The importance of reversibility
In order to remove this uncertainty a collection of industry-strength techniques has been developed, to standardize geographical information. Geographical data may derive from several information sources, which may sometimes be conflicting. Belief theory allows information coming from different sources to be combined to produce an inference result that can help in taking a decision with some degree of certainty. In cases where the addition of new information, coming from a conflicting source, makes a theory inconsistent, Revision techniques are applied in order to identify what information must be retracted in order to maintain consistency. The Revision process can be seen as a special case of the fusion process, which deals with merging several sources. Revision may be seen as the fusion of two weighted sources where weights are assigned with regard to importance; however fusion generally is more complex than revision. Intelligent agent's beliefs are represented by epistemic states, originated from the Greek words episteme (knowledge). Epistemic states often are represented by total pre-orders through which a set of beliefs is encoded about the real world based on available information. In the context of the project the encoding of total pre-orders based on polynomials has been proposed which enables revision rules to be reversible. In this approach, the total pre-orders are encoded by polynomials equipped with lexicographic order. In this way, formalising the change of total pre-orders according to the incoming observation is made feasible. Moreover, as each interpretation is assigned a polynomial weight, it is possible not only to keep track of the sequence of observations but also to reverse back to previous pre-orders. Furthermore, an alternative approach of epistemic states is provided by means of weighted (or stratified) belief bases. The weights are polynomials, which allow a total preorder to be recovered. The results obtained for the reversibility of revision has opened the door for the addition of the property of reversibility to some known fusion operators, both in semantic and syntactic approaches.
