31

(5)

What is an explanation?

36

(3)

Smart inductive generalizations are abductions

39

(4)

Conclusion

43

(2)

Abduction as epistemic change: a Peircean model in Artificial Intelligence

45

(14)

Atocha Aliseda

Introduction

45

(1)

Abduction and induction

46

(1)

The notion of abduction

47

(4)

Epistemic change

51

(3)

Abduction as epistemic change

54

(3)

Discussion and conclusions

57

(2)

Abduction: between conceptual richness and computational complexity

59

(18)

Stathis Psillos

Introduction

59

(1)

Ampliative reasoning

60

(2)

Explanatory reasoning: induction and hypothesis

62

(2)

Abduction

64

(5)

Abduction and computation

69

(4)

Conclusions

73

(4)

Part II The logic of abduction and induction

On relationships between induction and abduction: a logical point of view

77

(12)

Brigitte Bessant

Introduction

77

(1)

Abduction and induction: one is an instance of the other

78

(1)

Abduction and induction: different with a common root

79

(3)

Abduction and induction: totally different

82

(2)

Abduction and induction: a logical inference

84

(2)

Conclusion

86

(3)

On the logic of hypothesis generation

89

(18)

Peter A. Flach

Introduction

89

(1)

Logical preliminaries

90

(3)

Explanatory reasoning

93

(4)

Confirmatory reasoning

97

(8)

Discussion

105

(2)

Abduction and induction from a non-monotonic reasoning perspective

107

(10)

Nicolas Lachiche

Introduction

107

(1)

Definitions

108

(3)

Abduction and explanatory induction

111

(1)

Abduction and descriptive induction

111

(3)

Discussion

114

(1)

Conclusion

115

(2)

Unified inference in extended syllogism

117

(16)

Pei Wang

Term logic and predicate logic

117

(2)

Extended syllogism in NARS

119

(4)

An example

123

(2)

Discussion

125

(8)

Part III The integration of abduction and induction: an Artificial Intelligence perspective

On the relations between abductive and inductive explanation

133

(20)

Luca Console

Lorenza Saitta

Introduction

133

(1)

Generality and informativeness

134

(3)

A general definition of explanation

137

(3)

Inductive and abductive explanations

140

(5)

Analysis of inference mechanisms in the literature

145

(3)

Related work

148

(3)

Conclusions

151

(2)

Learning, Bayesian probability, graphical models, and abduction

153

(16)

David Poole

Introduction

153

(3)

Bayesian probability

156

(5)

Bayesian networks

161

(1)

Bayesian learning and logic-based abduction

162

(4)

Combining induction and abduction

166

(2)

Conclusion

168

(1)

On the relation between abductive and inductive hypotheses

169

(12)

Akinori Abe

Introduction

169

(1)

The relation between abduction and induction

170

(6)

About the integration of abduction and induction

176

(3)

Conclusion

179

(2)

Integrating abduction and induction in Machine Learning

181

(14)

Raymond J. Mooney

Introduction

181

(1)

Abduction and induction

182

(1)

Abduction in theory refinement

183

(5)

Induction of abductive knowledge bases

188

(3)

Conclusions

191

(4)

Part IV The integration of abduction and induction: a Logic Programming perspective

Abduction and induction combined in a metalogic framework

195

(18)

Henning Christiansen

Introduction

195

(2)

A metalogic framework for models of reasoning

197

(2)

Modelling a variety of reasoning processes

199

(5)

Implementation of the Demo system

204

(5)

Summary and related work

209

(4)

Learning abductive and nonmonotonic logic programs

213

(20)

Katsumi Inoue

Hiromasa Haneda

Introduction

213

(3)

Learning nonmonotonic logic programs

216

(7)

Learning abductive logic programs

223

(5)

Related work

228

(1)

Conclusion

229

(4)

Proof of Theorem 14.2

229

(4)

Cooperation of abduction and induction in Logic Programming

233

(20)

Evelina Lamma

Paola Mello

Fabrizio Riguzzi

Floriana Esposito

Stefano Ferilli

Giovanni Semeraro

Introduction

233

(1)

Abductive and Inductive Logic Programming

234

(5)

An algorithm for learning abductive logic programs

239

(2)

Examples

241

(7)

Integration of abduction and induction

248

(2)

Conclusions and future work

250

(3)

Appendix: Abductive proof procedure

250

(3)

Abductive generalization and specialization

253

(14)

Chiaki Sakama

Introduction

253

(1)

Preliminaries

254

(2)

Generalizing knowledge bases through abduction

256

(4)

Specializing knowledge bases through abduction

260

(4)

Related work

264

(1)

Concluding remarks

264

(3)

Using abduction for induction based on bottom generalization

267

(14)

Akihiro Yamamoto

Introduction

267

(2)

From abduction to induction

269

(1)

SOLD-resolution

270

(3)

Finding definite clauses

273

(5)

Finding unit programs

278

(1)

Concluding remarks

279

(2)

Bibliography

281

(20)

Index

301

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