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Reasoning About Uncertainty
Uncertainty is a fundamental and unavoidable feature of daily life; in order to deal with uncertainty 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 formalised 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.
Contents:
Prefacexiii
1Introduction and Overview1
2Representing Uncertainty11
3Updating Beliefs69
4Independence and Bayesian Networks121
5Expectation149
6Multi-Agent Systems189
7Logics for Reasoning about Uncertainty239
8Beliefs, Defaults, and Counterfactuals287
9Belief Revision331
10First-Order Modal Logic365
11From Statistics to Beliefs395
12Final Words431
References435
Glossary of Symbols459
Index463
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