Reasoning about Uncertainty

Reasoning about Uncertainty

by Joseph Y. Halpern
     
 

ISBN-10: 0262582597

ISBN-13: 9780262582599

Pub. Date: 09/01/2005

Publisher: MIT Press

Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertaintly intelligently, we need to be able to represent it and reason about it. In this book, Joseph Halpern examines formal ways of representing uncertainty and considers various logics for reasoning about it. While the ideas presented are formalized in terms of

Overview

Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertaintly intelligently, we need to be able to represent it and reason about it. In this book, Joseph Halpern examines formal ways of representing uncertainty and considers various logics for reasoning about it. While the ideas presented are formalized in terms of definitions and theorems, the emphasis is on the philosophy of representing and reasoning about uncertainty; the material is accessible and relevant to researchers and students in many fields,
including computer science, artificial intelligence, economics (particularly game theory), mathematics, philosophy, and statistics.

Halpern begins by surveying possible formal systems for representing uncertainty, including probability measures, possibility measures, and plausibility measures. He considers the updating of beliefs based on changing information and the relation to Bayes'
theorem; this leads to a discussion of qualitative, quantitative, and plausibilistic
Bayesian networks. He considers not only the uncertainty of a single agent but also uncertainty in a multi-agent framework. Halpern then considers the formal logical systems for reasoning about uncertainty. He discusses knowledge and belief; default reasoning and the semantics of default; reasoning about counterfactuals, and combining probability and counterfactuals; belief revision; first-order modal logic;
and statistics and beliefs. He includes a series of exercises at the end of each chapter.

Product Details

ISBN-13:
9780262582599
Publisher:
MIT Press
Publication date:
09/01/2005
Edition description:
New Edition
Pages:
497
Product dimensions:
8.00(w) x 9.00(h) x 1.00(d)
Age Range:
18 Years

Table of Contents

Prefacexiii
1Introduction and Overview1
1.1Some Puzzles and Problems1
1.2An Overview of the Book4
Notes10
2Representing Uncertainty11
2.1Possible Worlds12
2.2Probability Measures14
2.2.1Justifying Probability17
2.3Lower and Upper Probabilities24
2.4Dempster-Shafer Belief Functions32
2.5Possibility Measures40
2.6Ranking Functions43
2.7Relative Likelihood45
2.8Plausibility Measures50
2.9Choosing a Representation54
Exercises56
Notes64
3Updating Beliefs69
3.1Updating Knowledge69
3.2Probabilistic Conditioning72
3.2.1Justifying Probabilistic Conditioning77
3.2.2Bayes' Rule79
3.3Conditioning with Sets of Probabilities81
3.4Evidence84
3.5Conditioning Inner and Outer Measures89
3.6Conditioning Belief Functions92
3.7Conditioning Possibility Measures95
3.8Conditioning Ranking Functions97
3.9Conditioning Plausibility Measures97
3.9.1Constructing Conditional Plausibility Measures99
3.9.2Algebraic Conditional Plausibility Spaces101
3.10Jeffrey's Rule105
3.11Relative Entropy107
Exercises110
Notes116
4Independence and Bayesian Networks121
4.1Probabilistic Independence121
4.2Probabilistic Conditional Independence124
4.3Independence for Plausibility Measures126
4.4Random Variables129
4.5Bayesian Networks132
4.5.1Qualitative Bayesian Networks132
4.5.2Quantitative Bayesian Networks135
4.5.3Independencies in Bayesian Networks139
4.5.4Plausibilistic Bayesian Networks141
Exercises143
Notes146
5Expectation149
5.1Expectation for Probability Measures150
5.2Expectation for Other Notions of Likelihood153
5.2.1Expectation for Sets of Probability Measures153
5.2.2Expectation for Belief Function155
5.2.3Inner and Outer Expectation159
5.2.4Expectation for Possibility Measures and Ranking Functions161
5.3Plausibilistic Expectation162
5.4Decision Theory164
5.4.1The Basic Framework164
5.4.2Decision Rules166
5.4.3Generalized Expected Utility170
5.5Conditional Expectation176
Exercises177
Notes185
6Multi-Agent Systems189
6.1Epistemic Frames190
6.2Probability Frames193
6.3Multi-Agent Systems196
6.4From Probability on Runs to Probability Assignments201
6.5Markovian Systems205
6.6Protocols207
6.7Using Protocols to Specify Situations210
6.7.1A Listener-Teller Protocol210
6.7.2The Second-Ace Puzzle213
6.7.3The Monty Hall Puzzle216
6.8When Conditioning Is Appropriate217
6.9Non-SDP Systems221
6.10Plausibility Systems231
Exercises232
Notes235
7Logics for Reasoning about Uncertainty239
7.1Propositional Logic240
7.2Modal Epistemic Logic243
7.2.1Syntax and Semantics244
7.2.2Properties of Knowledge245
7.2.3Axiomatizing Knowledge249
7.2.4A Digression: The Role of Syntax251
7.3Reasoning about Probability: The Measurable Case254
7.4Reasoning about Other Quantitative Representations of Likelihood260
7.5Reasoning about Relative Likelihood263
7.6Reasoning about Knowledge and Probability268
7.7Reasoning about Independence271
7.8Reasoning about Expectation273
7.8.1Syntax and Semantics273
7.8.2Expressive Power274
7.8.3Axiomatizations275
Exercises278
Notes283
8Beliefs, Defaults, and Counterfactuals287
8.1Belief288
8.2Knowledge and Belief291
8.3Characterizing Default Reasoning292
8.4Semantics for Defaults294
8.4.1Probabilistic Semantics295
8.4.2Using Possibility Measures, Ranking Functions, and Preference Orders298
8.4.3Using Plausibility Measures301
8.5Beyond System P306
8.6Conditional Logic311
8.7Reasoning about Counterfactuals314
8.8Combining Probability and Counterfactuals317
Exercises318
Notes327
9Belief Revision331
9.1The Circuit-Diagnosis Problem332
9.2Belief-Change Systems339
9.3Belief Revision342
9.4Belief Revision and Conditional Logic354
9.5Epistemic States and Iterated Revision356
9.6Markovian Belief Revision359
Exercises361
Notes363
10First-Order Modal Logic365
10.1First-Order Logic366
10.2First-Order Reasoning about Knowledge373
10.3First-Order Reasoning about Probability376
10.4First-Order Conditional Logic381
Exercises390
Notes392
11From Statistics to Beliefs395
11.1Reference Classes396
11.2The Random-Worlds Approach398
11.3Properties of Random Worlds403
11.4Random Worlds and Default Reasoning411
11.5Random Worlds and Maximum Entropy416
11.6Problems with the Random-Worlds Approach420
Exercises423
Notes429
12Final Words431
Notes433
References435
Glossary of Symbols459
Index463

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >