@techreport{TR-DCC-93-12,
number = {DCC-93-12},
author = {Hansen, Pierre and Jaumard, Brigitte and Poggi de Aragão, Marcus V. S.},
title = {{Boole}'s Conditions of Possible Experience and Reasoning under Uncertainty},
month = {June},
year = {1993},
institution = {Department of Computer Science, University of Campinas},
note = {In English, 21 pages.
\par\selectlanguage{english}\textbf{Abstract}
Consider a set of logical sentences together with probabilities
that they are true. These probabilities must satisfy certain
conditions for this system to be consistent. It is shown that an
analytical form of these conditions can be obtained by enumerating
the extreme rays of a polyhedron. We also consider the cases
when: (i) intervals of probabilities are given, instead of single
values; (ii) best lower and upper bounds on the probability of an
additional logical sentence to be true are sought. Enumeration of
vertices and extreme rays is used. Each vertex defines a linear
expression and the maximum (minimum) of these defines a best
possible lower (upper) bound on the probability of the additional
logical sentence to be true. Each extreme ray leads to a
constraint on the probabilities assigned to the initial set of
logical sentences. Redundancy in these expressions is
studied. Illustrations are provided in the domain of reasoning
under uncertainty.
}
}