FIRST INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Ghent, Belgium
30 June - 2 July 1999

ELECTRONIC PROCEEDINGS

Veronica Biazzo and Angelo Gilio

A Generalization of the Fundamental Theorem of de Finetti for Imprecise Conditional Probability Assessments

Abstract

In this paper, based on a suitable generalization of the coherence principle of de Finetti, we consider imprecise probability assessments on finite families of conditional events and we study the problem of their extension. Then, we extend some theoretical results and an algorithm, previously obtained for precise assessments, to the case of imprecise assessments and we propose a generalized version of the fundamental theorem of de Finetti. Our algorithm can be also exploited to produce coherent lower and upper probabilities. Moreover, we compare our approach to similar ones, like probability logic. Finally, we apply our algorithm to some well known inference rules under taxonomical knowledge.

Keywords. Conditional events, imprecise probabilities, generalized coherence, coherence, natural extension, extensions, algorithms, probability logic, probabilistic deduction, probabilistic satisfiability.

The paper is available in the following formats and sites:

Authors addresses:

Dipartimento di Matematica
Citta` Universitaria
Viale A. Doria, 6 - 95125 Catania
Italy

E-mail addresses:

Veronica Biazzo biazzo@liotro.dipmat.unict.it
Angelo Gilio gilio@dipmat.unict.it


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