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Minimizing Regret in Dynamic Decision Problems Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Transitive Reasoning with Imprecise Probabilities

Authors : Angelo Gilio, Niki Pfeifer, Giuseppe Sanfilippo

Published in: Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Publisher: Springer International Publishing

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Abstract

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent \(\text{ p-consistent }\) sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

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previous chapter Explaining Bayesian Networks Using Argumentation
next chapter On the Algebraic Structure of Conditional Events
Footnotes
1
For proving total coherence of \(\mathcal {I}\) on \(\mathcal {F}\) (resp., \(\mathcal {F}'\)) it is sufficient to check that the assessment \(\{0,1\}^3\) on \(\mathcal {F}\) (resp., \(\mathcal {F}'\)) is totally coherent ([19, Theorem 7]), i.e., each of the eight vertices of the unit cube is coherent. Coherence can be checked, for example, by applying Algorithm 1 of [19] or by the CkC-package [2].
 
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Metadata
Title
Transitive Reasoning with Imprecise Probabilities
Authors
Angelo Gilio
Niki Pfeifer
Giuseppe Sanfilippo
Copyright Year
2015
Book
Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Print ISBN: 978-3-319-20806-0

Electronic ISBN: 978-3-319-20807-7

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20807-7_9

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