  This paper relates comparative belief structures and a general view of belief
management in the setting of deductively closed logical representations of
accepted beliefs. We show that the range of compatibility between the classical
deductive closure and uncertain reasoning covers precisely the nonmonotonic
'preferential' inference system of Kraus, Lehmann and Magidor and nothing else.
In terms of uncertain reasoning any possibility or necessity measure gives
birth to a structure of accepted beliefs. The classes of probability functions
and of Shafer's belief functions which yield belief sets prove to be very
special ones.
