Non-Prioritized Ranked Belief Change

Traditional accounts of belief change have been criticised for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is the framework of Ghose and Goebel for non-prioritised belief change based on default theories [8]. A novel feature of this approach is the introduction of disbeliefs alongside beliefs which allows for a view of belief contraction as independently useful, instead of just being seen as an intermediate step in the process of belief revision. The Ghose-Goebel approach is, however, restrictive in assuming a linear ordering of reliability on the received inputs. In this paper, we extend the Ghose-Goebel framework by replacing the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced. This extension brings along with it the problem of dealing with inputs of equal rank, a situation that cannot occur in the Ghose-Goebel setup. We provide a semantic solution to this problem which contains, as a special case, AGM belief change on closed theories.