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
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100 1 |a Coletti, Giulianella 
245 0 0 |a Probabilistic Logic in a Coherent Setting  |h Elektronische Ressource  |c by Giulianella Coletti, R. Scozzafava 
250 |a 1st ed. 2002 
260 |a Dordrecht  |b Springer Netherlands  |c 2002, 2002 
300 |a IV, 291 p  |b online resource 
505 0 |a 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 --  
505 0 |a 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 --  
505 0 |a 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 
653 |a Logic 
653 |a Mathematical logic 
653 |a Logic 
653 |a Artificial Intelligence 
653 |a Mathematical Logic and Foundations 
653 |a Artificial intelligence 
653 |a Probability Theory and Stochastic Processes 
653 |a Probabilities 
700 1 |a Scozzafava, R.  |e [author] 
710 2 |a SpringerLink (Online service) 
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989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Trends in Logic, Studia Logica Library 
856 |u https://doi.org/10.1007/978-94-010-0474-9?nosfx=y  |x Verlag  |3 Volltext 
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520 |a 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