Handbook of Defeasible Reasoning and Uncertainty Management Systems

1. Front Matter

   Pages i-v

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2. Volume Introduction

   1. Introduction

      • Jürg Kohlas, Serafín Moral

      Pages 1-4

3. Fundamentals

   1. Computation in Valuation Algebras

      • Jürg Kohlas, Prakash P. Shenoy

      Pages 5-39

   2. Consequence Finding Algorithms

      • Pierre Marquis

      Pages 41-145

4. Algorithms for Logical Formalisms

   1. Computing Specificity in Default Reasoning

      • Salem Benferhat

      Pages 147-177

   2. Possibilistic Logic: Complexity and Algorithms

      • Jérôme Lang

      Pages 179-220

   3. Probabilistic Argumentation Systems

      • R. Haenni, J. Kohlas, N. Lehmann

      Pages 221-288

5. Algorithms for Numerical Formalisms

   1. Probabilistic Networks

      • Finn V. Jensen, Steffen L. Lauritzen

      Pages 289-320

   2. Probabilistic Satisfiability

      • Pierre Hansen, Brigitte Jaumard

      Pages 321-367

   3. Algorithms for Imprecise Probabilities

      • Andrés Cano, Serafín Moral

      Pages 369-420

   4. Algorithms for Dempster-Shafer Theory

      • Nic Wilson

      Pages 421-475

   5. Network-Based Decision Algorithms

      • Hong Xu

      Pages 477-510

6. Back Matter

   Pages 511-517

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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.

• algorithms
• complexity
• probabilistic network
• uncertainty

• University of Fribourg, Switzerland

  Jürg Kohlas

• Universidad de Granada, Spain

  Serafín Moral

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