When hyperpropositions meet... (Propositions, subtraction, merge, paraconsistent inference relations)

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.