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Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning

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Overview

Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The book shows that reasoning processes - the drawing on inferences and changing one's beliefs - can be viewed as belonging to the realm of practical reason by embedding logical theories into the broader context of the theory of rational choice. The book unifies lively and significant strands of research in logic, philosophy, economics and artificial intelligence. It elaborates on the relevant theories and provides a mathematically precise foundation for the thesis that large parts of theoretical reason can be subsumed under practical reason.

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Product Details

  • ISBN-13: 9780198503064
  • Publisher: Oxford University Press, USA
  • Publication date: 12/1/2001
  • Series: Oxford Logic Guides Series , #42
  • Pages: 400
  • Product dimensions: 6.30 (w) x 9.30 (h) x 1.20 (d)

Table of Contents

Overview 1
1 Doxastic states and their representation 9
1.1 The menagerie of doxastic states 9
1.2 Representing doxastic states 22
2 Epistemology and belief change 46
2.1 Epistemology, knowledge representation and revision 47
2.2 Lehrer's theory of knowledge: Central definitions 49
2.3 Lehrer's logical constraints for eliminations and replacements, and how to improve them 58
2.4 Epistemology and belief change - a symbiotic relationship 62
3 Changing doxastic states: Two complementary perspectives 65
3.1 Two dimensions of belief change 66
3.2 Three types of maxims of coherence for belief representation and revision 67
3.3 The vertical and the horizontal perspective: Direct and coherence-constrained belief change 75
3.4 Foundationalist and coherentist belief change 76
3.5 Relating belief change and nonmonotonic reasoning 91
3.6 The dialectics of the statics and the dynamics of doxastic states 93
3.7 Justifications in models of belief change 97
4 Concepts of theoretical rationality: Postulates for belief change and nonmonotonic reasoning 100
4.1 Black boxes, structures and rules of application 100
4.2 Postulates for rational contractions 102
4.3 Postulates for rational revisions 107
4.4 Postulates for rational nonmonotonic reasoning 111
5 Foundational belief change using nonmonotonic inference 120
5.1 Modelling the direct mode: Drawing inferences from information bases 121
5.2 Modelling the direct mode: Combining information and expectation 127
5.3 Logical properties of revision functions generated by the direct mode 136
6 A general concept of practical rationality: Constraints for coherent choice 141
6.1 General choice functions 144
6.2 The classical theory of rational choice 153
6.3 Rationalizable choice 154
6.4 Two kinds of revealed preferences 158
6.5 More conditions on choice functions 163
6.6 Remainder functions 164
7 Coherentist belief change as a problem of rational choice 167
7.1 How to give it up: Choices between models 172
7.2 Partial meet contraction 175
7.3 How to give up: Choosing worst sentences 177
7.4 Logical constraints for choice functions over sentences 182
7.5 Revision 185
7.6 Nonmonotonic inference 187
7.7 Representation theorems for semantically and syntactically choice-based contraction functions: A remarkable confluence of results 190
7.8 Linking choices between models and choices between sentences 208
7.9 What have we achieved? 213
7.10 Iterated belief change in the coherence-constrained mode 217
8 Revealed preferences: Understanding the theory of epistemic entrenchment 223
8.1 Basic principles 225
8.2 Entrenchments as revealed preferences: Translations 229
8.3 Postulates for epistemic entrenchment 236
8.4 The postulates translated 241
8.5 Implications 246
8.6 The semantics of epistemic entrenchment 249
8.7 Applying epistemic entrenchment in coherentist belief change: Two construction recipes 253
8.8 Functional and relational belief change 264
App. A: Proofs for Chapter 4 268
App. B: Proofs for Chapter 5 274
App. C: Proofs for Chapter 6 284
App. D: Proofs for Chapter 7 292
App. E: Proofs for Chapter 8 320
References 353
Index of Symbols 369
Index of Names 371
Subject Index 374
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