Non-prioritised ranked belief change

Traditional accounts of belief change have often been criticised for placing undue emphasis on the new belief provided as input. A recent proposal to address such issues is Ghose and Goebel’s [6] framework for non-prioritised belief change based on default theories. A novel feature of their 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. Their proposal allows for prior revision and contraction steps to be recorded and brought to bear in deciding the outcome of subsequent belief change steps, and supports the principles of deferred commitment and lazy evaluation [6]. It also deals appropriately with iterated belief change. The Ghose-Goebel approach is, however, somewhat restrictive in the sense that it assumes 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. These rankings have more structure than linear orderings since they allow us to express the strength of preferences. They are also less restrictive than linear orderings since they induce total preorders on inputs. The freedom brought about by the move from linear orderings to rankings brings along with it the problem of dealing in an adequate fashion with inputs of equal rank, a situation that cannot occur in the Ghose-Goebel setup. We provide a semantic solution to this problem by replacing inputs with logically weakened versions, from which an appropriate entailment relation is defined. Our account of non-prioritised ranked belief change satisfies desirable properties. It is in line with the suggestion that belief change operations should be trivial and that it is the underlying entailment relation that should be sophisticated. Most interestingly, it contains, as a special case, AGM belief change on closed theories.