Open logic based on total-ordered partition model

The problem of uniqueness of reconstruction in open logic is dealt with by introducing the concept of total-ordered partitions, an ordering structure for modeling belief degrees of knowledge, and redefining the reconstruction operation. Based on the resulting definition, a nontrivial condition for the convergency of cognitive processes is given. It is shown that if new knowledge is not always accepted with an extremely skeptical attitude and the changes of belief degrees follow the criterion of minimal changes, the cognitive process will converge. The results provide an approach to unifying two kinds of theories for knowledge base maintenance: belief revision and open logic.