Probabilistic Logic in a Coherent Setting

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 vie...

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Main Authors: Coletti, Giulianella, Scozzafava, R. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 2002, 2002
Edition:1st ed. 2002
Series:Trends in Logic, Studia Logica Library
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 11.2 Assumed or acquired conditioning?
  • 11.3 Coherence
  • 11.4 Characterization of a coherent conditional probability
  • 11.5 Related results
  • 11.6 The role of probabilities 0 and 1
  • 12 Zero-Layers
  • 12.1 Zero-layers induced by a coherent conditional probability
  • 12.2 Spohn's ranking function
  • 12.3 Discussion
  • 13 Coherent Extensions of Conditional Probability
  • 14 Exploiting Zero Probabilities
  • 14.1 The algorithm
  • 14.2 Locally strong coherence
  • 15 Lower and Upper Conditional Probabilities
  • 15.1 Coherence intervals
  • 15.2 Lower conditional probability
  • 15.3 Dempster's theory
  • 16 Inference
  • 16.1 The general problem
  • 16.2 The procedure at work
  • 16.3 Discussion
  • 16.4 Updating probabilities 0 and 1
  • 17 Stochastic Independence in a Coherent Setting
  • 17.1 “Precise” probabilities
  • 17.2 “Imprecise” probabilities
  • 17.3 Discussion
  • 17.4 Concluding remarks
  • 18 A Random Walk in the Midst of Paradigmatic Examples
  • 18.1 Finite additivity
  • a Reconciliation
  • 8.1 The “subjective” view
  • 8.2 Methods of evaluation
  • 9 To Be or not To Be Compositional?
  • 10 Conditional Events
  • 10.1 Truth values
  • 10.2 Operations
  • 10.3 Toward conditional probability
  • 11 Coherent Conditional Probability
  • 11.1 Axioms
  • main definitions
  • 19.2 Fuzziness and uncertainty
  • 19.3 Fuzzy subsets and coherent conditional probability
  • 19.4 Possibility functions and coherent conditional probability
  • 19.5 Concluding remarks
  • 20 Coherent Conditional Probability and Default Reasoning
  • 20.1 Default logic through conditional probability equal to 1
  • 20.2 Inferential rules
  • 20.3 Discussion
  • 21 A Short Account of Decomposable Measures of Uncertainty
  • 21.1 Operations with conditional events
  • 21.2 Decomposable measures
  • 21.3 Weakly decomposable measures
  • 21.4 Concluding remarks