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Probabilistic Logic in a Coherent Setting

  • Book
  • © 2002

Overview

Authors:
  1. Giulianella Coletii

    1. University of Perugia, Italy

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    You can also search for this author in PubMed   Google Scholar

  2. Romano Scozzafava

    1. University of Roma “La Sapienza”, Italy

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-6
    Download chapter PDF

  2. Introduction

    • Giulianella Coletti, Romano Scozzafava
    Pages 7-15

  3. Events as Propositions

    • Giulianella Coletti, Romano Scozzafava
    Pages 17-24

  4. Finitely Additive Probability

    • Giulianella Coletti, Romano Scozzafava
    Pages 25-29

  5. Coherent probability

    • Giulianella Coletti, Romano Scozzafava
    Pages 31-35

  6. Betting Interpretation of Coherence

    • Giulianella Coletti, Romano Scozzafava
    Pages 37-42

  7. Coherent Extensions of Probability Assessments

    • Giulianella Coletti, Romano Scozzafava
    Pages 43-48

  8. Random Quantities

    • Giulianella Coletti, Romano Scozzafava
    Pages 49-51

  9. Probability Meaning and Assessment: a Reconciliation

    • Giulianella Coletti, Romano Scozzafava
    Pages 53-56

  10. To Be or not To Be Compositional?

    • Giulianella Coletti, Romano Scozzafava
    Pages 57-59

  11. Conditional Events

    • Giulianella Coletti, Romano Scozzafava
    Pages 61-72

  12. Coherent Conditional Probability

    • Giulianella Coletti, Romano Scozzafava
    Pages 73-97

  13. Zero-Layers

    • Giulianella Coletti, Romano Scozzafava
    Pages 99-108

  14. Coherent Extensions of Conditional Probability

    • Giulianella Coletti, Romano Scozzafava
    Pages 109-115

  15. Exploiting Zero Probabilities

    • Giulianella Coletti, Romano Scozzafava
    Pages 117-126

  16. Lower and Upper Conditional Probabilities

    • Giulianella Coletti, Romano Scozzafava
    Pages 127-136

  17. Inference

    • Giulianella Coletti, Romano Scozzafava
    Pages 137-161

  18. Stochastic Independence in a Coherent Setting

    • Giulianella Coletti, Romano Scozzafava
    Pages 163-190

  19. A Random Walk in the Midst of Paradigmatic Examples

    • Giulianella Coletti, Romano Scozzafava
    Pages 191-213

  20. Fuzzy Sets and Possibility as Coherent Conditional Probabilities

    • Giulianella Coletti, Romano Scozzafava
    Pages 215-240
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Keywords

About this book

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.

Authors and Affiliations

  • University of Perugia, Italy

    Giulianella Coletii

  • University of Roma “La Sapienza”, Italy

    Romano Scozzafava

Bibliographic Information

  • Book Title: Probabilistic Logic in a Coherent Setting

  • Authors: Giulianella Coletii, Romano Scozzafava

  • Series Title: Trends in Logic

  • DOI: https://doi.org/10.1007/978-94-010-0474-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2002

  • Hardcover ISBN: 978-1-4020-0917-4Published: 31 October 2002

  • Softcover ISBN: 978-1-4020-0970-9Published: 31 October 2002

  • eBook ISBN: 978-94-010-0474-9Published: 06 December 2012

  • Series ISSN: 1572-6126

  • Series E-ISSN: 2212-7313

  • Edition Number: 1

  • Number of Pages: IV, 291

  • Topics: Logic, Mathematical Logic and Foundations, Artificial Intelligence, Probability Theory and Stochastic Processes

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