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Propositional, Probabilistic and Evidential Reasoning

Integrating Numerical and Symbolic Approaches

  • Book
  • © 2001

Overview

Authors:
  1. Weiru Liu

    1. School of Information and Software Engineering, University of Ulster at Jordanstown, Newtownabbey Co. Antrim, Northern Ireland UK

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  • The reader gains relatively complete knowledge about how a pure numerical, pure symbolic, or hybrid system behaves
  • Systemati review of the work on integrating numerical and symbolic approaches
  • Illustration by a large number of examples
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 77)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Introduction

    • Weiru Liu
    Pages 1-27

  3. Incidence Calculus

    • Weiru Liu
    Pages 29-54

  4. Generalizing Incidence Calculus

    • Weiru Liu
    Pages 55-77

  5. From Numerical to Symbolic Assignments

    • Weiru Liu
    Pages 79-99

  6. Combining Multiple Pieces of Evidence

    • Weiru Liu
    Pages 101-118

  7. The Dempster-Shafer Theory of Evidence

    • Weiru Liu
    Pages 119-158

  8. A Comprehensive Comparison of Generalized Incidence Calculus and Dempster-Shafer Theory

    • Weiru Liu
    Pages 159-182

  9. Assumption-Based Truth Maintenance Systems

    • Weiru Liu
    Pages 183-195

  10. Relations Between Extended Incidence Calculus and Assumption-Based Truth Maintenance System

    • Weiru Liu
    Pages 197-221

  11. Conclusion

    • Weiru Liu
    Pages 223-244

  12. Back Matter

    Pages 245-274
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Keywords

About this book

How to draw plausible conclusions from uncertain and conflicting sources of evidence is one of the major intellectual challenges of Artificial Intelligence. It is a prerequisite of the smart technology needed to help humans cope with the information explosion of the modern world. In addition, computational modelling of uncertain reasoning is a key to understanding human rationality. Previous computational accounts of uncertain reasoning have fallen into two camps: purely symbolic and numeric. This book represents a major advance by presenting a unifying framework which unites these opposing camps. The Incidence Calculus can be viewed as both a symbolic and a numeric mechanism. Numeric values are assigned indirectly to evidence via the possible worlds in which that evidence is true. This facilitates purely symbolic reasoning using the possible worlds and numeric reasoning via the probabilities of those possible worlds. Moreover, the indirect assignment solves some difficult technical problems, like the combinat ion of dependent sources of evidcence, which had defeated earlier mechanisms. Weiru Liu generalises the Incidence Calculus and then compares it to a succes sion of earlier computational mechanisms for uncertain reasoning: Dempster-Shafer Theory, Assumption-Based Truth Maintenance, Probabilis­ tic Logic, Rough Sets, etc. She shows how each of them is represented and interpreted in Incidence Calculus. The consequence is a unified mechanism which includes both symbolic and numeric mechanisms as special cases. It provides a bridge between symbolic and numeric approaches, retaining the advantages of both and overcoming some of their disadvantages.

Authors and Affiliations

  • School of Information and Software Engineering, University of Ulster at Jordanstown, Newtownabbey Co. Antrim, Northern Ireland UK

    Weiru Liu

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