Uncertain inference. (English) Zbl 1023.03002

Kyburg, Henry E. jun.; Teng, Choh Man

Cambridge: Cambridge University Press (ISBN 978-0-521-00101-4/pbk; 0-521-80064-1/hbk; 978-0-511-61294-7/ebook). xii, 298 p. (2001).

An overview of a wide variety of approaches to uncertainty and uncertain inference is provided within a unified framework. After a historical introduction by Mark Wheeler, the reader is introduced to first-order logic, the probability calculus, conditional probability and an overview of the different interpretations of probability. Chapter 5 deals with nonstandard measures of support, while the next two chapters review nonmonotonic reasoning and belief revision. Chapters 8 and 9 are devoted to statistical inference and evidential probability. The last three chapters deal with semantics, applications and scientific inference. The book will be of interest to students and researchers in several fields, such as philosophy, computer science, artificial intelligence, game theory and economics.

Reviewer: G.Bonanno (Davis)

MSC:

03-02	Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03B48	Probability and inductive logic
68T37	Reasoning under uncertainty in the context of artificial intelligence
68T27	Logic in artificial intelligence
03B42	Logics of knowledge and belief (including belief change)
03B60	Other nonclassical logic
03-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
00A30	Philosophy of mathematics
60A05	Axioms; other general questions in probability
62A01	Foundations and philosophical topics in statistics

Keywords:

uncertainty; uncertain inference; conditional probability; nonmonotonic reasoning; belief revision; statistical inference; evidential probability; scientific inference