Preliminary considerations on the modelling of belief change operators by metric spaces

In this paper, a possible worlds framework for representing general belief change operators is presented. In common with many approaches, an agent’s set of beliefs are specified by a subset of the set of possible worlds. The central intuition is that there is a distance given between every pair of possible worlds, giving the similarity of one world to another; the set of worlds together with this distance form a metric space. An operator such as revision is defined as expected: in revising by proposition A, the revised belief state is characterised by those worlds closest to the worlds characterising the agent’s original beliefs in which A is true. We propose that a suitable fundamental change operator is one where an agent’s beliefs are decreased as a result of the agent becoming more skeptical to a specified degree. This approach is compared and contrasted with the central quantitative framework for belief change, that due to Spohn.