Conditional Inference and Logic for Intelligent Systems: A Theory of Measure-Free Conditioning

Abstract

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.