Reasoning with belief structures: non monotonic compatibility relations

Our concern is with getting information about one variable using knowledge of a second variable. We use of Dempster-Shafer belief structure to provide a representation, in a granular form, of knowledge about a variable when we have some uncertainty in our knowledge. We introduce compatibility relations for representing the possible joint values of two variables. Our inference scheme involves using a compatibility relation and a belief structure on one variable to infer a belief structure on the second variable. Our concern is with the representation of different types of compatibility relations. A distinction introduced is between monotonic and non-monotonic compatibility relations. We provide for the representation of both types.