## A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of EvidenceThe 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. |

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### Contents

3 | |

The Mathematical Concept of a Hint | 32 |

Support Credibility Plausibility and Possibility | 40 |

Combining Hints | 61 |

Probabilistic AssumptionBased Reasoning | 82 |

RuleBased Systems With Unreliable Rules | 136 |

Compatible Frames of Discernment | 156 |

Reasoning on Compatible Frames | 188 |

Diagnostics | 281 |

Temporal and Spatial Reasoning | 305 |

A General Theory of Hints | 353 |

Structure of Support and Plausibility | 370 |

Dempsters Rule in the General Case | 383 |

Closed Random Intervals | 393 |

410 | |

418 | |

### Other editions - View all

A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of ... Juerg Kohlas,Paul-Andre Monney No preview available - 2014 |

A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of ... Juerg Kohlas,Paul-Andre Monney No preview available - 1995 |

### Common terms and phrases

according to theorem algorithm assumed assumptions Boolean algebra Boolean function called Chap Cl(vi clauses cliques combined hint compatible frames compute condition conditional independence conjunctive normal form considered consonant hint contains corresponding covering Markov tree defined degree of support Dempster's rule denote density deterministic hint disjunctive normal form elements elimination sequence example family of compatible finite focal sets following theorem formula frame of discernment Furthermore given graph G hence hint H hypergraph hypothesis implies intervals lemma likelihood function linear program minimal contradictions minimal quasi-supports monotone node observation partition pl(H plausibility functions possible precise hint prime implicates probability measure probability space probability theory procedure Proof of Theorem proposition prove quasi-support of h random variables refining reliability theory represented respect restriction result Sect Shafer shows sp(H subsets of 69 support and plausibility support function suppose theory of hints Tree-Alg vector