Conditional inference and logic for intelligent systems : a theory of measure-free conditioning
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Bibliographic Information
Conditional inference and logic for intelligent systems : a theory of measure-free conditioning
North-Holland , Distributors for the U.S. and Canada, Elsevier Science Pub. Co., 1991
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Includes bibliographical references and index
Description and Table of Contents
Description
This work is concerned with addressing an anomoly involving probability and logic. This includes the interpretation and evaluation of implicative statements in natural language, compatible with conditional probability. One of the chief motivations for investigating this problem has been the need to formalize rigorously the appropriate connections between conditional probabilities and the underlying production rules in expert sytems. This is accomplished through the development of a comprehensive theory of conditional events and an associated logic. The results of this effort should be of prime use in the design and evaluation of inference rules in expert systems, and also, allow for a new expansion of probability to include at the syntactic level the concept of conditioning. The monograph is intended for two audiences: AI researchers who are primarily interested in the management of uncertainty in expert systems, and mathematicians in the fields of probabilistic modeling, logic, and algebra.
Table of Contents
Introduction. Motivation and objectives. State-of-the-art. Outline of main contributions. Overview of the book. A Survey of Previous Work on Conditional Events. Implicative Boolean algebras and Lewis' triviality result. Division of events. Three-valued logic. Coset form of conditional events. Logical operations among conditional events. Notes. Derivation of Conditional Events. Generalities. Conditioning operators. Conditional events. Logical Operations on Conditional Events. The extension problem. Conditional logical operations. An order relation and related concepts. Connections with three-valued logic. Comparison of various systems of logical operators. Connection with qualitative probability. Algebraic Structure of Conditional Events. Basic algebraic properties. An abstraction of the space of conditional events. Semi-simple MV-algebras. Conditional Events and Probability. Uncertainty measures on conditionals. Conditional probability evaluations. Random conditional objects. Qualitative conditional independence. Conditional Probability Logic. Essentials of probability logic. Syntax and basic properties. Truth conditional semantics. Additional properties of CPL. Fuzzy Conditionals. Generalities on fuzziness. Fuzzy logics. Syntax representation of fuzzy sets. Fuzzy conditionals. Probability qualification. Iterated fuzzy conditionals. Iterated Conditioning and Miscellaneous Issues. Iterated conditioning. Non-monotonic logics on conditionals. Operations on cosets of regular rings. Miscellaneous issues and open problems. References and Bibliography. Subject Index.
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