Probabilistic Logic in a Coherent Setting

  • Giulianella Coletii
  • Romano Scozzafava

Part of the Trends in Logic book series (TREN, volume 15)

Table of contents

  1. Front Matter
    Pages i-6
  2. Giulianella Coletti, Romano Scozzafava
    Pages 7-15
  3. Giulianella Coletti, Romano Scozzafava
    Pages 17-24
  4. Giulianella Coletti, Romano Scozzafava
    Pages 25-29
  5. Giulianella Coletti, Romano Scozzafava
    Pages 31-35
  6. Giulianella Coletti, Romano Scozzafava
    Pages 37-42
  7. Giulianella Coletti, Romano Scozzafava
    Pages 43-48
  8. Giulianella Coletti, Romano Scozzafava
    Pages 49-51
  9. Giulianella Coletti, Romano Scozzafava
    Pages 53-56
  10. Giulianella Coletti, Romano Scozzafava
    Pages 57-59
  11. Giulianella Coletti, Romano Scozzafava
    Pages 61-72
  12. Giulianella Coletti, Romano Scozzafava
    Pages 73-97
  13. Giulianella Coletti, Romano Scozzafava
    Pages 99-108
  14. Giulianella Coletti, Romano Scozzafava
    Pages 109-115
  15. Giulianella Coletti, Romano Scozzafava
    Pages 117-126
  16. Giulianella Coletti, Romano Scozzafava
    Pages 127-136
  17. Giulianella Coletti, Romano Scozzafava
    Pages 137-161
  18. Giulianella Coletti, Romano Scozzafava
    Pages 163-190
  19. Giulianella Coletti, Romano Scozzafava
    Pages 191-213
  20. Giulianella Coletti, Romano Scozzafava
    Pages 215-240

About this book

Introduction

The approach to probability theory followed in this book (which differs radically from the usual one, based on a measure-theoretic framework) characterizes probability as a linear operator rather than as a measure, and is based on the concept of coherence, which can be framed in the most general view of conditional probability. It is a `flexible' and unifying tool suited for handling, e.g., partial probability assessments (not requiring that the set of all possible `outcomes' be endowed with a previously given algebraic structure, such as a Boolean algebra), and conditional independence, in a way that avoids all the inconsistencies related to logical dependence (so that a theory referring to graphical models more general than those usually considered in bayesian networks can be derived). Moreover, it is possible to encompass other approaches to uncertain reasoning, such as fuzziness, possibility functions, and default reasoning.
The book is kept self-contained, provided the reader is familiar with the elementary aspects of propositional calculus, linear algebra, and analysis.

Keywords

Bayesian network Boolean algebra Conditional probability Extension Probability theory calculus fuzziness fuzzy fuzzy sets linear algebra logic propositional calculus random walk uncertain reasoning uncertainty

Authors and affiliations

  • Giulianella Coletii
    • 1
  • Romano Scozzafava
    • 2
  1. 1.University of PerugiaItaly
  2. 2.University of Roma “La Sapienza”Italy

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-010-0474-9
  • Copyright Information Kluwer Academic Publishers 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4020-0970-9
  • Online ISBN 978-94-010-0474-9
  • Series Print ISSN 1572-6126
  • About this book