Studies On Some Problems In The Theory Of Contraction Inference

Belief change is one of important research topics in Artificial Intelligence. In certain sense, approaches suggested in this field can be broadly classified into two categories: coherentist and foundationalist approaches to belief change. In the former category, the best known is AGM theory which is a milestone in this field. In the latter category, Nebel, Fuhrmann and Hansson may be representative persons who suggest studying changes of base-generated belief sets.Recently, Bochman has introduced a framework of belief change in which both AGM theory and the theory of base change can be reconstructed by defining appropriate operations on the associated epistemic states. In this sense, we think that Bochman's framework provides a general theory of belief change. Bochman also introduces a new kind of nonmonotonic inference relation so-called contraction relation and shows that contraction relations correspond to contraction operations on epistemic states. Of course, as pointed out by Bochman himself, further work is needed.This paper pays attention to some open problems appeared in literature concerning contraction inference relation. The contributions of this paper include the following:We establish the representation results for other contraction inference relations satisfying some special postulates.We introduce the notion of specific standard epistemic state and the notion of normal condition. Based on the above two notions we make an initial step to answer the following question: What kind of contraction inference relations that may be represented by standard epistemic states can be characterized by existent types of postulates?...