Probabilistic Logic in a Coherent Setting
(Sprache: Englisch)
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,...
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Klappentext zu „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 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.
Inhaltsverzeichnis zu „Probabilistic Logic in a Coherent Setting “
1. Introduction2. Events as Propositions
3. Finitely Additive Probability
4. Coherent probability
5. Betting Interpretation of Coherence
6. Coherent Extensions of Probability Assessments
7. Random Quantities
8. Probability Meaning and Assessment: a Reconciliation
9. To Be or not To Be Compositional? 10. Conditional Events
11. Coherent Conditional Probability
12. Zero-Layers
13. Coherent Extensions of Conditional Probability
14. Exploiting Zero Probabilities
15. Lower and Upper Conditional Probabilities
16. Inference
17. Stochastic Independence in a Coherent Setting
18. A Random Walk in the Midst of Paradigmatic Examples
19. Fuzzy Sets and Possibility as Coherent Conditional Probabilities
20. Coherent Conditional Probability and Default Reasoning
21. A Short Account of Decomposable Measures of Uncertainty
- Bibliography
- Index
Bibliographische Angaben
- Autoren: R. Scozzafava , Giulianella Coletti
- Softcover reprint of the original 1st ed. 2002, 300 Seiten, Maße: 16 x 24 cm, Kartoniert (TB), Englisch
- Verlag: Springer Netherlands
- ISBN-10: 1402009704
- ISBN-13: 9781402009709
- Erscheinungsdatum: 31.10.2002
Sprache:
Englisch
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