Can we forget how we learned? Doxastic redundancy in iterated belief revision

Abstract

Forgetting a belief acquisition episode may not cause information loss because of the others. Checking whether it does is not obvious, as the contribution of each belief revision is not isolated from the others, and the same information may be given not directly but by deduction. An algorithm for checking whether forgetting reduces information is given for a number of iterated belief revision operators: lexicographic, natural, severe, plain severe, moderate severe, restrained, very radical and full meet revisions. It may take exponential time in the worst case, which is expected given that the problem is coNP-hard, even in the Horn restriction. It is in coNP for homogeneous sequences of lexicographic revisions.