Views over probabilistic data contain correlations between tuples, and the current approach is to capture these correlations using explicit lineage. In this paper we propose an alternative approach to materializing probabilistic views, by giving conditions under which a view can be represented by a block-independent disjoint (BID) table. Not all views can be represented as BID tables and so we propose a novel partial representation that can represent all views but may not define a unique probability distribution. We then give conditions on when a query's value on a partial representation will be uniquely defined. We apply our theory to two applications: query processing using views and information exchange using views. In query processing on probabilistic data, we can ignore the lineage and use materialized views to more efficiently answer queries. By contrast, if the view has explicit lineage, the query evaluation must reprocess the lineage to compute the query resulting in dram...