  Various semantics for studying the square of opposition and the hexagon of
opposition have been proposed recently. We interpret sentences by imprecise
(set-valued) probability assessments on a finite sequence of conditional
events. We introduce the acceptability of a sentence within coherence-based
probability theory. We analyze the relations of the square and of the hexagon
in terms of acceptability. Then, we show how to construct probabilistic
versions of the square and of the hexagon of opposition by forming suitable
tripartitions of the set of all coherent assessments. Finally, as an
application, we present new versions of the square and of the hexagon involving
generalized quantifiers.
