## Handbook of Defeasible Reasoning and Uncertainty Management Systems: Volume 5: Algorithms for Uncertainty and Defeasible ReasoningDov M. Gabbay, Philippe Smets, Jürg Kohlas Reasoning under uncertainty is always based on a specified language or for malism, including its particular syntax and semantics, but also on its associated inference mechanism. In the present volume of the handbook the last aspect, the algorithmic aspects of uncertainty calculi are presented. Theory has suffi ciently advanced to unfold some generally applicable fundamental structures and methods. On the other hand, particular features of specific formalisms and ap proaches to uncertainty of course still influence strongly the computational meth ods to be used. Both general as well as specific methods are included in this volume. Broadly speaking, symbolic or logical approaches to uncertainty and nu merical approaches are often distinguished. Although this distinction is somewhat misleading, it is used as a means to structure the present volume. This is even to some degree reflected in the two first chapters, which treat fundamental, general methods of computation in systems designed to represent uncertainty. It has been noted early by Shenoy and Shafer, that computations in different domains have an underlying common structure. Essentially pieces of knowledge or information are to be combined together and then focused on some particular question or domain. This can be captured in an algebraic structure called valuation algebra which is described in the first chapter. Here the basic operations of combination and focus ing (marginalization) of knowledge and information is modeled abstractly subject to simple axioms. |

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### Contents

Computation in Valuation Algebras | 5 |

Consequence Finding Algorithms | 41 |

Computing Specificity in Default Reasoning | 147 |

Complexity and Algorithms | 179 |

Probabilistic Argumentation Systems | 221 |

Probabilistic Networks | 289 |

### Other editions - View all

Handbook of Defeasible Reasoning and Uncertainty Management Systems ... Dov M. Gabbay,Philippe Smets,Jürg Kohlas No preview available - 2000 |

Handbook of Defeasible Reasoning and Uncertainty Management Systems Dov M. Gabbay,Philippe Smets No preview available - 2014 |

### Common terms and phrases

abductive explanation algorithm applied Artificial Intelligence assumption-based theory Bayesian networks belief function boolean bounds calculate called closed world assumption CNF formula combination complete computing prime implicates conditional probabilities consequence finding considered consistent constraints convex set corresponding decision problems deduction default rules Defeasible Reasoning defined DEFINITION Dempster-Shafer Dempster-Shafer theory denote Didier Dubois efficient elimination example extended finite focal sets formula from PROPPS given graph inconsistent inference influence diagram Jaumard join tree Kean and Tsiknis knowledge base Kohlas L-prime linear literal logical consequence logical equivalence marginal mass function mass potentials method minimal normal notion obtained optimal polynomial possibilistic logic prime implicates Probabilistic Logic probabilistic satisfiability probability distribution Proc production field proof propagation propositional logic quasi-supporting reasoning representation represented resolution strategy resp restrictions result scenarios set of clauses Shafer Shenoy specific subset Theorem tion transparent nodes uncertainty valuation algebras value node variables

### References to this book

Uncertainty and Information: Foundations of Generalized Information Theory George J. Klir Limited preview - 2005 |