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140122  eng 
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a 9789401004749

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 ZeroLayers  12.1 Zerolayers 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 

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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 

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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

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1 

a Scozzafava, R.
e [author]

710 
2 

a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

490 
0 

a Trends in Logic, Studia Logica Library

856 


u https://doi.org/10.1007/9789401004749?nosfx=y
x Verlag
3 Volltext

082 
0 

a 160

520 


a The approach to probability theory followed in this book (which differs radically from the usual one, based on a measuretheoretic 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 selfcontained, provided the reader is familiar with the elementary aspects of propositional calculus, linear algebra, and analysis
