Kernel contraction and base dependence: redundancy in the base resulting in different types of dependence
Mehrdad Oveisi, James P. Delgrande, Fred P. Popowich, Francis Jeffry Pelletier · 2015
The AGM paradigm of belief change studies the dy-namics of belief states in light of new information. Finding, or even approximating, dependent or rel-evant beliefs to a change is valuable because, for example, it can narrow the set of beliefs consid-ered during belief change operations. Gärdenfors’ preservation criterion (GPC) suggests that formu-las independent of a belief change should remain intact. GPC allows to build dependence relations that are theoretically linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance rela-tions. There are already some studies, based on GPC, on the parallelism between belief change and dependence. One study offers a dependence re-lation parallel to AGM contraction for belief sets. Another study links base dependence relation to a more general belief base contraction, saturated ker-nel contraction. Here we offer yet a more general parallelism between kernel contraction and base dependence. At this level of generalization, differ-ent types of base dependence emerge. We prove that this differentiation of base dependence types is a result of possible redundancy in the base. This provides a theoretical means to distinguish between redundant and informative parts of a belief base. 1