A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence (Lecture Notes in Economics and Mathematical Systems (425))

The subject of the book is an approach to the modeling of and the reasoning under uncertainty. It develops the Dempster-Shafer Theory as a theory of the reliability of reasoning with uncertain arguments. A particular interest of this approach is that it yields a new synthesis and integration of logic and probability theory. The reader will benefit from a new view at uncertainty modeling which extends classical probability theory. Front Matter....Pages i-xiii Front Matter....Pages 1-1 Introductory Examples....Pages 3-31 The Mathematical Concept of a Hint....Pages 32-39 Support, Credibility, Plausibility and Possibility....Pages 40-60 Combining Hints....Pages 61-81 Probabilistic Assumption-Based Reasoning....Pages 82-135 Rule-Based Systems With Unreliable Rules....Pages 136-155 Compatible Frames of Discernment....Pages 156-187 Reasoning on Compatible Frames....Pages 188-242 Front Matter....Pages 243-243 Statistical Inference....Pages 245-269 Describing Uncertainty in Dynamical Systems....Pages 270-280 Diagnostics....Pages 281-304 Temporal and Spatial Reasoning....Pages 305-351 Front Matter....Pages 353-353 The General Model of a Hint....Pages 355-369 Structure of Support and Plausibility....Pages 370-382 Dempster’s Rule in the General Case....Pages 383-392 Closed Random Intervals....Pages 393-409 Back Matter....Pages 410-422 An Approach To The Modeling Of And The Reasoning Under Uncertainty. The Book Develops The Dempster-shafer Theory With Regard To The Reliability Of Reasoning With Uncertain Arguments. Of Particular Interest Here Is The Development Of A New Synthesis And The Integration Of Logic And Probability Theory. The Reader Benefits From A New Approach To Uncertainty Modeling Which Extends Classical Probability Theory.