With each proposition P we associate a set of proposition (a hyperpropositi
on) which determines the order in which one may retreat from accepting P, i
f one cannot fully hold on to P. We first describe the structure of hyperpr
opositions. Then we describe two operations on propositions, subtraction an
d merge, which can be modelled in terms of hyperpropositions. Subtraction i
s an operation that takes away part of the content of a proposition. Merge
is an operation that determines the maximal consistent content of two propo
sitions considered jointly. The merge operation gives rise to an inference
relation which is, in a certain sense, optimally paraconsistent.